In mathematics we define most things precisely, and usually the solutions to problems are presented as a step by step progression starting from clearly defined things and finishing with an answer that is proven to be a correct solution.

But it is sometimes useful to jump straight to consideration of a final solution, asking “Suppose there were a solution to this problem, let us call this solution X, what properties must X have?”

This can be a useful approach and, even for problems that turn out to have no valid solutions, we would still consider the signifier “X” to be something that we have succesfully ascribed meaning to: we could talk about “X” to other mathematicians and they would respond back to us in a manner that we can predict based upon the supposition that they share with us an understanding of what “X” is intended to refer to.

The same applies when we consider the meaning of words, rather than the meaning of mathematical symbols.  Words can acquire meaning inductively, based upon sense data, the way a child learns language.  But words can also be defined deductively, as solutions to problems set up by applying logical conjunctions to propositions or by analogy.

And, as with “x”, just hypothetical definitions can be useful and should be considered meaningful, even if there is no actual thing to which they can refer, or it is unknowable as to whether the referent exists.

Brain in a Vat

Putnam (Putnam, 1981) argues that a Brain in a Vat couldn’t think or reason about Brains or Vats because the thing it referred to as “Brain” could only be the simulation of a Brain fed to it by the supercomputer maintaining its illusory world, rather than the actually piece of flesh sitting in the jar.   However suppose the Brain engaged in thoughts upon the following lines:

I am going to refer to the world accessible to my sense data as “World 1″, and use the phrase “Type 1 Brain” to refer to the sort of physical thinking organ that my senses tell me exist in World 1.

I am going to refer to the virtual world running on the computer on my desk as “World 2″, which is a subset of World 1, and use the phrase “Type 2 Brain” to refer to the locus of thought of any being whose perceptual universe is limited to World 2.

I am going to refer to any hypothetical superset of World 1 that is larger than World 1 as “World 0″, and use the phrase “Type 0 Brain” to refer to a hypothetical type of thing that bears the same relationship to Type 1 Brains as Type 1 Brains do to Type 2 Brains.

The phrase “Type 0 Brain” does indeed contain the word “Brain” which the Type 1 Brain originally defined, as a child, by reference to parts of World 1 that it could sense.  But the phrase itself is more than the sum of its constituent parts.  It is a hypothetical definition, and as such can be said to meaningfully refer to things the Type 1 Brain will never directly sense.

If, for instance, the Type 1 Brain wrote down in on a piece of World 1 paper “Hello World 0, please reply”, a computer programmer in World 0 examining the bits of data in the computer running the World 1 simulation could decode this message and program the simulation to make appear a piece of paper in response, carrying the message “Hi, this is Frank, how are you enjoying my simulation, would you like me to make you a pet unicorns ?”.   They could engage in  a meaningful dialog, even though the Type 1 Brain would still be limited to its Type 1 senses.

And, just as a mathematician can consider what properties a valid solution would have to have, and perhaps elliminate some from consideration by demonstrating that two contradictory properties would both be required, by engaging in thought about our hypothetical World 0, and then looking around our World 1 and noticing the lack of pet unicorns, we can start to place constraints upon what World 0 is likely to contain.

Doubt all that can be doubted?

Descartes (Descartes, 1641) advocated starting by doubting all that can be doubted.   But that takes us nowhere, because everything can be doubted.

The Ken Thompson Hack (Thompson, 1984) explains why, once the security on a machine has been fully breached, you can not necessarily detect this by using the compromised tools.  The same applies to reason.  We may think that valid syllogisms always produce true conclusions if given true premises.  Indeed, that may even be how we define what “valid” means.  But our only means of deciding which syllogisms are valid depend upon our memory and those same syllogisms.

Suppose Frank, a World 0 computer programmer, in order to write a paper on the nature of logic, decided to see if he could create a World 1 simulation in which all the intelligent inhabitants thought that “If A can see B, and B can see C, then A can see C” was a valid syllogism.  Could he do it?  Well, he might have to ensure that evolution gave the beings in the simulation visual telepathy so that, in most cases, the reasoning did work in practice and the beings didn’t die off.  But yes, there is no intrinsic reason why he could put a routine in the simulation that ensure that whenever a particularly philosophically inclined World 1 being started trying to reason it out, the conclusion was places in his thought stream that the syllogism was valid.

Indeed, there is no intrinsic difficulty preventing Frank from including in the simulation a method for the beings to arrive at conclusions that was more reliable than reason, such as sacrificing an animal while chanting certain words, then meditating for a few minutes and awaiting an internal emotion or insight inclining the being towards or away from certain options they were deciding between.

Don’t doubt just for the sake of doubting

So, if doubting everything gains us nothing, can we gain anything by doubting some things but not others?

To answer that it is helpful to consider our purpose.  What Descartes was seeking, that he hoped to gain by his method of doubt, was truth and certainty.  That, alas, is overly ambitious, but suppose we think of reason as a tool with many uses.  People can try to use the tool to find pure truth, but it can also be used in everyday life to helping us avoid mistakes and delusions.  So, setting aside the possible existence of other tools, let us restrict ourselves to the purpose of honing the tool of reason, and ask ourselves how we may use doubt to increase the effectiveness and reliability of this tool.

Reason

The first thing we can allow ourselves to stop doubting is reason itself, because doubting it has no predictable advantage for our purpose.  Our purpose allows us no outside check on the effectiveness of  reason compared to outside tools, and, if we are being deluded by some higher agency into thinking that various invalid syllogisms are valid, there is nothing that reason can tell us about the consequences of that so, as far as reason is concerned, following the syllogisms we believe to be valid might be just as effective at reaching true conclusions as rejecting them.  And, since we have no basis to decide which syllogisms to reject as pranks by Frank, and Frank could just as easily be fooling us into thinking invalid some syllogisms that actually are valid, we do not reduce the false-positive rate of our tool by not making the assumption.  So:

WORKING ASSUMPTION 1 : First-order logic is sound

Probability

Deductive reasoning, by itself, can’t take us far enough to affect our decisions.  It needs something to work upon, and for that we need inductive reasoning (of the non-mathematical kind) and, for that we need probability.  The minimum set of axioms needed is Zermelo and Fraenkel’s extensions of Paeno, with the addition of the axiom of choice, which mathematicians refer to as ZFC.

WORKING ASSUMPTION 2 : ZFC

Occam’s razor

Duns Scotus wrote (translated) “Plurality is not to be posited without necessity” which is a dictum that can be traced back to much earlier philosophers, and is best known in the version attributed to Occam.  The reason why this is wise advice has now be demonstrated by Hutter (Hutter, 2005) who has proven that, other things being equal, the simpler theory is actually more likely to be true (Reay, 1988).   This is a key result however, since it is a direct consequence of our first two working assumptions, we don’t need to list it as an additional one.

Reality

So we now we have a way to make decisions, we have a decision to make.  Consider the standard mental model of how ‘reality’ functions.   There is an external world which our body perceives through our senses that translate into electrical and chemical changes in the physical brain, some of which our conscious ‘mind’ is aware of and experiences subjectively as qualia and these, plus what we think of as our direct perception of our memories and thought processes constitute our internal worldview based upon which our conscious (and subconscious) mind reacts or makes decisions that direct our body and our further thoughts and emotions, which get stored as further memories.

Which parts of this model must we choose not to doubt, for our purpose, or are there at this point several possibilities that still leave reasoning as an effective tool?

Some would argue that we might be brains in a vat, so we should definitely doubt the reliability of an apparent regularities in the external (World 1) reality, and so the logical starting point is to accept our own existance and the qualia as that ‘we’ perceives them.

Others argue that various psychiatric ailments are known to interfere with memory and sense of self; and that the body’s perception system has known defects (eg optical illusions) which makes assuming an objective shared external reality a more reliable starting point.

If we craft the wording of our next working assumption carefully enough, we can remain agnostic on this point, accepting both possibilities, and using Occam’s Razor to allocate probabilities to them.

WORKING ASSUMPTION 3 : There is sufficient regularity to the reality that can be accessed or modeled by the reasoning process we identify as our own being, that we can apply inductive reasoning to it with better than random results.

Time

A corollary of adding this third working assumption is the nature of time, because it assumes the concept of results – of testability.  The concept of having a model of how reality works, using reasoning to form a prediction based upon that model, then later getting a result (an action guided by that prediction achieving or failing to achieve the anticiapted result) at a later time.

It is logically possible that Frank only started his simulation running 5 seconds ago, and everything we think happened before that time is merely what we were programmed to think by the initial starting state.  It is also possible that there are regularities in the simulation, but that at midnight Frank is going to upload a software patch that changes the laws of nature in the simulation, and that everything will work differently from that point on.

This is known as The Problem of Induction.  Just because induction has worked in the past, that’s no evidence that induction will work in the future, because that would be using induction to support induction which is circular reasoning.

However we can bootstrap induction supporting induction if we can find an initial reason to think that induction is even just slightly more likely to be correct than not.  And Occam’s Razor gives us that reason, because the theory that Frank will upload a software patch a midnight contains an additional piece of information (the time of the change), which increases its Chaitin-Kolmogorov complexity (Chaitin, 1987).

Our third working assumption isn’t quite the same as ontological naturalism or Hume’s Principle of Uniformity of Nature, but it leans sufficiently far in that direct that we can perform physics, while still leaving open the technical possibility of a World 0 and supernatural intervention in World 1.

And alternative formulation of our third working assumption might be “There are, in our lives, at least some decisions (choices between possible options for an action to take) where reason can help us predict what some of the likely consequences would be of choosing each option, with better than random odds.”

From ‘Is’ to ‘Ought’

These first three working assumptions are sufficient to let us function in reality, and act towards goals.  But they tell us nothing about what goals to set.  For that we need one final step:

WORKING ASSUMPTION 4 : At least some of the decisions in our life will matter.

This a safe assumption to make because, if none of the decisions matter, then our decision (to make a false working assumption) doesn’t matter (because it is one of the decisions we made in our life).

Once we have this fourth working assumption, we may apply Occam’s Razor to the various competing theories of what matters, to find the simplest that has at least as much predictive power as any of the others.

References

Chaitin, G. J. [1987] “Algorithmic Information Theory“ Cambridge University Press ISBN: 0521343062

Descartes, René [1641] “Meditations on First Philosophy” http://www.wright.edu/cola/descartes/

Hutter, Marcus [2005] “Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability” ISBN 3-540-22139-5 http://www.hutter1.net/ai/uaibook.htm

Putnam, Hilary Whitehall [1981] “Reason, Truth, and History” ISBN-10: 0521297761

Reay, Douglas William Windle [1988] “Reay’s Lemma” http://www.toothycat.net/wiki/wiki.pl?ReaysLemma

Thompson, Ken [1984] “Reflections On Trusting Trust” http://cm.bell-labs.com/who/ken/trust.html

Preliminary Discussion

                It is useful to begin by saying a brief bit on logic. Logic concerns itself with consequence, which has been referred to as truth-preservation. An analysis of consequence is performed by demonstrating the validity of arguments such that:

(Logical Consequence) Some conclusion C is a consequence[4] of a set of premises P iff in a case where all the premises of P are true, it is a case where C is true.

The “cases” referred to above are laid out by truth-conditions. Systems of logic provide truth-conditions for that which will be parsed through them[5], or rather, what will be a consequence of what. For example, I might provide the following condition (Where P and Q are the ‘things’[6] being parsed):

P ^ Q is true in some case iff P is true and Q is true in the same case.

In providing such a truth-condition I have enabled the system to demonstrate the validity of the following:

P ^ Q

_____

P

If P ^ Q is true then P is true, or in other words, P is a consequence of P ^ Q. The question is whether or not there are multiple ways to understand, or lay out, the aforementioned cases. Logical pluralism rejects the position[7] that there is only one way to determine whether or not some argument is formally valid, or put differently, that there is but one true logic[8].  It proposes instead that there are multiple ways of specifying cases (truth-conditions), all of which are true. If you were to ask the logical particularist whether some argument were valid he or she would maintain that there is only one answer to that question. The logical pluralist would reject that statement.

