‘Where’s Wally?’, The Value of Circular Arguments and the Münchhausen Trilemma

The Munchhausen trilemma poses a pickle for philosophers, especially those who fancy knowing something at some point. A brief examination of Wikipedia alone shows the catch-22. It says that, to know if knowledge is true, you must provide a proof. However, this leaves three options which are not satisfying. I will show why these options are not appealing, but then why circular arguments do have a use in understanding some key concepts and axioms. If you have somewhere to be[1] you can cut to the chase and go to the Where’s Wally? section straight away.

A well-rounded argument

First, you might use a circular argument. For example:

The Bible is the source of all moral truth

Proposition: The Bible is the source of all morality.

Question: How can I trust the Bible?

Answer: The Bible is inspired by an omniscient God

Question: How can I know the Bible is inspired by an omnipotent God?

Answer: Ah, it says so in the Bible.

While this exchange may make us feel more certain the Bible is not self-contradictory, it does not make us confident that the proposition is true, as it is only true if it is true. From a position of uncertainty this is not very helpful, as it does not provide any evidence or new argument to persuade you. Further, it is easy to construct a similar argument about the opposite, or contradictory, statement. [2]

The Bible is not the source of all moral truth

Proposition: The Bible is not the source of all morality

Question: Why is this the case?

Answer: I know there are non-Biblical moral truths or that there is no moral truth

Question: why is Q true?

Answer: Of course, there are non-Biblical moral truths or no moral truth, as the Bible is not the course of all morality

At this point, the title of the essay appears a little pointless, but first on the other parts of the trilemma. If we don’t want to use a circular argument, we might use a set of axioms to prove it.

Don’t worry – all my opinions are axiomatic!

However, if we want to pick the ‘right’ axioms, surely, we will need to show they are the right ones or use an argument? If, for example, in maths chose random axioms without careful though we might find contradictions everywhere. Maybe we say that if b=ac, b/a = c (e.g. 4 = 2*2, 4/2 =2). Careful consideration makes us realise this does not hold if a=0, as then, for example.  0=0*1=0*2. Therefore 0/0 = 1 = 2. There is the further issue that we may feel uncomfortable with axioms anyway (get used to them!), that they are just ‘assumptions’ (maybe not!).

Turtles all the way down…

The final option is the ‘infinite regress’, that we prove each proposition with a previous proposition and the one before with another proposition. Unfortunately, even if this made sense humans might struggle with the number of steps. Also, one wonders what one could do with such a proof.

E.g. Let A(N) mean the proposition A(N) proves A(N-1).

We could get with an infinite regress, with A(1) – meaning the statement A is true – as our starting point.

A(1) <- A(2) <- A(3) ………………

But just as easily could get:

A’(1) <- A’(2) <- A’(3) …………

All cats are red

An example ‘proof’ might be

Proposition: ‘All cats are red’ is true

Question: Why?

Answer: Because ‘all cats are red and all dogs are red’ is true

Q: why?

A: Because ‘all cats and all dogs and all fish are red’ is true

Q: Why…….

Yet the same argument could be used with A’ instead of A. Nevertheless, each statement follows from the previous. One might point out that my argument is contradictory here, as I assume that it is watertight – while questioning if watertight proofs exist – and a whole host of assumptions. This is ‘true’, yet this is not meant to show the necessary truth of the arguments which deny the ability to prove a statement, just the difficulties implied if many things we want to be true are true, such as mathematics or logic, as these arguments do work of logic and mathematics hold.

Where’s Wally?

Don’t look for Wally just yet!

In ‘Where’s Wally?’ you have to find Wally amongst a very crowded picture. Yet if I told you to look again where the circle is, it is obvious where Wally is. While he was in your picture all along and was in front of your eyes, it is only when you see him that you know he is there – despite the fact that he was there all along (see picture below). Similarly, we now see the value of a circular argument. We say that an axiom is true, and having said it, we know it is true, just as when I say where Wally is it is obvious he is there. However, the clutter of everyday experience and thought can clutter our conscious mind from seeing what is true from experience, similar to how the clutter on the beach obscured where Wally was – even though he was in my vision all along. This understanding is undeniable insofar as it is a description and realisation of what you are currently experiencing but was shrouded in plain sight.

