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Sunday 4 December 2016

The Executioner's Argument

Can you behead an entity that has no body? It seems tricky, to say the least, yet this is what I intend for this post or, more accurately, to cut the body off from the head.

The post title is a reference to a discussion in Alice's Adventures in Wonderland by Lewis Carroll, in which the King ordered the beheading of the Cheshire Cat, who appeared only as a disembodied head. The executioner argued that it wasn't possible to decapitate something that was all head, and had no body. The King argued that it was perfectly possible.
Some suggest that much of Carroll's work of nonsense was an allegory, bemoaning the state of education in Victorian England, especially in Carroll's chosen field of mathematics and logic (there's also a suggestion that the pictures of the Mad Hatter in the original edition were meant to represent the great Bertrand Russell).
Anyhoo, is it possible? It's a thorny logical problem, to be sure. From what are you decapitating the capital? It's my intention to decapitate something that has no body in this post, by simply destroying the head with some simple logic.

There seems to be a burgeoning of late of a branch of apologetics known as presuppositionalism. It appears to be a method for little more than simply frustrating counter-apologists. It's pretty effective, too, because it can be difficult to pin down a position to argue from. 

As an interesting aside, I had a bit of a chat the other day with Sara Uckelman, lecturer in logic at Durham University, that included this exchange:
If you want to know what my answer to this question is, see Who, What, When, Where, How, Why? The Art of Philosophy. It gels fairly well with Sara's response, but goes into considerably more detail.

Let's talk first about what presuppositionalism is, and how it manifests in apologetics and debate.

Presuppositionalism in Christian apologetics is, at root, the belief that the Christian worldview is the only rational one, and that the bible is the revealed, inerrant word of god. It mostly proceeds by attempting to expose logical flaws in other worldviews. This is problematic in and of itself, not least because it represents several fallacies before we even begin to examine it, not least the false (di)chotomy (or however many worldviews it encounters) and our old friend petitio principii, or begging the question. Moreover, as the above exchange should be highlighting, a central problem is identification of failures of presupposition, and this framework asserts for itself that its presuppositions cannot be wrong.

The way it approaches the task is to show that other worldviews can't account for certain things, and concludes that they're self-refuting on that basis. Among other things, I intend to show here that the presupp stance is most definitely self-refuting on the basis that every tactic it employs to refute another worldview applies equally to presuppositionalism, thus the apologist refutes his own position.

Let's start gently, though, and simply show that presuppositionalism fails on its own terms. In order to do that, we need do no more than find a single instance of something the hokey blurble gets wrong. Can we do that?

Well, errrr...

Just kidding, of course. It's trivial to find something, because the only thing that's actually consistent about this book of turgid drivel is the wrong in it. Classifying bats as birds, insects with four legs*, the idea that you can affect wholesale changes in the genome by having parents bump uglies alongside coloured sticks. And that's barely scratching the surface.

Time to get serious, then. 

The strongest argument arising from presuppositionalism is that atheism - or secular humanism, to cite an example employed in a recent debate between Matt Dillahunty of the Atheist Debates Patreon project and Matt Slick, head cook and bottle-washer at CARM(dot)org - is self-refuting because it can't account for the laws of logic. 

Let's do a bit of unpacking here, because it will save some tedious work later on.

Slick asserts first of all - quite incorrectly - that the laws of logic aren't the same sort of thing as physical laws, the laws of the universe. This is rooted in an abject failure to grasp just what physical laws are.

It's a common misconception that physical laws are rules that the universe must obey. This misses the mark in one important aspect, an aspect we touched on in a slightly different context in The Map Is Not The Terrain when discussing dictionaries and definitions. In that post, we discussed the fact that dictionaries, popularly thought to be prescriptive, are actually descriptive of usage. In the same way, physical laws are descriptions of observed behaviours. Specifically, they're descriptions of the relationships between observed quantities. They describe interactions between one entity and another arising from the properties of said entities..