The Presuppositionalist’s Logical Laws[9]

                In much of the literature I have come across and in my discussions with presuppositionalists as they defend their thesis re logic they state that the non-believer cannot account[10] for the truth of the so-called Law of Non-Contradiction (LNC), Law of the Excluded Middle (LEM) and the Law of Identity (LI). These titles denote particular propositions found in, at least, Classical Logic (let the following ‘P’s stand for any sentence letter or compound sentence:

LNC: ~(P ^ ~P)

LEM: (P v ~P)

LI: A <-> A

These propositions are tautologies under Classical Logic and while their being named “laws” by some; they possess no special status over any other tautology under Classical Logic, such as:

((A v B) ^ (A -> C) ^ (B -> C)) -> C

Tautologies are formulae which are always true in their systems by virtue of the logical rules, regardless of the truth-value assignment of some sentence letter or compound sentence. That is to say, the mere syntax of the system is sufficient for the truth of tautologies. As an example, take the LEM: (P v ~P) is always true because the logical rules for Classical Logic state that a disjunction is only false when both disjuncts are false and whatever truth-value assignment we give to P, one of the disjuncts in the LEM will be true (Classical Logic only has two truth values: T/F) and that is sufficient for the truth of the entire disjunction.

I suspect that the presuppositionalist will want to disagree with my statement above, that the logical rules of a system are sufficient for the truth of that system’s tautologies. The presuppositionalist will claim that the existence of God stands in some truth-making relation to the tautologies (and everything other truth the system parses). It seems abundantly clear, however, that the logical rules are enough. I suspect the presuppositionalist would posit God as a necessary and sufficient condition, in some fashion, to the truth of the LEM (for example, and to remain consistent).

I have heard two common expositions of the truth-making relationship between the existence of God and the LEM (or any other logical truth). One maintains that the LEM is a reflection of God’s nature. I do not know precisely what is meant by this particular suggestion. What does it mean to be a ‘reflection’ in this context? How is the LEM a reflection? What is it about God’s nature that causes the LEM to be reflected? The questions are numerous. The other suggestion is that the LEM (or any other logical truth) is a reflection of the way God thinks. Similar questions arise to this suggestion as well. In order to move the discussion forward, we can at least concede that both suggestions suggest that there is something about God that makes (in some way) the LEM true.

Concerns

                Now, recall logical pluralism once more and consider some ternary logic (a three-valued logic) in which the LEM comes out false. The LEM essentially states “either true or false” but ternary logic introduces some third value (depending on the system that value might be: indeterminate, irrelevant, unknown, etc.) and so regards the LEM false. This system of logic will have a different logical rules than Classical Logic, in many ways it is a different language as French is different to English. The logical pluralist wants to maintain that this system is fundamentally no ‘better’ or ‘worse’ than Classical Logic (though different systems may in different contexts be more ‘useful’). This system will also have tautologies which differ from those of Classical Logic and the pluralist will maintain that they are true tautologies, given the particular ternary system.

Let us assume, though it may be difficult to do, that the logical rules of this system are not sufficient conditions for the truth of some proposition which entails the falsehood of the LEM, and that the existence of God is a necessary and sufficient condition of the truth[11]. If we take the relationship between the existence of God and the truth of the proposition to have something to do with his nature or thinking, then it seems that there is something about God’s nature or thinking that is making the LEM true in one instance and making the LEM false in the other. That is, where under Classic Logic God is making (a) (P v ~P) true, under some ternary logic he is making (b) ~(P v ~P) true.

The two propositions initially seem to be contradictions of each other, but because they are arising out of different logics, they are essentially arising out of different languages. If no translator were present, I think it obvious that “I am hungry” does not contradict “Je n’ai pas faim.” A contradiction only seems to arise when we parse one sentence from some other language into whichever one we are using. So, if I translate “Je n’ai pas faim” and I see that it is the negation of “I am hungry”, now I have some contradiction where prior to the translation/integration, I merely had foreign symbols. So where (P v ~P) and ~(P v ~P) seem to be contradictory, I suggest that this is only the case if taken into a common language where both are expressed and where the rules of that language determine them to be in contradiction. We should not be misled, in our example of (a) and (b) both instances use the same symbols but essentially arise from different languages. So, (a) as expressed in Classical Logic is only contradicted by (b) if it too is expressed in Classical Logic and so on.

Now, continuing along with our assumption that the existence of God (in some way) is a necessary and sufficient condition of the truth of the aforementioned propositions in their respective systems if they are to be non-contradictory, it seems that they must be non-translated. But, focusing on God’s thoughts, what might it mean to say that God’s thoughts (or thinking) act as the truth-maker for the truth of both statements, but that he thinks them in a manner analogous to thinking a statement in French and thinking a statement in English and not knowing the translation[12]? Surely if the statement is translatable, God knows the translation. Put in another way, God in some way makes (a) true in Classical Logic and (b) true in some ternary logic. Assume that by translating (a) into the system of (b), (a) is rendered false and by translating (b) into the system of (a), (b) is rendered false. Something about God (presumably an unchangeable something, according to the Reformed tradition) in this example makes (a) true and makes it false, and likewise with (b). How is one to make sense of this?

Perhaps it is the case that God possesses a system of logic which he translates both (a) and (b) into, and this logic is such that the contradiction yielded by the aforementioned translation “does not matter”. This would be to suggest that God-Logic[13] is dialtheist in some sense, permitting of contradictions in a non-explosive manner. This God-Logic however will of course have its own logical rules, but continuing with our assumption these are insufficient for any of the truths yielded, the truth-maker will have to be something about God. Now we also have something about God that makes the LNC, after translation into God-Logic, both true and false. If this is true then the presuppositionalist explanation regarding what logic is, or how the existence of God relates (in a necessary way) to logic, becomes quite unparsimonious, on one hand leaving being quite mysterious and barely serving as an explanation, and on the other having to invoke a God-Logic which all ‘subsidiary’ logics depend on for coherence.

It renders the position far less plausible, I think, than accepting that the logical rules of various logic systems are the necessary and sufficient conditions for their respective logical truths and that each system generating propositions which may conflict only when translated into another system where the logical rules generate the confliction is not a problem.

Though, at this point, the presuppositionalist may just want to rid themselves of logical pluralism. They may admit to the existence of these other logical systems but deny that they are the one true logic. In this case, as presuppositional logical particularists it seems that they would suggest there exists only one system of logic that is true and something about God stands in a necessary and sufficient truth-making relation to the truths of this system. They might further suggest then that all of this talk about other logics generating contradictions when translated is simply not a problem because that is what we should expect if the other systems are wrong. The problem with this route, I think, is that we do not appear to have any way of knowing which system of logic is the one true logic! From the various presuppositional writings it sounds like the consensus amongst them would be that Classical Logic is the one true logic, but why must one accept this? It would seem then that all of the talk about the “laws” of logic, which are just tautologies of a particular system, is quite possibly irrelevant and incorrect if there exists one true logic. We are in an uncomfortable epistemic position, the very thing from which presuppositionalism promised us deliverance.

                Thusly, the common presuppositionalist argumentation regarding logic and God’s necessity hitherto has, I think, some explanatory work to undertake. It is currently far from convincing that one should reject the sufficiency of a system’s logical rules regarding the truth of some proposition arising from that system in favor of adopting the presuppositionalist view on the matter.

[2] ‘Experience’ should be taken very loosely.

[3] This list is not exhaustive, but is indicative of the usual discussions as per my experience.

[4] One can also make sense of the principle by replacing ‘consequence’ with ‘follows from’.

[5] Provided that what is parsed is capable of being expressed given the system.

[6] Most commonly a claim of some type

[7] Hereby referred to as logical-particularism

[8] The particularist will not deny the existence of other systems of logic any more than the religious particularist denies other religions; he or she will merely deny their truth.

[9] I find it a source of confusion that presuppositionalists only seem to refer to three particular tautologies of a particular system. I do not understand the restriction, but perhaps sake of simplicity plays a role.

[10] I cannot find a conceptual analysis of their usage of ‘account’ though it seems to mean a type of explanation.

[11] Again, that is to say it stands in some type of truth-making relation

[12] Assuming the translation will yield a contradiction.

[13] Thought of as an overarching logical system.

In keeping with the spirit of Lao Tzu, I would like to “respond intelligently, even to unintelligent treatment”. There were some points raised that I think should be responded to, some of which are more ‘personal’ in nature. Again, I must encourage everyone to listen to the recording prior to reading this response, as to obtain the appropriate context of the statements made by both parties. Some sections that follow may feel a tad bit nit-picky, but this is done on purpose. I think this will be a fun exercise in critically examining what’s being said by Slick during this radio show, and discerning just how much substance there is to all of it.

The Persecution

At 2:55 Festivus comes early with an airing of grievances! It is indeed true that recently there has been some hostility between DC (the ‘persecuted’) and some of the other users here at UP. Chat logs demonstrate that there has been hostility of the type outlined in the audio passage on both sides of the issue, that is, performed by both DC and others. In all cases disciplinary action was taken, however, the chat logs do not (to my knowledge) show any instance in which someone called DC “stupid for believing in a mythical god”. In fact, I suspect most of the users would frown on such a statement given how “New-Atheist-ish” it sounds. This is, of course, small potatoes when contrasted with where the audio journey will take us.

It may be worth mentioning that I’ve, personally, noticed what I think to be an interesting change in DC as of late. I have noticed that DC has become quick to pronounce his persecution at the hands of non-Christians when interacting with them in discussion. Now, I am not denying that Christians are indeed persecuted at times (I think it safe to say that every human being is persecuted at some time or another, and Christians are certainly human beings, sometimes persecuted because of their beliefs) but Slick offers a trinket of encouragement at 3:46 that makes it all too easy for the Christian to think that instances of disagreement are instances of Christian persecution, saying  ”If you’re not being attacked, you’re not doing the word of god”. There is some question as to what it means to “do the word of God” but the most charitable interpretation I can think of is that it means (or at least involves, largely) defending one’s Christian commitments. Given this statement we can know (via modus tollens) that if one defends Christian commitments, they will be attacked! Slick is quick to qualify that his principle is only meant to apply to situations of argument. What seems odd here is that by restricting the usage of his principle, he hasn’t actually told us anything interesting! Should it not be entirely obvious that if a Christian is in a situation where he/she is defending their Christian commitments, they are being attacked? If there’s no attack (or at least, a perceived attack) from where comes the need for a defense? Note a couple of things about Slick’s principle; firstly, it’s applicable to absolutely anyone. No matter who you are, or what you believe, if you are in a situation of argument and you are defending your position, you are being attacked. Secondly, note how the rhetoric is constructed in such a way that makes it very easy to affirm such persecution. The principle imposes itself on instances of discourse and fuels this notion of persecution. Consider, if you are an atheist and in the context of an argument, if you are defending atheism then you are being attacked. That’s great! But why think this is an instance of persecution rather than disagreement?

There is another way to interpret Slick’s statement, and that is to take “attack” to refer to a type of person-centered (rather than argument or idea centered) criticism. Something akin to the instances of hostility referred to above. I thought to include this interpretation of Slick’s principle first, but did not do so because it is uninterestingly false. Modified, it would be roughly: “In situations of argument, if you are defending Christian commitments, you are receiving person-centered attacks.” I doubt it will take much argument to show why this is false, but one absurd conclusion from Slick’s principle is that in every dialog ever had between a Christian and a non-Christian the only times where the Christian was *actually* defending Christian commitments are the times in which the non-Christian interlocutor retaliates fallaciously. All of those civil dialogs between prominent Christian philosophers and their opponents can be discarded, unless the opponent lashes out at some point. For added absurdity, look now to Jesus’ interaction with Nicodemus (John 3:1-21). In the defense that Jesus offers in response to Nicodemus’ questions, Nicodemus does not attack Jesus. If Matt Slick is correct in what he has said here, Jesus was not doing the word of God. This seems too silly to take seriously, but again, the rhetoric is certainly useful in invoking feelings of the previously mentioned sort.

