Dana asked:

Is the nature of fundamentally understanding reality intrinsically illogical, and would this subsequently imply that reality itself is fundamentally illogical (since reality is defined by perception/ understanding)?

Since a fundamental explanation for reality must explain itself (be a selfcontained explanation), it would be, by definition, unsubstantiated by external means, and therefore without any external evidence supporting it. Thus, any final or fundamental explanation for what we call “reality” must be unexplained by any external reasoning, thereby making it illogical as it would have no means of inference by which to prove such an explanation, and such the ability to make such an inference is essentially the means by which we define something to be logical, if I am not mistaken.

How could an ultimate theory or understanding of reality and everything possibly retain any sense of reason without continuing forever and reaching no definite conclusion (and therefore not truly being an “ultimate” theory or understanding of reality and everything)? Is mankind’s quest for understanding inherently limited despite our greatest efforts? Because reality seems to contain an innate tendency to refute logic at its most fundamental level.

Also, this would lead to many consequences, such as the inability for science, or logic, to ever refute God, since logic itself breaks down at the essence of existence, and therefore the rules by which we govern any means of defining what explanations may or may not be sensible.

Answer by Julian Plumley

Your initial question is: ‘Is the nature of fundamentally understanding reality intrinsically illogical?’ There are a couple of problems with this: I am not sure what the nature of an understanding might be; ‘illogical’ has to be made more precise; ‘fundamentally’ does not really add anything except emphasis. So I think the question needs to be slightly modified as follows: ‘Is the notion of understanding reality self-contradictory?’

Your second question is: ‘Would [the notion of understanding reality being self-contradictory] subsequently imply that reality itself is fundamentally illogical (since reality is defined by perception/ understanding)?’ This question is already an abbreviated argument, which might be expanded as follows.

1. The notion of understanding reality is self-contradictory.

2. Reality is defined by perception and understanding.

3. Therefore, reality is self-contradictory.

Is the argument valid? No. Whose perception and understanding is this talking about, and of what? Presumably, mankind’s perception and understanding of reality. There is also an ambiguity between the use of ‘reality’ in 1 and in 2. In 1, I think ‘reality’ refers to everything, the whole world, so let’s say ‘Reality’ (capitalised). In 2, ‘reality’ means ‘the reality of a thing’ or it’s individual nature. There is also a hidden step getting from 2 to 3. So we can repair the argument as follows.

1′. The notion of mankind’s understanding Reality is self-contradictory.

2′. The reality of a thing is defined by mankind’s [perception and] understanding of that thing.

3′. If the reality of a thing is defined by something self-contradictory, then that thing is self-contradictory.

Therefore 4. Reality is self-contradictory.

The argument is now sound if the premises are true, but are they? For 3′, if the nature (reality) of X is defined by Y, and Y is self-contradictory, does that make X self-contradictory? Arguably, yes. If we define the nature of the red Queen’s favourite rose garden arrangements as round squares, then those arrangements are themselves self-contradictory. For 1′ – this is argued for later. For 2′ – this is a highly controversial, irrealist viewpoint. It says, with Protagoras, that ‘Man is the measure of all things’. I will not take this point further, since there is ample literature on that subject.

So 1′ is the key to both of your questions. Is understanding Reality logically impossible? You offer an argument in its defence as follows.

5. A fundamental explanation for reality must explain itself (i.e. be a self-contained explanation).

6. So it [a fundamental explanation for reality] would be unsubstantiated by external means, and without any external evidence supporting it.

7. So there is no means to prove it [infer it] from anything else.

8. Anything that cannot be proved is illogical.

Therefore 9. It is illogical.

In this argument, you have shifted your ground from ‘understanding’ to ‘explanation’. But these are different notions. An explanation goes from an explanans to an explanandum, and these have to be two different propositions, or the explanation in not satisfactory. But ‘understanding’ is not the same – not everything we understand stands in need of explanation. And understanding is not always propositional: e.g. understanding what the colour red is like is knowledge-by-acquaintance, not ‘knowledge-that’. The argument also has some hidden steps and has to be repaired as follows.

10. If the explanation of something is self-contradictory, then the notion of understanding that thing is self-contradictory. [i.e. Something can only be understood if it can be explained.]

5′. Any explanation of Reality [by mankind] is included in Reality.

Therefore 6′. There is no explanans of Reality that is independent of Reality.

11. All valid explanation proceeds via logical inference from an explanans that is independent of the explanandum to the explanandum.

Therefore 7′. There is no valid explanation of Reality.

8′. Any non-valid explanation is self-contradictory.

Therefore 9b’. Any explanation of Reality is self-contradictory.

Therefore 1′. The notion of mankind’s understanding Reality is self-contradictory.

So how about the premises of this argument? As I stated above, I do not think 10 is true. Explanation and understanding are not connected in this way. 5′ seems true, since we are part of Reality. 11 is not true, since there are perfectly good inductive explanations. But the requirement for logical inference is superfluous. The core idea of your argument is that the explanation is internal, not that it is non-inferential. 8′ is not true, but this might be improved by translating your ‘illogical’ as ‘self-contradictory or meaningless.’

Overall, this argument for 1′ is going not going to work in this way. But your underlying problem is that you cannot see a way we can ever reach a final understanding of Reality, if we are embedded in Reality. So you ask: ‘How could an ultimate theory or understanding of reality and everything possibly retain any sense of reason without continuing forever…?’

To me, it looks like you are using a foundationalist theory of knowledge: we can only know things that we can logically infer from other things that we know. (And we can understand what we know.) But this cannot get us very far. There is very little about the world that we infer logically, as against inductively. And there is not enough self-evident knowledge to start from to build up foundationalist knowledge.

Mankind’s major project for understanding Reality is Science. (And you could add Theology, too, if you like.) Science uses mainly a coherence theory of knowledge. The main criterion is that the findings of science do not contradict one-another, or the observations. Logical inference is used to test this (see Popper) but science is not built up from some self-evident foundation. The whole thing could shift radically if a single law was shown to be false. (And this nearly happened recently with the putative discovery of faster-than-light neutrinos.) So in this way, the project of science cannot ever finish, it will always remain tentative. But this does not make it self-contradictory, nor does it refute logic.