Similarly, logical laws are descriptions of principles of thought, specifically dealing with contradictions. Is it possible for a contradiction to obtain in the universe? That's a question we can't answer with any robustness, but it certainly appears that it isn't, and we proceed on that basis. Like physical laws, they're subject to the problem of induction (setting aside whether we'd recognise a true contradiction). 

We discussed the three laws of classical thought in Deduction, Induction, Abduction and Fallacy, the earlier offering on how logic is used in the sciences. In summary, they all basically say the same thing, yet they apply in a subtly different ways. They are as follows:

1. No proposition can be both true and false simultaneously - the Law of Non-contradiction (LNC).
2. Nothing can be both what it is and not what it is - the Law of Identity.
3. For any proposition, either that proposition is true, or its negation is true - the Law of the Excluded Middle (LEM).
I know that my friend and mathematics guru Phil Scott, who we met in Definitions and Axioms, thinks that the case for these laws of thought is massively overstated at the very least, and he makes a compelling case, which lends weight to what I'm saying here. Ultimately, although they've shaped our thought since antiquity, they can best be thought of as useful guidelines, or indicators of when we should look more carefully at our reasoning and conclusions. 

I'll say no more about this for the moment, not least because Phil has expressed an interest in addressing this in another guest post, which will be a treat. The point here is that we should treat these laws of logic, and indeed logic itself, as not having truth-value, but as being useful guides.

Let's look at them in a little more detail. The first is fairly straightforward (though possibly the most contentious). In Paradox! A Game for all the Family! we looked at some well-known instances of where contradictions had been thought to have arisen. I asserted - correctly, I think - that there were no genuine paradoxes. The nearest we got to one was Russell's Paradox, which arises in na├»ve set theory. This comes about via the assumption that things can be collected into sets without restriction based on some property. This assumption then leads to the idea of a set of all sets that don't contain themselves as a member. If this set does not contain itself as a member, then it must be a member of the set, which means it can't be a member of the set, so it must be a member of the set, and round and round and round (you may want to read that through a few times; it confused the holy fuck out of me). As Phil likes to say, 'here we go again; first we discover recursion'.

The point here is that, when we encounter a situation in which two or more mutually exclusive circumstances obtain in our thought, it's a very good indicator that something's gone a bit pear-shaped.

The second is the law of identity. This states that something cannot be both what it is and not what it is at the same time. Can a stone be not a stone? Again, this is pretty much intuitive, and requires no real justification. It's basically another formulation of the LNC, because for something to be what it is and not what it is at the same time is a contradiction. These are mutually exclusive, binary states.

Note that this doesn't preclude something being what it is and simultaneously something else, which is perfectly acceptable. A stone, for example, can be a sculpture, while still being a stone. There is no contradiction there.

The third is the law of the excluded middle. This states that, for any proposition, either the proposition is true or its negation is true. This law must be treated with some care, not least because it only applies to binary states and is often misapplied in the fallacy of the excluded middle. That there is a fallacy with the same form as the law tells us something important about how it works. I won't belabour the point with this one, not least because I gave this a complete treatment in Fuzzy Logic, Classification and the Fallacy of the Excluded Middle.

Ultimately, these principles of thought are pretty much common sense and, like physical laws, they arise from the properties of thought. They're a guide to ensuring that our thoughts are coherent and avoid absurdity. In reality, insofar as they're 'true' at all, they require no justification, they're simply brute facts, i.e., they cannot fail to obtain.

Indeed, it should be noted that, on the view of the theist who believes in an interventionist deity, any foundation they might have is severely undermined, not least because, to borrow a phrase from David Edwards, who we met in Radionuclide Dating is Rigorous, any universe containing an entity who can tell the laws of the universe to take a hike whenever it suits his administrative convenience is a universe in which absurdity abounds, making science and indeed logic impossible. 

What this entire position boils down to, then, is very much akin to the assertions of creationists in one of their pet arguments against evolution, namely that it can't account for the origin of life. This overlooks the fact that evolutionary theory doesn't have to account for this, because the origin of life is the remit of a completely different field of science. Evolutionary theory is the central theory of biology, while abiogenesis is the remit of organic chemistry. Moreover, and again like the evolution/abiogenesis issue, the explanation offered by the presuppositionalist isn't actually an explanation, it's merely an assertion that an explanation exists. They can't give you any content, or any justification that suggests how god might have gone about instituting these laws, or the laws of the universe, or anything else. Remember that anything that explains everything explains nothing. It's unfalsifiable, and thus has no epistemological utility or value.