Strangely, at 5:04, Slick tells DC that these people (the ‘attackers’) are not insulting ‘him’, they are insulting a ‘figure’ (referring to his screen name, I assume). The use of language here becomes a bit confusing, if ‘DC the person’ is not being insulted, what has Slick been talking about all this time? He then concludes from this that ‘DC-the-person’ just has to “take it”… but take what? We were just told that he’s not being attacked! This appears to be the second instance of a sentence which doesn’t really say much of anything. I find sentences of this type to be particularly interesting in counselling-type conversations, they are the blank cheques of language. I find they are often thrown about and fully left to the counseled to interpret, the end result of course that they are often interpreted as favorable to the perception of the status of whatever ailment is being discussed at the time. Sylvia Browne seems to do it, and now, Matt Slick?

At 5:11 Slick graciously remarks that those who engage in the aforementioned hostility are “servants of the evil one”. As far as I know, I’ve not been hostile in this way to DC and so thankfully am excluded from being a servant of the evil one (for the time being) . Not only are these people servants of the evil one, but DC is told at 5:21 that if he lets them get to him, he will become depressed and start to doubt everything! Not only is this section a glaring instance of a special type of ad hominem we like to call ‘poisoning the well‘, the things DC is being steered away from are curious. Apparently, becoming depressed and starting to doubt things are some very bad things to go through, but I’ve heard numerous conversion stories that start out precisely like that: “Well Karl, I was really depressed and I started to doubt everything… [fast forward 5 minutes] Hallelujiah!” In fact, DC is an example of one of these folks himself (I will not repeat the story here, as I do not know if he would approve, but you can ask him yourself!), but for DC these things led to a great realization. I suppose going through depression and intense doubt is only bad, and should only be avoided, if they do not lead to Jesus. But, what if DC feeling these things indicates yet another coming great realization (surprised face)?! At any rate, what Matt Slick seems to be doing here is, in fact, poisoning the well against those would would attack DC. Of course, he is being attacked because these people are servants of the evil one who despise the lessons of righteousness he espouses, they couldn’t possibly have a point, because they seek only to persecute!

At 6:00 DC is told that “… when you ruffle the feathers of the bad guys… [inaudible]… but you have to understand that in the demonic realm that there’s going to be a certain amount of attack that comes to you… and, plus, if you just hear how bad you are in so many different ways it has an effect on you as well.” A few things, firstly… the bad guys? This well is getting awfully poisoned! Demonic realm? No comment. I did however find the last portion interesting, it’s spoken in a rather negative tone saying that “if you just hear how bad you are in so many different ways it has an effect on you as well”. The tone and the context leads me to think that the effects which Slick is referring to are negative effects. If this is what he means, I would agree with him that hearing how bad you are over and over has negative effects. Empirical verification of this fact can be obtained by sitting in the CARM chat room and listening to some Christians talk about, as they often do, what terrible, worthless, abominations of human beings they all are. Now I’m no psychiatrist, but I’m not sure that partaking in such a discussion is good for your mental health (were we not just implicitly told that we should avoid depression? If this doesn’t cause depression, what does?!). I find the differences in reactions to negative labels particularly interesting, as they seem to change in different contexts. Consider: Christian #1: “Hey, you’re a terrible human being!” Christian #2: “Thanks, you too!” vs. Non-Christian #1: “Hey, you’re a terrible human being!” Christian: “Help, I’m being persecuted!”

Slick confesses at 6:34 that “It is difficult to love the people who are in the [service] of Satan. It is difficult to try and reason with them, and they express hatred. You love them, and they are vile to you.” There are a couple of gems here, but most importantly look at how the term “hatred” is used. Remember, it’s hatred folks, not disagreement, but hatred! He continues, “How do you maintain an attitude of love for them by not being affected by their ungodly demonic attacks?” Correction on my previous sentence, it’s ungodly demonic attacks folks, not disagreement. It seems astoundingly easy to feel persecuted when instead of finding yourself in a disagreement, you find yourself in some remake of Constantine!

Moving along, 7:50: “There are times when I say to myself I’m not being loving enough, and I pray, Lord forgive me, I’m not being loving enough…” 8:48: “You’ll notice, I go in the chat room, you notice I’m very quick to hit the ban button… I am not going to put up with any crap from these idiots… I’ll tell you why, because what they do, they are spiritual vampires, they will suck you dry…”

Well no wonder DC and Matt feel persecuted, with demons and vampires already around, they are one werewolf away from being in a Twilight film! But in all seriousness, I just want to draw attention to the interesting juxtaposition between Matt’s statements. Perhaps it would be easier to love these people, if you didn’t paint them as idiotic demon spirit-suckers. But, more seriously, this is another clear instance of well poisoning.

Moving forward a bit, DC questions why, on this site, no other Christians stepped in to help him defend his position. At 12:33 Slick remarks that “…you will find Christians, for example, who will say ‘you are a bigot, you don’t know what you’re talking about, you’re in sin’ and these are the ones that are aiding and abedding the enemies of the gospel.” At this point we seem to be moving away from statements that, I contend, bring about or strengthen a persecution mindset, and we are moving towards what seems to be almost a type of paranoia. “You can’t even trust some Christians, as they are in cahoots with the demon soul-suckers. Who are these Christians that are in cahoots? Oh, well the ones who disagree with you!” What does this do to the idea of Christian edification?

Atheism

Just when you thought it couldn’t get any better, at 16:45 Slick remarks: “When you tackle atheists, because these usually are atheists and liberal wackos, they don’t believe in the Christian God… it’s an easy thing to do… it’s really easy to beat atheists.” Now, I’m not sure how we suddenly jumped from the persecution of DC to talking about atheists, but it happened.

The chat continues: Matt: “You said it was an atheist website, right?” DC: “Yup.”

Hold the phones! UP isn’t an atheist website. Sure, lots of articles are written by atheists (theists, UP wants your contributions!) but the majority of our chat users (where DC spends all of his time here on UP) are non-atheists. I don’t know why he thinks we’re an atheist website (maybe it makes the plot of the persecution story juicier?), but let me put the kibosh on that right now. We’re certainly not a Christian website, but we are not an atheist website.

At 17:12 Slick remarks, with regard to atheists, that: “… you’ve already got them beat. The way to do this is to be strategic. You’ve got to understand that what atheists like to do is gang up on you, you’ll say one thing and they will come in fifty different directions… and complain that you don’t know this and that.” At this point, Slick has appeared to have stopped consoling DC and is now gearing him for battle (Go Team Edward!), but not before he poisons the well yet again and commits the fallacy of hasty generalization. In fact, to avoid repeating myself, roughly all of his chat about “atheists” and what they do commits this fallacy. Further, Matt’s discussion about ‘atheists’ and how they respond to arguments and the like suggests to me that Matt should interact with some more philosophically minded atheists. I’ve extended an invitation to interact with him a couple of times, but as you’ve heard while listening to this radio excerpt, he does not like to engage in written format. He has invited me to phone into the radio show, but I think the issues with some of his particular thoughts far too complicated to be discussed via that format. Though, at 18:30 Matt would have you believe that the reason I’ve not called up is because I know I’m going to get my “clocks cleaned”. I’d like to know how he thinks he knows such things, but needless to say, that statement is probably based on yet another instance of fallacious reasoning. Granted, while we’re playing this game, let me join in and say that the reason Matt Slick will not engage in written dialogue with me is because he’s afraid he’ll get his “clocks cleaned”! Hey, that was kind of fun…

18:37: “Now what they’re going to do is hide, and lie, and cheat, and steal. Just consider them like that.” If you’re confused, you’re not alone! Perhaps we should thank Matt here though, since he did restrain himself from mentioning our demonic soul-sucking practices in this particular example. Not only do I not understand the relevance of this point, I find his usage of “just consider them like that” interesting as well. We’ve poisoned this well so much that the residents of the city are drinking alcohol for hydration! Is he actually telling DC to just consider atheists as those who hide, lie, cheat and steal? Do I even need to list the fallacies at play here?

At 18:50 Slick begins to draw some battle plans. “Here are some principles: use what they say against them… it’s very easy to do. You have to understand something, they do not have the proper basis of rational thought, nor do they have the basis of moral objectivity. They don’t have those things…” He continues on recounting a dialog between him and some atheist wherein he “stumps” them by asking, “how do you know?” I think the same question needs to be extended to Slick based on the statements he’s just made. 19:52: “She has now hung herself [by making an assertion]… when they make assertions, ask them to verify their assertions.” I feel just eerie listening to this, it really is some sort of battle plan (though it kindly left out the bit about how you can defeat us by driving stakes through our hearts!).

Aside from DC’s monumental misunderstanding of moral nihilism espoused in the latter portion of minute 21 (how can things be morally permissible if there exists no morality?) Matt continues with his instruction, at 21:48 he states “…in order to [use the atheists statements against them] you’re going to have to study logic… you should learn [list of fallacies]…” I will politely recommend that this instruction be adjusted inward. What Matt seems to take to be the goal of logic, I doubt is actually the goal of logic. But, further, he tells us about a girl who said she enjoyed the content on his website, but could not trust it because Matt is a Calvinist. Matt identifies this as an instance of the genetic fallacy. At 22:32 he says, “… the information on the website needs to be studied on its own merits and not judged by the source, but by what it is.” Well let’s hold the phones again, Matt seems to tread awfully close to committing this fallacy throughout the discussion. I find it curious that he acknowledges that arguments need to be considered on their own merits, but spends a considerable amount of time teaching DC how to argue against atheists and not particular atheistic arguments. Interesting, yes?

The reason I feel so uncomfortable about discussions like this is that its all too similar to putting guns on children and sending them out to shoot people. Matt Slick has given DC a particular rhetorical technique to use, but he’s not given him any explanation as to why his analysis is correct. I find that to be some scary stuff indeed.

At 24:11 he goes on to suggest that in arguing with atheists DC should think about where their argument leads. Just a minor point of clarification, if Slick is suggesting a proof by contradiction, hooray. If he’s not, he’s implicitly utilizing another fallacious method of reasoning, namely, the fallacy of the slippery slope! If he does that, he’ll just commit a whole bunch of other fallacies! (There’s an example of it, just for fun!)

Oh, another added bonus, at 25:31 Matt actually utilizes the fallacy of the slippery slope. Doesn’t he offer a course on logic on his website? Oh well, at least he doesn’t soul-suck.

The next portion is largely uninteresting, as I find it to be the usual confused chatter about morality. I strongly suggest a course in ethics for Mr. Slick, however.

At 28:20 something really strange happens. Earlier, DC identified with Matt an instance of fallacious reasoning known as the genetic fallacy, but now DC actually commits the fallacy! He says: “Even if an atheist gives you a formal argument, and you don’t understand it at the time, if you put enough time into it, you start to look at where the worldview is coming from, you can tear it to pieces.” What?! Why didn’t Matt Slick, our resident logician for the day, call DC out on this fallacy? Maybe fallacies are only fallacies when used by vampires!

Conclusion

I could go for quite awhile, I think, but I don’t want to make this too long to read. Admittedly, I have been facetious in places but I hope at the very least I’ve drawn out some issues that are interesting to think about. The encouragement or provocation of “Christian Persecution-(ism?)” from fellow Christians, the vilification of non-Christians, and the arming of ill-prepared Christians with quick-draw tactics forgoing teaching with any real rigor. When all is said and done, this conversation at least gives the non-theist a basis for claiming persecution. I’ve never felt more vilified in my life!

Before I begin, I would like to make the point that the claims in my paper do not need to be true for the TAG to be defeated (with regard to logic, in this circumstance). The TAG fails due to the fact that logical conventionalism is coherent. Zao briefly touches upon this point, which I will address later, but I want to make it clear that my paper attempts to go beyond the mere claim that “logic does not presuppose God” and suggest something closer to the idea that it cannot.