A revelation: green is green. 

Perhaps one of the simplest examples is for you to look at something, say the wall. Note its colour: you cannot deny the truth, say of the greenness, which you are experiencing – even though you might deny the attribution of the greenness as coming from an external wall through photons into a retina and a brain. The greenness in your experience cannot be denied. Yet you were probably not consciously thinking before this ‘hmmm, greenness as a concept is necessarily true and is there’. Awareness of this was submerged by ‘what is for lunch today’, or ‘this essay took up this much of my time to tell me things can and are green!’. This is a particularly obvious case to get us started.

Lost in thought…

Another example, today I had the thought: ‘I perceive my thoughts to be spatially located, similar to that I perceive pain to be spatially located’. I was not consciously aware of this until I said it, yet it was apparent as soon as I thought it that, indeed, I did not feel my thoughts were inside that wall, or my foot, but actually within my head! (And at the very least, they felt spatially located and I could locate where they were not, i.e. not in my foot, or your head). Below Wally is circled! Now he is pointed out to you, it is obvious that he is there.

An ‘I’ for an ‘I’

I will not go into greater detail here, but in experience there also seems to be a concept of an ‘I’ and a ‘not I’ woven into it. This may be so essential to our experience, or at least to our thinking, acknowledging an ‘I’ is near inescapable in English. I feel present in a certain space and have control over it, in contrast to what I move through which my effects and control over are completely different. I.e. my conscious self is confined in some way, and thus I interact with things which I do not experience as my conscious self.

In a dream for example, I interact with things which are ‘not-I’. This means my conscious self does not experience them in the same way as it experiences its vision, temporal and spatial position. This is the case even if the same brain or body might be producing the dream!

I am not denying the possibility one might not experience an ‘I’ in certain circumstances. This is because we might be looking at a different Where’s Wally? picture. For example, it is conceivable that a hermit who has spent their entire life training in meditation to lose the sense of an ‘I’ might have a fundamentally different experience  than me.

Alas, there is a catch. There is no guarantee that there are useful axioms relating to what we want to prove. The Trilemma at least holds when double-guessing where to look as we make merely hopeful estimates that axioms will be related to what we want to know. Further, it is difficult to know if you have successfully found ‘Wally’ [an a priori or self-evidently true axiom]. In the picture above I circled something which merely looked like Wally. In fact, to slightly stretch the analogy too far, I don’t know where Wally [the axioms I should look for] is at all. I read philosophy despite the Trilemma in the hope someone will point Wally out to me!

Wally Regained

In my melodrama and dubious extended metaphors, I slightly fibbed. I did actually find the Wally in the picture, now correctly circled. As the picture is slightly grainy, below is a link to the actual image. 


Optional extra: Arghhh – but what about dreams!?

The existence of dreams provides a potential criticism of this which runs like:

Q: In dreams I think certain things are true which aren’t, couldn’t this apply to real life?

A: Uhm…….

Q: I mean, I seem to be certain of all kind of whacky things in a dream, such as I might have superpowers, or have the ability to read people’s mind. If I did what you said, wouldn’t I conclude the dream-world is true for some dreams?

The distinction here is twofold. First, I am convinced that the nature of my perception in dreams is different to that I have while awake. Thus, what we might know when awake could be totally different to what we could know in a dream. For example, my thinking and thoughts in the dreams remember being in is definitely less sharp.

Secondly – but less importantly – there is an important way in which the dream is true and exists, and we don’t know enough about what consciousness and reality is to deny what the dream self does. Maybe I live a double life, both equally valid? 


[1] Or perhaps just know a priori that the Münchhausen Trilemma is a problem!

[2] In fact, we can do this more generally. If a proposition P->A, and A->P we get: if P’ is true then A’ is true, i.e. P’->A’ as if A is true then both P’ and P would be true. And if A’ is true that implies P’ is true, as if P were true that would imply A not A’ were true. Therefore for every circular argument of this form there is one which proves the contrary.

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