In this light, we can say simply that logic 'exists', and proceed from there, without asserting anything at all about the foundations, in precisely the same way that we can say that life 'exists' (this is a problematic term to use in this context, because life isn't a thing, it's a behaviour, and failing this distinction is at the root of an awful lot of shoddy thinking; the same can be said for mind and consciousness, for precisely the same reasons).

While recovering from a hand injury that made typing difficult (no, not wanker's cramp), I was asked to look at another argument, namely the 'argument from reason', popularised by C.S. Lewis. Similar in content to the presuppositionalist stance detailed above, it's an argument against philosophical naturalism and for the existence of god. It asserts, via very convoluted reasoning, that if naturalism is 'true', then the basis of all beliefs is explained by non-rational means (the firing of neurons), and no belief can be rationally inferred. He goes on to conclude that, to avoid infinite regress, there must be a rational entity at the bottom of it all to serve as a foundation. Sound familiar? It should, because it's pretty much identical to the stance of Matt Slick above.

There are all sorts of flaws in this, but I'm again conscious that this is getting to be quite a lengthy submission, so we'll go straight for the jugular.

The first thing to note is that I'm not a philosophical naturalist, which is sufficient to defeat Lewis' argument in and of itself.

Philosophical or metaphysical naturalism is the position that nature is all that exists. I'm entirely agnostic on this point, although I see no good reason to suppose that anything exists beyond nature. Science is not a framework that entails philosophical naturalism. It is a framework that entails methodological naturalism or, as Hawking and Mlodinow put it in The Grand Design, 'model-dependent realism'. This, however, doesn't assert naturalism as 'true', it simply employs a naturalistic stance as a method. This is sufficient to undercut the argument, if not defeat it.

Science deals with phenomena. It asserts nothing about the ontology of those phenomena, and it certainly doesn't deal with them as noumena, to borrow a Kantian term. Noumena are the ontological counterpart of phenomena, which is to say that noumena are the proper constituents of reality. While we have no good reason to suppose that phenomena and noumena are different things, we also can't assert categorically that they're the same. More importantly, we don't have to. We deal with phenomena and build our models dealing with how they behave and interact.

Furthermore, Lewis' argument commits a pretty egregious false conflation, because he's treating the mechanism of belief - the firing of neurons - with the content of belief, or knowledge, and suggesting that if all we have is brain activity, then we can have no knowledge, because we can't rely on reasoning that is purely mechanical. This is a horrible bit of shoddiness in thinking, no matter how sophisticated it looks. The mechanisms by which our brains work are entirely irrelevant to the fact that they do work, and that we can show via simple logic that what they produce is knowledge.

In the end, as with the presupp's assertion about God being the explanation for logic, all we have at the foundation of this stance is assertion, which is no foundation at all. It also commits an extremely basic logical fallacy, namely affirming the consequent. You can find a full exposition of this fallacy in Deduction, Induction, Abduction and Fallacy, linked above.

In short, presuppositionalism is unsound in the extreme, and can be dismissed on that basis alone.

Can you behead a bodiless cat? 

Nits, crits and comments welcome, as always.

*Leviticus 11:19 and 23 respectively
Genesis 30:37-39


  1. Thank you for this, Tony. The Presuppers are annoying in their persistent assertions. The way I see it is that their base assertion that god essentially is the foundation of and justifies all logic, beliefs etc is that they are using a top down model which depends on human imagination, while the naturalistic model depends on starting with what we can observe and test for and moves from there.

    1. Exactly right, Guy. The naturalistic approach is pragmatic.

      Daniel Dennett talks about the distinction between a crane and a skyhook. The presupp approach is skyhook all the way, while an observation-based approach is a crane.

      Thanks for flagging the issue with commenting, by the way. I found the solution.


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