The Criticisms

In my paper, I remark:

It seems to me that some hybridization of any of the mentioned means of justification may bring about a new means of justification. For example, a hybridization of an a priori and conventionalist system may succeed in providing the justification of logic sought by Bahnsen, but in a manner wherein the new system may be thought of as unique to both previous a priori systems, and forms of conventionalism.

Zao takes issue with this, stating:

Mitch starts off on the wrong foot immediately by proposing a hypothetical “hybridization” of two positions which is also “unique” to those other positions. So, is it a “hybrid” or is it “unique”?

I don’t think that one needs to choose between something being a hybrid, or unique. It’s doesn’t seem to be an either/or situation. For example, take gas-powered automobiles  and electric automobiles and combine the two concepts so that we create a gas-electric hybrid. In this circumstance we have a car that is unique in that there is a property that members of the previous categories do not have, namely, the property of being both gas and electric powered. Must we agree with Zao’s criteria that because this car is a hybrid, it cannot be unique or vice versa? I don’t think so, in fact it seems to me that it may be unique by being a hybrid!

Zao suggests that if there is such a system, I should present it rather than bringing it up as a hypothetical because it isn’t an objection. I think, however, if Zao understood me correctly he(?) would see that I merely rely on the possibility of a system and that this possibility is enough to make the point I wanted to make.

He also takes issue with the formal presentation of the TAG I’ve included in my paper which I’ve borrowed from Sean Choi. Zao states:

…advances have been made in presuppositionalism which have shown Choi’s position to be mistaken. Don Collett has argued effectively (in Revelation and Reason edited by K. Scott Oliphint) that Van Til’s conception of presuppositional semantics is identical to the Strawson/Van Fraasen semantics, which makes a clear distinction between “presupposition” and “implication.” (Even John Frame has accepted Collett’s argumentation in this respect.)

Choi presents his formulation of the TAG as a traditional transcendental argument (a la Kant) which would suggest (in this context) that the existence of logic implies the existence of God. Strawson in attempting to formalize a sufficient theory of presupposition proposes something similar to the following:

P presupposes Q if and only if Q is true provided P is true or P is false.

Where P is logic and Q is God, if one is to use this formulation instead of the previous, we would not say that the existence of logic implies God but that even the denial of the existence of logic also presupposes God. But what real difference does this make to our discussion? If I’m missing something then I wait to be informed, but it seems to me that even under this view the claim that “Both the truth of P or falisity of P presupposes Q” will reduce, in our discussion, to the claim that “logic presupposes the existence of God” since I am not denying the existence of logic. In other words, what difference does this make to any of my subsequent criticisms insofar as they pertain to the presuppositionalist ideas I mention?

This much can be said about the entire section of my paper where I introduce Choi’s formalism. It is of course nice to have something with which to work, but I am not dependent on this formulation. The arguments in my paper can be extended and applied to any (as I can conceive) assertion that amounts to “logic presupposes God.”

I go on to criticize Bahnsen’s idea of the “impossibility of the contrary” stating:

But what might this mean for our discussion? If Bahnsen is permitted to carry on with his criteria, then if any a priori, a posteriori or conventionalist justifications of logic are shown to be false (and subsequently, the worldviews that house and depend on them) all other formulations which properly fall under those headings will also be false (worldviews included) since they employ the same proposition, namely, ‘Christianity is false’. Of course, this is not sound reasoning unless the shared proposition is what is causing the justification to be false. Bahnsen needs to show that ‘Christianity is false’ is the ‘false-making’ proposition of all non-Christian worldviews, and it doesn’t seem that this is possible by any means other than (i) showing that all possible non-Christian justifications will have ‘Christianity is false’ as the onlyproposition in common (for if there is even one other proposition shared by these worldviews, how might one disqualify that proposition as possibly being the ‘false-maker’?), and (ii) showing that Christianity is not false. The obvious problem is that if (ii) is shown, the TAG becomes superfluous as it is no longer needed; one has already arrived at the truth of Christian theism, and for (i) to be shown, one still has to have an awareness of “every single variation of unbelieving philosophy.”

Zao replies that the false-maker of the proposition is its axiomatic nature. But I cannot see any reason to accept the claim that every worldview which has the proposition “Christianity is false” has that proposition as an axiom.

He states:

If the most basic presupposition of a non-Christian worldview is “not Christianity” (which appears to be definitional, given the above framework), then it is the basic nature of the presupposition which exerts a rational controlling influence on all other worldview content. It is not merely one proposition among many, floating loose and free in a certain worldview, but is rather foundational.

Again, why is this true? It seems to me that the only reason for claiming that “Christianity is false” is the most basic presupposition of non-Christian worldviews lies simply in identifying them as non-Christian worldviews. That is to say, I might identify some worldview as being non-Mitchist because I see that their worldview does not utilize what I utilize as my axiomatic foundation but I cannot see how this entails that “Mitchism is false” becomes their foundational axiom. It also seems that depending on who is looking at Bob’s worldview, he has several other axioms! For instance, what if a Muslim is looking at Bob’s worldview, does he now have as a foundational axiom that “Islam is false?” If a Hindu is looking at his worldview, does he now have as foundational the axiom that “Hinduism is false?” It even seems that atheists can analyze Zao’s worldview under his own criteria and suggest that he has as a foundational axiom that “Atheism is false” as his most basic presupposition.

Further, imagine Bob the Buddhist who has as his foundational axiom “Buddhism is true.” If we take Zao’s criteria, then since Bob the Buddhist can be identified as possessing a non-Christian worldview it follows that he has, also as a foundational axiom that “Christianity is false.” We can say that he’d also have as foundational axioms, under Zao’s criteria, propositions such as “Islam is false,” “Confucianism is false,” and “Scientology is false.” It seems more proper to say that Bob merely has the axiom “Buddhism is true” (if even this), and that he deduces from this postulate all of the other aforementioned propositions. That is to say, “Christianity is false” is not an axiom for Bob, it’s a deduction and so like other deductions it is “floating loose and free”. If we are to follow Zao’s criteria, it seems we render the term “axiom” meaningless. In fact Bob would have possibly an infinite number of axioms about religions of which he has not even heard! I see no reason to accept such absurdity.

In further response to my mention of Fristianity, Zao responds:

Being quite thoroughly familiar with various Fristianity objections, I had to chuckle at this one. I apologize for it, but I did. Let’s be perfectly clear here: an atheist can get zero cash value out of the Fristianity objection in debate with a Christian. Are you planning on being baptized in the name of the Father, Son, Holy Spirit and “Fred” anytime soon, Mitch?

The Fristianity objection, if sound, merely shows that the central claim of presuppositionalism is false. That is, if the Fristianity objection holds then it is false that no non-Christian theistic methods can possibly justify X, Y, Z. This is all I was intending to show.

Moving right along we come to my application of a Euthyphro-like dilemma to the laws of logic. Similar to many Christians with regard to the actual Euthyphro dilemma, Zao takes the route of stating:

The Christian’s argument is that logical laws are a reflection of God’s thought which is in accordance with God’s nature, which are all necessary.

But analyze what I said in the section, as Zao even quoted himself:

Frame essentially makes the claim that it is logically impossible for the nature of God to change. But the standard Frame is using to identify logical possibility is allegedly the nature of God. As such, his claim appears to be represented more accurately as:

(C)  Based on God’s nature it is logically impossible for God’s nature to be different because God is necessarily a rational God

This does not seem to assist in any regard as what is rational is allegedly determined by God’s nature. So to argue that God’s nature must be the way it is because God is necessarily rational seems to only appeal to a standard of rationality that is separate from God, otherwise it is clearly circular.

In what manner would it be the case that God’s nature was not rational? It does not seem that a God who forms the basis of logical principles and thereby is the standard of rationality can ever be irrational (though he may certainly appear irrational when judged by a foreign standard). That is to say, if one wants to state that the Christian God forms the basis of rationality and the logical principles thereby in effect cannot be anything other than what they are, they must be appealing to a standard of logic that is separate from God’s nature as to appeal solely to God’s nature does not sufficiently answer the question; it is a non-answer.

If Zao does not think that (C) is circular, I suggest he read a bit closer. He says that my dilemma is circular in itself because the first horn “…asserts that there is a meaningful sense in which logic is independent of the thought of God.” What is the implication of the aforementioned circularity in basing them on God? It seems to me that, as a direct implication, we must conclude that the necessary principles of logic indeed are external to God just as is the case with necessary moral principles and the original Euthyphro dilemma. I have not, as Zao has suggested, assumed that they are independent to show they are independent, I’ve formulated a dilemma and shown that given the alternatives are incoherent we have no choice but to accept that logical principles exist independently of God.

We might even supplement this by raising a point that was conveyed to me by a fellow UP.net member. Zao stated that the logical laws are a reflection of God’s thought and that God thinks logically. Moving over the seemingly obvious incoherence in such a statement, one might want to ask what it even means to say that God thinks logically? Logic permits us to deduce from premises, distinguish conclusions and so on. But God, if he is omniscient, surely does not have to do any of these things to have knowledge. God does not “reason” to his conclusions, he simply knows them. To say that the logical laws are reflections of God’s logical thinking stands in opposition to the idea that God knows all there is to know. Truly omniscient beings do not require logic, because they do not require a means to apprehend knowledge. This, I think, just adds to the incoherence of stating that logical principles reflect God’s rational thought.

In my section entitled “God and the Abstract” I offered an argument which is basically as follows:

The dependence relationship between “God exists” and “logical principles exist” seems problematic. If God is the source of all things other than himself, and he depends on nothing for his existence, surely the relationship must be asymmetrical (with primacy granted to God), but it appears not to be. It can be shown, in fact, that God depends on logical principles for his existence.

Lewis’ counterfactual semantics tell us that ‘any proposition is counterfactually implied by a necessarily false proposition’. Since “logical principles do not exist” is a necessarily false proposition, it counterfactually implies any proposition whatsoever.[21] So it is also true that if logical principles did not exist, neither would God. Thus, God depends on logical principles for his existence.

The relationship between the existence of logical principles and the existence of God would be asymmetrical iff God depended on nothing for his being and logical principles depended wholly on him. In this regard, the relationship of dependence is one-way; logical principles depend on God but not vice versa. If dependence is asymmetrical, then logic cannot depend on God as it has been shown that God depends on logic.

The asymmetrical relationship can be depicted further: where P refers to logical principles and Q refers to God. If P depends on Q asymmetrically, then the worlds in which P is true must be a proper subset of the worlds in which Q is true. Since it is the case that the principles of logic hold in every world, and the set of all worlds is not a proper subset of any other set of worlds, the laws of logic cannot depend on anything, including God.

Zao responds:

Given the nature of the points under contention (the existence of God and the relationship between God and logic), to argue that “logical principles do not exist” counterfactually implies that God depends on logical principles for his existence is to beg the question in a rather bald and obvious sort of way. How about, “God does not exist” is a necessarily false statement? Given that TAG is intended to argue for the necessary existence of God, to assume the contingency of God’s existence upon logic in order to prove God is contingent upon logic is, well, unpersuasive (to put it mildly).

I might be mistaken, but it seems to me that Zao interprets my argument as an argument against the existence of God. This is not the case, however. I can accept both the necessary existence of God and the necessary existence of logical principles, and still deny the type of relationship that the presuppositionalist is proposing. It’s not the necessary existence of either of these things that is the issue, it’s the proposed asymmetrical relationship between God and logic. I think Zao has really misunderstood the thrust of my argument here.

After a point about my brief treatment of divine simplicity and Trinitarianism (I agree, that could be a paper unto itself!) Zao closes with a very brief criticism of logical conventionalism. Zao states:

Finally, we have a section where logic is said to be both conventional while necessary and universal. This is rather fun. It’s like something from Alice in Wonderland. “Sentence first – verdict afterwards!

This is a claim that is thrown around a lot, and it is a claim that is just simply false. There simply is no problem with logic being conventional, while having its principles be necessarily true. Zao is welcome to either read the literature cited in my paper, the brief treatment here or wait for an upcoming article I’m expecting authored by a logician.

Conclusion

Again, the arguments in my paper are not needed to show that the TAG fails, the mere coherence of Conventionalism serves as a defeater for the endeavor. What my arguments seek to show is that logic cannot be based on God in any such implied way. I can only say that Zao’s brief treatment of Conventionalism towards the end of his post seems to violate his own suggestion of “… [understanding] the matter for [one's self] before attempting to criticize…”

P.S: I’d like to politely ask that in the future Zao link to my articles rather than pasting them in full. I’d also like to ask that he adds a hyperlink to the specific post he’s writing about. Thanks!

“Like I said before, you are arguing against a straw man. The explanation you offered in your paper fails to account for the preconditions of intelligibility. You are simply making an attempt at showing how an atheistic/evolutionary world view accounts for the preconditions of intelligibility, but the fact that these preconditions exist demands that the Christian world view be true. ” (spelling corrections mine)

What I have tried to explain is that Joshua should simply take my arguments and run them as an internal critique in his own worldview, a sort of internal reductio. The soundness of my article, if truly sound, will not be limited to one worldview. That is to say, if my argument truly does establish its conclusion it will do so if parsed through his own worldview and if that conclusion is such that it shows that his worldview cannot account for logic, then all the worse for his worldview! He may not simply beg the question in favor of his position after seeing the outcome of my criticisms. To this suggestion he has responded:

The conclusion of your argument is based on your ignorance of the very foundation for the Christian world view. There were certain aspects of the Christian world view that you simply ignored, and the ones that you documented were misrepresented. Now, if its that important to you, I will go ahead and sift through your article one paragraph at a time and comment on the ones that are faulty.

This is a pretty heavy charge, but I look forward to his analysis. I do recommend, of course, that it take into account the following material.

With that said, in an effort to quell any further attempts at avoiding the ‘meat’ of my paper due to an “inability to account for the laws of logic,” I will present the conventionalist justification of logic. In my discussions with presuppositionalists they have seemed to largely misunderstand the system and in turn create strawmen of their own to argue against. We must be cognizant now that the TAG as I’ve outlined in the previously linked paper or the statement that only the Christian worldview can account for the laws of logic requires that no other justification be possibly true. If the presentation of conventionalism is coherent it saddens me to say that one will not even need to read my paper to show that TAG (and presuppositionalism) fails. Further, there are those who would assert that presuppositionalism is the true apologetic system in that it is the one that Christianity explicitly endorses. There are also those who say that presuppositionalism/TAG cannot possibly be false because of the guarantee given by scripture. For these people, there is much more at stake than merely the coherence of the TAG, they also risk the truthhood of Christianity.

If the TAG, and further, presuppositionalism, are the true exemplifications of Christianity it follows that their defeat is symbiotically a defeat of Christianity. We can demonstrate this with a simple modus tollens:

(1) If Christianity is true, then the TAG succeeds

(2) The TAG does not succeed

(3) Therefore, Christianity is not true

What of course needs to be shown is (2), and while I feel that I’ve shown it sufficiently in the aforementioned paper, as I’ve said there are those who wish to address my supposed “inabilities.” Let us analyze if the claim that conventionalism cannot possibly account for the laws of logic is true.

What is Conventionalism?

What follows will be a series of excerpts I’ve chosen from Creath’s article that I feel outline the conventionalist justification of logic quite well.

Carnap made a refreshing and welcome suggestion: the axioms can be construed as definitions (implicit definitions) and their assertion as commitment to a language containing the terms so defined. The axioms or postulates need no further epistemic justification because a language is neither true nor false, and one is free to choose a language in any convenient way. If someone else should choose other apparently conflicting postulates, there is in fact no disagreement because each postulate set is constitutive of the concepts it employs, and hence the one body of postulates is not denying what the other is asserting. In this manner the postulates are not even intended to reflect an antecedently and independently existing reality, but rather literally to create the claims they express.

It may be that some postulate sets are better than others. But the ‘betterness’ in question concerns their practical usefulness: some are more powerful or easier to use than others. In terms of epistemic justification or cognitive warrant they are all on a par. Indeed, they are the ‘meter sticks’ for the justification of anything else. Epistemically the choice among them is conventional, though the constraints imposed by pragmatic utility can be significant. For example, an inconsistent postulate set is not very useful. For most logicians of the period, including Carnap, every sentence as well as its negation would trivially follow from a contradiction. An inconsistent postulate set would therefore fail to draw any cognitively interesting distinctions among sentences or beliefs. Though the preference for consistent systems is treated as a pragmatic one, the pragmatic considerations are powerful indeed.

In this first excerpt we see some constant presuppositionalist claims addressed. If logic is conventional, can’t people just choose different conventions? If some people choose different conventions than others, they will be contradicting each other, so how do we know which one is true? The answers to these questions are laid quite simply in the excerpt. Each language or system of logic will have a set of definitions that require no further epistemic justification. Think about the English language, there are definitions of words but to ask why a certain word is defined as such rather than some other definition is a question that simply makes no sense for languages which are neither true nor false, they simply are. Further, if someone chooses some language different than ours (say, French), there is no contradiction because the French language cannot disagree with the English language because they are creating their claims independently of one another.

Pragmatism comes into play when want to decide which system to use. Now, keep in mind that Carnap is not proposing that people somehow “choose” their basic brain languages (the language upon which they would choose all other languages). This is as silly as suggesting that one should be able to choose their genetic makeup as to yield a certain eye-color. Our fundamental operating language, our basic logical brain language (logical because there is no such thing as non-logical languages) is not chosen by us, but rather is the precondition for all other choosing. For the systems we can choose, be it in mathematics or computer science, we use the ones that allow us to perform certain tasks. We would not choose a trivial system because anything follows from trivial systems, the answer to every proposition is “Yes,” clearly this is useless.

“This discussion of pragmatic usefulness and explication must not obscure, however, the epistemic core of Carnap’s doctrine. The choice among alternative postulate sets is epistemically arbitrary; the choice is a matter of convention. Moreover, the postulates themselves are the fundamental epistemic doctrine.”

Again, where choice is possible amongst systems the choice is arbitrary. Creath continues:

At this point it would be well to say a bit more about convention, for it is not always clear what is at stake in saying that something is a matter of convention (Quine, 1936). Plainly, when Carnap speaks of the semantic and epistemic features of our language as conventional, he does not mean to suggest that they are the products of some actual legislative assembly convened in antiquity. But shorn of such unhelpful metaphor, what does conventionality come to? The answer, in essence, is that to lay down a linguistic convention is to adopt a certain scheme of justification. This scheme involves two specific features: first, there are alternatives to certain aspects of the justificatory system; and, second, the choice among these alternatives is arbitrary in the sense that no justification is required for the choice. In particular, to say that postulates are laid down by convention commits one to the idea that there are alternative postulates that could have been chosen, but were not. It commits one likewise to the idea that no further epistemic justification for the choice of postulates is required. Conventions are not designed to reflect antecedent and independent facts; if they were thus designed one would have to show that they had done so. Rather, the postulates (together with the other conventions) create the truths that they, -the postulates, express.

So put, conventionalism is the adoption of a system of justification. Other systems could have been chosen, but weren’t and no justification is required for the choice. Further, conventionalist systems are not reflecting some external reality, they really are creating their truths. We will see a further explanation of this below.

Creath continues:

That the conventions constituting the system of justification are at bottom arbitrary poses no threat whatever to the objectivity of the postulates and their consequences. This was of particular concern to Carnap because he thought that all of logic and mathematics, insofar as the claims thereof can be assessed at all, is to be justified as are postulates and their consequences. Once a system of justification is chosen, i.e., once the various terms of the language are given a definite sense, it is a completely objective matter whether B is a consequence of A. It in no way depends on what any person may happen to imagine, think, believe, or know about these sentences. It is likewise a completely objective matter whether or not a given claim needs further justification. These things are no more subjective than the truth value of the claim “All swans are white”, given of course that the meanings of the terms are fixed. If the word ‘white’ has a sense different than it in fact does, then the truth value of the claim might be different, but this in no way impugns the objectivity of “All swans are white”.

Here we have an answer to the common presuppositionalist assertion that “if logical principles are conventional, they are not necessary.” As the quotation says, once we adopt a system of justification whether or not X is true, or Y is true is a completely objective matter. To quote myself in a previous discussion with presuppositionalist Chris Bolt:

There is a distinction between “object-level” and “meta-level”. Consider a meta-ethical circumstance, where an evolutionary account of morality may be charged with becoming eliminitivist. “if I do some good deed X just because I am programmed to, then X is not really good to do, it’s just part of my programming” But these statements are operating on different levels. Both the following propositions would be true: “X really is good to do” and “X really is just a part of my biological programing, and that’s the only reason I think X is good to do” A contradiction only occurs when both statements are taken to be expressing a proposition of the same level.

Applied to logic, “X is really necessarily true, everywhere, regardless of what anyone thinks, and regardless of anyone’s conventions. And X really is just part of a system of conventions I have adopted as part of my programming.”

Thus we can see that the common charges against conventionalism by the presuppositionalists are simply misunderstandings. Conventionalism does not entail that some logical systems will contradict others, nor does it entail that everything becomes subjective and that logical principles are no longer necessary. Now, so long as conventionalism is a possible justification of the laws of logic, the TAG (and for some people, Christianity) is simply defeated:

(1) If Christianity is true, the TAG succeeds

(2) If some system other than Christian Theism can possibly account for the laws of logic then that TAG does not succeed

(3) Conventionalism possibly accounts for the laws of logic

(4) The TAG does not succeed

(5) Therefore, Christianity is not true

Conclusion

In dispelling the myths surrounding conventionalism put forth by presuppositionalists it should be clear and evident that conventionalism is coherent. Further, given its coherence it is a possible justification of the laws of logic, showing that the TAG fails. Coupled with the criticisms in my aforementioned paper we are left with the possibility of a conventionalist justification and the impossibility of Christian Theistic justification. For certain Christians, these conclusions are nothing less than devastating. If their position is the one I’ve outlined in the syllogisms, not only can Christian Theism not account for the laws of logic, it is false altogether.

It should first be noted that ‘Pannenberg’ was indeed disqualified for failing to reply within the time limit. Hackenslash did technically win the debate though not, in my opinion, due to any coherent reasoning.

Prior to beginning my review, there is a matter of some relevance I wish to address:

“I don’t believe there is no God, I just lack belief that God exists”

For anyone who is conversant on the topic of theism vs. atheism, I am sure they have come across such a statement. At one point in my life I held this position as well (thanks to my girlfriend for reminding me, she is always there to make fun of my past faults). I have come to see now that this position is incoherent. It seems to me that some issues that will be dealt with in this discussion have been dealt with in a previous article of mine. I will not assume that one has read that article though, and given the date of its publication I might now be more concise in my explanations.

I propose, in line with the Stanford Encyclopedia of Philosophy, that the definition of an atheist is one who denies the existence of God. With that said, I acknowledge that there do seem to be a growing number of people who support the definition of atheism which states “a lack of belief in God”. I think that this can be attributed since Flew, to the propensity of the New Atheists.

What precisely does it mean to “lack belief in God?” Given that theism is the acceptance of the proposition “God Exists” either probabilistically or with certainty, it seems to be fairly obvious that atheism would be the rejection of the proposition “God Exists” either probabilistically or with certainty. However, proponents of the definition which states that atheism is simply a lack of belief, also state that they do not believe there is no God. Let’s call this definition of atheism simply NA. As such, the proponent of NA is attempting to take a wholly negative approach to the question, making absolutely no positive claims whatsoever. But is it not still true that they reject the proposition “God Exists?”

The NA proponent seems to want to reject both “God exists” and “God does not exist.” It seems to me that one can only do so if they accept a strong position of agnosticism or ignosticism, stating that knowledge of the existence of God is impossible in either regard. For if knowledge of God is even possible, rejecting the proposition “God exists” entails an acceptance of “God does not exist” since “God does not exist” is a negation of “God exists”. The NA proponent wants to erect some sort of middle ground where none exists.

Call the proposition “God Exists”, x. “God does not exist” is a clear negation of x so that it is not-x. As such we have two positions, x and not-x. Now, we can invoke the law of the excluded middle to see the clear consistency of this analysis: Either God exists or he does not exist. Further if God lacked existence he would simply not exist.

Now, consider Bob. We have two propositions, “Bob believes that God exists”, y, and “Bob does not believe that God exists”, not-y. Clearly, according to the law of the excluded middle it is the case that either y or not-y. That is to say, if y is false, not-y must be true. But might there still be room to squeeze in NA? I think not, in rejecting one horn of a dichotomy such as this, one immediately accepts the alternate horn. Might it mean something different, though, to say “Bob does not believe that God exists”, A, and “Bob believes that God does not exist?”, A*. If there is a difference, it lies in the motivations of the position. That is to say, I think one can only accept A while denying A* if A is following from a position of strong agnosticism/ignosticism. If a definition of God is coherent enough to converse about, ignosticism is rejected. Further, if one believes that knowledge of the existence of God is possible, then strong agnosticism is rejected. It follows then that if Bob believes that there is a definition of God coherent enough to converse about, and that knowledge about whether or not such a being exists is possible, then he cannot accept A as true while denying A*.

Why? Because rejecting the proposition that “God exists” as Bob would have to do to maintain A in the absence of either an agnostic or ignostic justification entails A* for if A* were false, A could not be true.

To simplify, I am proposing that the follow propositions lead to contradiction if taken as a set:

(1) Bob believes that the concept of God is coherent enough for discussion

(2) Bob believes that knowledge of the existence of God is possible

(3) Bob neither believes that God does or does not exist

That is, for (3) to be true, either (1) or (2) must be false. If (1) and (2) are true, (3) is untenable. So when Bob is faced with the proposition “God exists”, accepting it renders him a theist, rejecting it, if he rejects it on the basis of the falsehood of (1) makes him an ignostic. If he rejects it on the basis of the falsehood of (2) he is an agnostic. If he rejects it with the truth of (1) or (2) maintained he is an atheist and has thereby accepted both A and A*.

As such, I think that it is unfair that the atheist attempt to define themselves in this way so that they may be relieved of any burden of providing argument for their position while waiting for arguments to be presented from the other side. Even if all the arguments for the existence of God failed, we would not arrive at atheism.

Hackenslash’s Epistemology

I found ‘Pannenberg’’s opening case for the existence of God very strong. It is far too lengthy and technical to post, however one can simply click the link above to read it on their own. ‘Pannenberg’ outlined his logical and metaphysical assumptions in a very clear manner so that if there were any disagreements regarding them, they could be addressed. With that said, much of my focus will be on Hackenslash’s statements.

In his opening, in response to ‘Pannenberg’’s claim that he will “… defend the claim that there exists a metaphysically necessary being”, Hack responds:

Sorry, but even were I to grant the metaphysical necessity of this entity, that would not equal existence. Many things can be described as necessary without actually existing.

It should be clear to even a first year philosophy student that this statement is absurd. It is logically impossible that something be both necessary and non-existent. Hack’s statement is as incoherent as stating that 2+2=9.

Next, Hack quotes the logical assumptions outlined by ‘Pannenberg’ and actually presumes that he makes no such assumptions. He states that under his empiricism the only assumption made is that “we can know.” Surely this is incoherent, for even the proposition that “we can know” brings into question the “how” of one’s knowing, an issue perhaps even more important than our ability in the context of his discussion.

In regard to one of ‘Pannenberg’’s arguments, Hack states:

And here we slip into an assumption, which means it must be supported by empirical evidence before we can accept it as axiomatic. In order to support this, one would require omniscience.

From this, ‘Pannenberg’ accurately (based on his writing in this debate) outlines Hack’s epistemology as follows:

(H) For any cognizer C, and any superdefinitely true proposition P, C can know that P, just in case, C believes that P, P is true, and C has appropriate empirical epistemic justification for believing that P.

That is to say that according to Hack’s epistemology, if Bob knows P it is the case that he only knows P because he has appropriate empirical justification for believing the proposition which happens to be true. As Hack’s previous statement outlines, he even thinks this true of axioms. Amidst the myriad of problems with Hack’s view, one is perhaps the easiest to understand. Hack cannot know his own epistemology by his own critiera unless there is some empirical evidence which serves as justification. But what possible empirical evidence could justify Hack’s epistemology? A further problem is that (H) is attempting to specify the conditions of knowledge, but if it is truly a precondition to such knowledge then its own criteria must be assumed in any attempt to provide justification. Such that, as ‘Pannenberg’ accurately notes, if Hack is asked for justification of (H) he only knows what kind of justification to give. That is, as ‘Pannenberg’ states:

So, here we have a fundamental assumption which Hackenslash cannot throw off. He’s got to admit that all knowledge conducive beliefs meet the conditions specified by HJEP, even if the object of knowledge is HJEP itself. So we have an epistemic justificatory circle around HJEP on Hackenslash’s view….a circle he can’t get rid of.

What is even more troubling is that Hack sees this as some sort of attack on empiricism as a whole. That’s just false, it’s an attack on Hack’s specific type of empiricism. In fact, I don’t see any reason to suspect that ‘Pannenberg’ himself is not an empiricist! It’s clear at this point, when Hack states in regard to ‘Pannenberg’’s analysis of his epistemology:

Oooh, that sounds all intellectual. I see my opponent is out to get empiricism. How predictable. Well, bring it on, because it will stand against any attack. While I largely accept the above, there are some problems with it. Firstly, unlike my opponent’s sky-hook concept, which is top-down and about as circular as it can possibly get, rendering this whole line of argumentation hypocritical, empiricism is bottom-up, and it is supported by the simple fact thatit works.

It almost seems as if Hackenslash does not understand the criticism that has been laid against him. He also attempts to invoke a pragmatic justification of (H) stating that “it works”. But this surely is of no use to him for not only would a pragmatic epistemic justification contradict the very epistemology he’s espoused, it might even force him to accept theism should it be successfully shown that theism is a superior explanation that “works better.” It should be obvious to any rational thinking individual that the epistemology Hackenslash has espoused in his discussion with ‘Pannenberg’ is absurd, demonstrably false and wholly incoherent.

Modality

Hack also seems to lay a charge against modal logic as well. ‘Pannenberg’ presents Yablo’s account of modal knowledge:

(Yablo-Conceivability) p is conceivable for me, if I can imagine a world that I take to verify p.

This is merely stating that some proposition is conceivable if there is some possible world in which it is true – that is, p is conceivable if an attempt to think it would not entail a logical contradiction.

But Hackenslash takes this to mean something wholly other, he seems to assume that ‘Pannenberg’ is stating that if p can be imagined, then p is true in the actual world. ‘Pannenberg’ is not saying this and it’s a horrible strawman to make.

Now, immediately we should put away the notion that these possible worlds must exist actually. This would be the position of the modal realist, but we are in no way committed to this idea. In fact, possible worlds can be thought of as concepts, abstracta or merely propositions.

Hack states:

Possibility is not reality.

Which is absolutely false. Perhaps what he means to say is that what is true in some possible world need not be true in ours. This much is true insofar as what is true is a contingent truth. But for necessary truths, they must be true in our world insofar as our world, the actual world, is one such possible world (an obvious fact).

Hack further states:

‘Metaphysically possible worlds’ are, unless you can demonstrate otherwise in a critically robust manner, functionally equivalent to ‘making stuff up’.

Of course, he offers no argument for this. Nor is it clear that even if possible worlds met the criteria of “making stuff up” that necessary truths still would not apply. It is even further exemplified that Hack has no idea as to what he is arguing against:

OK, where is the evidence that these possible worlds exist. Where is the evidence that any of this made-up nonsense applies to this world?

Of course one must wonder whether or not Hack is asking “where is the evidence that these possible worlds actually exist”, something that to anyone other than a modal realist is completely irrelevant and riddled with a lack of comprehension. Briefly put, possible worlds are conceivable states of affairs and modal logic is our logic of possibility. If there is some basis for rejecting a system which has been shown to be complete, Hack has not provided any such reason. One can only assume that Hack rejects it because he fails to understand it. Just because I can conceive of a possible world in which I am blue, does not mean that I am blue, obviously. Hack seems to think that this is what modal propositions are stating. Of course, if some proposition is true in every possible world and we discover this through the use of modal logic then it indeed follows that such a proposition is true in our world as well. That is, as per axiom s5, if something is merely possible it need not be true in our world, but if something is possibly necessary then it follows logically and inescapably that such a proposition is true in our world (see: Axiom S5).

Debate Resolution

Due to the fact that ‘Pannenberg’ did not respond Hackenslash won by default, but oddly enough the moderator awarded him a victory on debating points as well. It seems that the misunderstandings which Hack espoused were even shared by the moderator at RDF, and perhaps by even more of the community. Such is the folly of the ‘New Atheism’, they constantly proclaim themselves as being the intellectually elite, the reasoned, and the freethinking. This debate, and the many other examples of the ‘New Atheistic’ failure, stand as testaments to the falsity of these claims. While many of the ‘New Atheists’ may excel in the science, they falter when they presume the sciences as the be-all and end-all. While they proclaim themselves the reasoned they continually fail to demonstrate an understanding of anything outside of their respective fields. While they claim to be freethinking, the ‘New Atheist’ movement resembles a religion moreso than some religions!

There are objections to be made with regards to ‘Pannenberg’’s argument, but they would not be the espousal of a self-refuting epistemology coupled with a misunderstanding of basic philosophy presented to us by Hackenslash.

In my personal conversations with Hackenslash, he’s repeatedly expressed the idea that the existence of God is a scientific matter. This thinking is in line with Dawkins’ writing in The God Delusion but seems absolutely absurd. Surely the question of the existence of a being who’s mere possibility is ruled out methodologically by science, cannot be a scientific question. For if it is such a question, science has begged the question against the existence of God since the beginning.

A Plea

I would ask that atheists who currently have their atheistic justifications on a scientific basis critically rethink their positions. I am not convinced that science provides a firm justification of atheism, at least, not science devoid of philosophy (I think of Quentin Smith here as someone who couples science and philosophy to make his case for atheism). Philosophy is the only means by which one can reach a reasoned position on the existence of God whether it be theism or atheism. I would also urge any theistic readers to not be intimidated by the claims that a science devoid of philosophy has disproven the existence of God. It is in fact, impossible for science to do given it’s methodological restrictions. I am not saying that one should ignore our known scientific facts (since often they might make good cases for God) but rather that one be very skeptical of claims that science has pronounced atheism victorious, because this is not the case at all.

As should be evident from the debate between ‘Pannenberg’ and Hackenslash, the New Atheists are not the intellectual heroes of our modern world. And while Hackenslash has called me an “ignoramus” it is perhaps yet another irrational outburst from a scientistic individual, though oddly this time, aimed towards another atheist.

Logic is not logical by any certain measure. The skeptic Agrippa is credited with outlining this problem and due to its three tier approach it is known as Agrippa’s Trilemma. The Trilemma takes the form that truth, or absolute certainty, can never be obtained without committing one of three fallacies:

(1)  Infinite regress (or non-solution).

(2) An uncertain, non-absolute assumption, foundation or axiom.

(3) Circular reasoning.

(1) is the overly Socratic child continually asking “why?” or classically Zeno’s “Achilles and the Tortoise” paradox. One can only get close to the answer without ever solving it: there is always another “why?” or that little bit more distance to run.

(2) is the basis that the majority of philosophies employ to justify their beliefs, retorsion/reliabilism/ a god and any other number of foundations. The problem each of these foundations has is they often appeal to popularity and belief or simply lacking proof altogether.

(3) is simply stating that it is logical to use logic, to not do so is to encourage absurdity.

The Trilemma is a simple thought exercise that leads to the profound conclusion that we cannot prove logic itself, yet the problem is not insurmountable provided you are willing to compromise. On one side we have logic, the system of processes by which we obtain reasoning in any particular situation. The key word is system. Within the system of logic a great many things can be proven certain or true yet to try and qualify the system itself is folly. On the other side we have absurdity, the notion that everything is without meaning or purpose including trying to qualify absurdity itself.

This leads us to two possibilities:

1. Either everything (including this statement) cannot be grasped, judged and subsequently utilised

or

2. Logical thought is correct and we should adhere to the principles contained within its system.

There can be no compelling reason to live a life by absurd consequences, nor try to understand anything more than their potential existence whereas the logical system binds us to reasonable thought and has agreed consequences. In other words while there is no absolutely truthful reason we can ever prove to use logic, neither is there a way to prove we should not use logic.

Therefore, while we can never be absolutely certain, we see that the system of logic is the only acceptable method for addressing our reasoning and that seeking absolute certainty at any foundational level is illogical.

I have received some feedback on my previous article, The Case Against Presuppositionalism. I have decided to outline some received objections and deal with them accordingly. If you have not done so already, you should read the previous post before continuing.

I presented quite a lengthy criticism of presuppositionalism in my previous post and I am operating under the assumption that you have read the material. As such, I will condense and reformulate my arguments and answer some received objections afterwards:

Argument #1: That logical principles are not contingent on God

(1) Logical principles are either dependent on God or not dependent on God (premise)

(2) Logical principles are dependent on God if and only if (i) logical principles are created by God or (ii) logical principles are part of God’s nature (premise)

(3) If logical principles are dependent on God they are not logically necessary, they are contingent (premise)

(4) It is logically necessary that the principles of logic be necessarily true (premise)

(5) Therefore, the principles of logic are necessarily true (from 4)

(6) If the principles of logic are necessarily true they are not contingent (premise)

(7) Therefore the principles of logic are not contingent (from 4, 6)

(8) Therefore logical principles are not created by God nor exist as part of God’s nature ( from 2,3,4,5,6,7)

(9) Therefore, logical principles are not dependent on God

The above argument is a summation of many points in my previous article and shows the absurdity in claiming that logical principles depend on God for their existence.

The deduction proof is:

1. G(l) v ~G(l) (tautology)
2. G(l) <-> (Cr(l) v Na(l))
3. G(l) -> (~N(l) ^ C(l))
4. N(T(l))
5. T(l) conclusion
6. T(l) -> ~C(l)
7. ~C(1) conclusion
8. ~Cr(l) ^ ~Na(l)
9. ~G(l) conclusion

Argument #2: That presuppositionalism presumes an Ontological Argument

(1′) Logical principles are either dependent on God or not dependent on God (premise)

(2′) Logical principles are dependent on God if logical principles are part of God’s nature (premise)

(3′) If logical principles are a part of God’s nature there can be no logical principles if God does not exist (premise)

(4′) If there are no logical principles without the existence of God the proposition ‘God does not exist’ entails that the LNC fails (premise)

(5′) There is a possible world, w1, in which God does not exist (premise)

(6′) In w1 the LNC must hold as logical possibility is determined by the LNC (from 5)

(7′) It is the case that in w1 the LNC holds even though God does not exist (from 5,6)

(8′) Is not the case that logical principles are dependent on God

This argument is sound insofar as (5′) is true. If the presuppositionalist wants to assert that (5′) is false, they MUST present an Ontological Argument which exemplifies that God exists necessarily (that he exists in every possible world), they may not merely assume that conclusion.

Argument #1: Objections and Replies

1. Even if logic is part of God’s nature it is still logically necessary

It simply cannot be the case that logic is both contingent upon God’s existence and logically necessary, it MUST be one or the other. It seems to be the understanding of presuppositionalists that nothing can exist independently of God but this is a very elementary mistake in the philosophy of religion as logically necessary abstract objects MUST exist independently.

To quote Keith E. Yandell

“It is logically consistent with monotheism that there exist abstract objects that possess logically necessary existence. Abstract objects have no causal powers, are not self-conscious or even conscious and exercise no creation of providence. They are of little if any religious interest. It is a necessary truth that if X has logically necessary existence then there is nothing Y such that Y is distinct from X and X depends on Y for X’s existence. So if ‘there are abstract objects that have logically necessary existence’ is true, it is also true that there exists something whose existence does not depend on God. God’s status as Creator and any coherent notion of divine sovereignty, does not require that something that cannot depend for its existence on anything else depend for its existence on God or deny that the existence of such things is logically possible. But the only candidates for being something of this sort would seem to be things that exist with logical necessity.” (Philosophy of Religion: A Contemporary Introduction pg. 373, Keith Yandell)

As Yandell says:

It is a necessary truth that if X has logically necessary existence then there is nothing Y such that Y is distinct from X and X depends on Y for X’s existence

As such:

It is a necessary truth that if logic has logically necessary existence then there is no God that can exist distinct from logic and it be the case that logic depend on God for its existence

One might argue that Yandell’s statement does not apply here as it was not asserted that logic and God exist distinct from each other but rather that God’s nature is logical. This simply characterizes yet another misunderstanding of logic. Logic is not attributable to one being or concept but rather only to the relationships between two or more concepts or arguments. Thus, whereas it may be possible that when God’s nature is analyzed, it is coherent and orderly this is not to say that God’s nature IS logic. In fact, it is to say something wholly different.

Assume a situation where God performs an action, A. God’s action must presuppose the LNC as God cannot do act A and not A at the same time. God cannot also have property P and not P at the same time. In this respect, it is the case that God’s nature corresponds to necessarily existent logical principles. So whereas God MUST presuppose logic, it is not clear that logic presupposes God, rather we have good reasons to reject that logic presupposes God.

Argument #2: Objections and Replies

1. This entire possible world matter is just silliness

Possible world semantics (or modal logic) is simply a form of reasoning to discern logical necessity/contingency. The fact that we say there is a possible world where X does not mean that there is an actual world where X, merely that X could possibly be the case (even though it might not be). For an easy to understand overview: Modal Logic on Wikipedia

2. The premise, (5′), can be shown to be false from the mere fact that without God you cannot prove anything!

This is, of course, the precise issue being discussed and so one should not beg this question. However, it is not the case that if without God nothing can be proven, God must exist necessarily. Such an argument:

(1”) Without God, one cannot prove anything

(2”) Therefore God exists necessarily

is a complete non-sequitur.

Why must God exist in all possible words because without him, nothing can be proven? There can exist a possible world in which there is nothing to be proven and as such, according to the criteria assumed by such a formulation, God would not exist in such a world or his existence would be arbitrary.

Non-argument specific: Objections and Replies

1. You still have not accounted for logic

The notion of “justifying logic” is a peculiar one. It is clear and evident that logical principles exist as logically necessary abstractions, furthermore, logical principles are axioms and as such they are not subject to any proof or justification outside of themselves.

(10) If something needs justification/accounting from an external source that thing is logically contingent and not logically necessary

(11) The principles of logic are logically necessary

(12) The principles of logic are not logically contingent (from 11)

(13) The principles of logic do not require justification/accounting from an external source

It is difficult to see what is even meant by “justifying/accounting” for logic.

Presuppositionalism is a branch of apologetics which, instead of offering the classical arguments in favor of God’s existence, attempts to show that any worldview which does not presuppose the Christian God is internally incoherent. This type of apologetic has been defended by the likes of Van Til, Greg Bahnsen and John Frame. Defenders of presuppositional apologetics with whom I am more familiar include the folks over at Choosing Hats.

Presuppositional apologetics have always seemed to be more of a set of debating tactics rather than a epistemic system. However it is pertinent to treat it as what it claims to be for the sake of discussion.

Spawning from presuppositional apologetics is an argument known as the TAG, or the Transcendental Argument for the Existence of God. Presuppositionalism produces nowhere else (to my understanding) a formal argument for its claim. As such, if one wants to thoroughly provide a critique of presuppositionalism, it seems necessary that they offer a critique of the TAG as well.

Presuppositionalism Stated

Succinctly, presuppositionalism argues that the Christian God is necessary for the intelligibility of various features of human understanding (logic, morality, meaning). It does so by making a transcendental argument. Transcendental arguments take the following form:

A: For X to be the case, Y would have to be the case, because Y is a precondition of X

B: X is the case

C: Therefore, Y is the case

Contextualized, this argument becomes:

A: For there to be intelligibility in the world, God must exist because God is a precondition of intelligibility

B: There is intelligibility in the world

C: Therefore, God exists

The support for A is often a series of claims that non-Christian worldviews cannot make sense of the various features of human understanding coupled with the notion that if it is impossible for non-Christian worldviews to justify intelligibility and intelligibility exists, it must thereby only be justified by a Christian worldview.

It is also important to note that presuppositionalists state that their reasoning operates using two axioms. To quote a presuppositionalist with whom I have debated:

• As a Christian, I have two axiomatic, interrelated foundations for my epistemology, and for everything else I encounter through the grid of that epistemology. The Triune God of Scripture – who created the universe and all it contains; who established and even now maintains the laws which govern that creation. That is foundation one.
• The self-revelation of that self-existent, self-conscious, self-sufficient, omniscient, omnipotent, all-wise, immutable, eternal, and sovereign God; The Scriptures of the Old and New Testament, are the self-communication of the extent, nature, and specifics of His eternal properties – which are the guarantor of the laws and assumptions which we, as creatures in the image of that God, require to operate rationally and coherently. That is foundation 2.

God as an axiom

For the purposes of this discussion, I will focus on the claim that logic is dependent on the Christian God. Presuppositionalists do not stop merely at logic, but assert that morality, science, etc all presuppose their Christian God. I’ve chosen to address only the logic portion of these claims because I see it as the most important issue, and if it can be shown that logic does not depend on the Christian God it seems that presuppositionalist apologetics are defeated.

First and foremost, one should note the peculiarity of the espoused axioms of presuppositionalism. They are in fact, not axioms. My colleague Dawson Bethrick outlines this comprehensively on his blog, but I wish to do so in a slightly different manner.

A statement must satisfy three conditions to be considered axiomatic:

• It must be irreducible to prior concepts
• It must be self-evident to introspective and extrospective acts of cognition
• It must be undeniable without direct contradiction

The concept of “God” fails to meet each of these:

• One can reduce the concept of God to an unembodied mind, thereby rendering the concept of God as non-foundational
• The concept of God is not self-evident to all acts of cognition
• The denial of God does not lead to direct contradiction, in stating that “God does not exist” one is making use of various axioms but not presuming the existence of God.

As such, we can reject the notion that God is an axiom.

Logic and God

As stated, the presuppositionalist will say that the very existence of logic (or logical absolutes) depends on the existence of the Christian God. Philosopher Michael Martin analyzes this claim in his Transcendental Argument for the Non-existence of God (TANG). This argument is often dismissed by presuppositionalists, but I have yet to hear a compelling case as to why such a dismissal occurs.

The portion of the TANG which deals with logic is as follows:

1. Logic presupposes that its principles are necessarily true.

2. According to the brand of Christianity assumed by TAG, God created everything, including logic; or at least everything, including logic, is dependent on God.

3. If something is created by or is dependent on God, it is not necessary — it is contingent on God.

4. If principles of logic are contingent on God, they are not logically necessary.

5. If principles of logic are contingent on God, God could arrange matters so that a proposition and its negation were true at the same time. But this is absurd. How could God arrange matters so that New Zealand is south of China and that New Zealand is not south of it?

6. Hence logic is not dependent on God, and, insofar as the Christian world view assumes that logic is so dependent, it is false.

The argument is formally valid, so we must discover whether or not it is sound. Premise (2) is usually called into question as being a misunderstanding. For many Christians God did not create the laws of logic, it is claimed that they exist as part of God’s nature.

In taking the statement that “Logic exists as an intrinsic part of God’s nature”, one can deduce that if God did not exist than there would be no logical absolutes. That is to say if God does not exist, the law of non-contradiction can be denied.

But is this the case? We can cite such an argument from Van Til himself in his “The Defense of the Faith” (pg 256-257):

(7) If the Christian God did not exist, then predication would operate against a background of bare possibility.

(8) If predication operates against a background of bare possibility, the predication of P to x ( x is P) may be reversed and ~ P might be predicated of x ( x is ~ P)

(9) But if the predication of P to x ( x is P) is reversed and ~ P is be predicated of x ( x is ~ P), then the Law of Non-contradiction must be denied.

(10) Therefore, If the Christian God did not exist, then the Law of Non-contradiction must be denied

For the readers who are not particularly philosophically inclined, the above argument is saying that the law of non-contradiction (which states that someone cannot be X and not X simultaneously) can be denied if God does not exist. Thereby attempting to show that if God does not exist we can say that the apple is orange and that the apple is not orange, because there is no law of non-contradiction.

Interestingly enough, (7) makes mention of a background of bare possibility which presumably refers to logical possibility. But in order to have logical possibility, one must have the law of non-contradiction. That is to say, logical possibility is determined by the law of non-contradiction. The premise hinges on being an incoherent notion.

(7) further states that if predication operates via logical possibility, then we may reverse the predications completely. The suggestion is to say that we can have an apple be orange at one time and not orange at another time. Granted, but this is no way necessitates that the apple can be orange and not orange simultaneously. Henceforth, (9) is false. Reversing the predicate does not change the Law of Non-Contradiction. As such, the argument is unsound and we can reject (10).

Perhaps the modern presuppositionalist would object to Van Til’s formulation, asserting that the mere denial of God’s existence is logically absurd outright. Such an assertion would state that it is incoherent to deny the existence of God because of his very nature (he necessarily exists).

Consider the following:

(11) It is not the case that it is not that P and not P (law of non-contradiction denied, meaning it would be possible for your apple to be both orange and not orange simultaneously)

(12) It is not the case that God exists

In attempting to affirm (11), one arrives at an obvious logical incoherence. How could an apple be both orange and not orange simultaneously? In this sense, it is logically incoherent to affirm (11). But is it as logically incoherent to affirm (12), as the presuppositionalist states?

There is no self evident incoherence in affirming (12) and thereby denying that God exists. The only way there would be such an incoherence is if we applied a premise which stated:

(13) It is logically necessary that God exists

With the establishment of (13) it becomes obviously incoherent to affirm (12) and deny the existence of God. But how can the presuppositionalist assert (13)?

To say that it is logically necessary that God exists is to affirm the conclusion of an Ontological Argument. It is essentially saying that God cannot fail to exist because of his nature. But the presuppositionalist has chosen to forego classical arguments for the existence of God and thereby cannot support this claim! Why should one accept that it is logically necessary that God exists without an Ontological Argument to defend such a conclusion?

In effect, the presuppositionalist has shot themselves in the foot by choosing to dismiss classical arguments for the existence of God. The presuppositionalist requires one, but is unable to use one (by virtue of their own apologetic).

It should also be further noted that (13) is often confused for another premise. There is a difference between God necessarily existing and God (if existing) necessarily having no beginning or end.

Consider:

(14) It is logically necessary that if at any time God existed, then at every time He existed

While (14) is required in presumably every branch of Christianity, and with good philosophical warrant, (13) isn’t.

Conclusion

As such, we can reach a couple of conclusions:

Firstly, God cannot be asserted as an axiomatic concept. Secondly, if logic is created or dependent on God, than it is not necessary and insofar as logic presupposes that its principles are necessarily true, logic simply cannot be based on the Christian God. Furthermore, if one is to say that logic exists necessarily as a part of God’s nature it becomes a logical consequence that denying the existence of God would lead to the denial of the law of non-contradiction. Since it has been shown that such is not the case without assuming the conclusion of a successful ontological argument we can reject this notion altogether.

At this point it seems that presuppositionalist apologetics are dead in the water. By its very nature presuppositionalism has rejected the classical theistic arguments and such arguments have become the very thing needed to keep presuppositionalism afloat.

This article is a response to an article by Bolt, which was a direct response to Dawson Bethrick. I am not addressing the post specifically, but rather the assertion that inductive reasoning must presuppose the Christian God.

This is an assertion based upon Chris Bolt’s presuppositionalist worldview and makes the claim that non-Christian worldviews cannot account for the uniformity of nature and as such, cannot justify their use of inductive reasoning. For those unfamiliar, the uniformity of nature (or rather the principle of the uniformity of nature) states that “the future will resemble the past” and is used in inductive reasoning to make statements such as “The Sun will rise tomorrow”.

Before I move on, I should outline for those who are unfamilar, the differences between Deductive and Inductive reasoning.

A deductive argument is that where the truth of the conclusion follows necessarily from previous premises.

Example:

1. All men are mortal

2. Mitch is a man

3. Therefore, Mitch is a mortal

(3) follows logically and inescapably from (1) and (2).

An inductive argument is probabilistic:

(1) Almost all men from Canada speak English

(2) Mitch is from Canada

(3) Therefore, Mitch speaks English

Whereas in a deductive argument it is impossible for the premises to be true and the conclusion to be false (provided the argument is valid/sound), in an inductive argument the premises may be correct and the conclusion false.

It is proposed that scientific reasoning is largely inductive in nature, moving from specifics (observing white swans repeatedly) and drawing conclusion for the whole (there are no black swans). In doing so, Science would invoke the principle of the uniformity of nature, presuming that in certain circumstances the future will resemble the past. For example, because the sun has risen everyday in the past, it is probable that it will rise tomorrow. Though it is, of course, possible that the sun may not.

Bolt, and all presuppositionalists seems to be very skeptical of inductive reasoning (or at least, Godless inductive reasoning) and they owe this skepticism to the likes of Bertrand Russell and David Hume as both of these philosophers raised important skeptical questions about the usage of inductive reasoning. But since they have raised such issues, there has been ample response to the so called “problems of induction” from the philosophical community.

Someone skeptical of inductive reasoning might state that there are no strong inductive arguments or go even further to suggest that all inductive arguments are equal and none are “better/stronger” than any other. For example, an inductive skeptic might say that it is no more probable that the sun will rise tomorrow because it has in the past, than that it will not. Blanket claims may be made further, stating that inductive reasoning is actually irrational!

Many inductive skeptics in the past have agreed that if we can make certain assumptions about the world, such as the uniformity of nature), then inductive reasoning could be justified. However, these same skeptics assert that these assumptions cannot be made without justification and to justify them would assume inductive reasoning outright.

According to philosopher Michael Martin:

On the standard interpretation of Hume that Bahnsen [a presuppositionalist scholar] accepted, Hume is supposed to have shown that probabilistic arguments — what I characterized above as inductive arguments– are unjustified. However, it is open to question that Hume held this modern view. A detailed analysis of Hume’s works has shown that by “probabilistic argument” Hume meant a certain type of deductive argument. Hume believed that all such arguments presuppose the uniformity of nature, but he did not attempt to show that probabilistic arguments in the modern sense are unjustified. Thus, appeals to Hume prove very little about whether inductive, that is, probabilistic arguments, are justified.

To claim that inductive reasoning is outright irrational, largely depends on what one defines as “rational”. Indeed, many philosophers have argued that the “problem of induction” is to simply be done away with, not requiring a solution. Philosophers such as Strawson and Edwards have further argued that the problem of induction rests on linguistic confusions rather than a sound philosophical basis. Further, as Martin states, philosophers Gemes goes on to say that inductive skepticism can be reduced into absurdity and that the position of inductive skepticism cannot be coherently formulated and should not be taken seriously.

Presuppositionalist literature, specifically the writings of Bahnsen, do not directly answer any of the above criticisms of inductive skepticism. Though, to his credit, Bahnsen cites many writings of Russell on the subject, but the very passages he cites have been pointed out to be confusion on Russell’s part by philosopher Frederick Wills in his “Will the Future be like Past?”

Of course there is even debate in the philosophical community as to whether or not science does actually presuppose a justification of induction and whether or not in doing so, there can be a pragmatic vindication. As Reichenbach says, “If there are any true inductive generalizations, the consistent use of induction will discover them in the long run.”

The point is made further, that one should simply continue to use induction until it refutes itself by E. H. Madden, “One uses induction because it makes getting through life easier and although we don’t know whether induction will continue to have this effect, the only way to discover if it will is to continue to use it.”

As such, it is clear and evident that unlike Bahnsen and most presuppositionalists would have you believe, the issue of inductive skepticism is far from settled. As philosopher Michael Martin suggests, it’s still an open question in philosophy and until the issue of inductive skepticism has been settled (on either side of the issue), the assertion that induction is somehow clearly open to challenge and that science is impossible without it remain completely in doubt.

But of course, if inductive skepticism is valid, it effects not only a non-Christian worldview but the Christian worldview as well! Christianity must provide a justification for the use of inductive reasoning just as any other worldview must.

Christianity claims to have a guarantee to the uniformity of nature. But how can this be when Christian apologists themselves says that it is possible that God may have morally sufficient reasons for allowing evil in the world. Can we not then conclude, for example, that God may have morally sufficient reason for allowing a hurricane or other natural disaster and we are just in the dark as to the justification?

Now suppose further that the very uniformities of nature will fail to hold in the future. As Martin illustrates, imagine that after the year 1998 all the emeralds in the world will be blue and all rubies will be green. Insofar as God could have morally sufficient reasons for a natural disaster, he could have sufficient reasons for causing such a departure from the normal. Just as we can account for all the evil in the world by appealing to God’s sufficient reasons, so too could the same apply for any departure from a preconceived uniformity of nature!

Simply because we do not know of any such departures God has made in the past, does not necessitate he will not do them in the future. This wouldn’t even be a deception on the part of God (as Bolt might protest) as he never assured us that our expectations about the future would be true.

In response to the above point, Greg Bahnsen (and presumably most other presuppositionalists) appeal to passages in their Scriptures to justify belief in the uniformity of nature. One such being Gen. 8. 20-22 wherein God said to Noah that He would continue the seasons. In response, Martin outlines four basic problems with scriptural appeals such as this.

Firstly, why suppose that the passages are true? Why suppose that Noah was even real, and why suppose that he made a covenant with God to continue the seasons?

Secondly, what of the interpretation of the passage? Should we interpret it to mean that nature will be uniform in the usual sense? Surely all the seasons can be continued with huge changes in the uniformity of nature. Winter may come and snow could be green, in Spring flowers could have no smell and Summer could bring us some pink grass! God does not say in detail how he would continue the seasons.

Third, Martin presses further, God’s promise is compatible with inductive chaos in most of the Universe. God says “that while the earth remains, seed time and harvest, cold and heat, summer and winter, day and night, shall not cease” (Gen 8. 22) and this passage shows no incompatibility with a state of affairs in which the present laws of nature do not hold outside of the Earth. So while the Earth may remain as God said, what of elsewhere in the Universe?

Lastly, why must we suppose that God would keep his covenant with Noah? There is no inconsistency with God breaking a promise so long as he has morally sufficient reason to do so. Furthermore, what if God is not responsible for the failure of the uniformity of nature but rather Satan is! Perhaps Satan decided to work his evil by bringing inductive chaos into the world, and God does not interfere because he does not want to deprive Satan of his free will.

So with inductive skepticism still an issue that is hotly debated and for all intents, “up in the air”, why should we presume the issue settled at all, much less settled with a Christian worldview. It is evident that even if we are to accept that there is an inherent problem in inductive reasoning, it does not follow that a Christian worldview allows us to leave this problem behind. Furthermore, as is the case with many presuppositionalist assertions, even if the Christian worldview must be assumed to make sense of X it does not follow that it is true.