h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Hi Lucinda,

Nice article! Circular reason is everywhere - I think you're quite right. I've heard it referred to as a "closed system" in philosophical circles: when a theory relies on nothing but elements of its own theory to support itself, often resting on one highly contentious premise (as in your bible example).

However, circular reasoning is a reason to be suspicious of an argument, not a reason to reject it out of hand. Descartes' famous "I think therefore I am" argument in which he attempts to prove his own existence (although at this stage he's not sure what "he" really is) is also a circular argument. He's trying to prove his own existence, yet the argument starts with "I", which is exactly what he's supposed to be proving!

"I" think therefore "I" am.

On other matters, I've been thinking of either writing an article (or, more likely) a university project on "how to win arguments" using philosophical techniques. I'm about to move house, so it'll be a medium term project rather than a short term one, but if you're (or anyone else who reads this) interesting in collaborating, that would be great!

Best wishes

Otto.

Aye - I base my world view on Pragmatism, which is a pretty tightly self-dependent principle. I like "closed system" as a name - it sums it up well, actually

I'll try not to write a thesis here, but I just recently finished a philosophy degree at university and just love this stuph.

Is circular reasoning a fallacy? Ironically (you'll see why in a moment), the answer is yes and no.

Take the most mostest fundamental law of logic, the Law of Non-Contraditcion. It states that no proposition ,p, can be both true and false at the same time. This is symbolized:

not (p and not-p) or ~(p and ~p).

That is the first law that all other laws of logic derive from, much the same way as '1 is a number' is one of the fundamental axioms of arithmetic (it is, you know). (The above irony, "...answer is yes and no", is because the idea is a true answer is never 'yes and no'.) An example would be:

The statement '2+2=4 and it is not the case that 2+2=4' is not true.

What does this have to do with circular reasoning, you ask. Well, the only proof for the Law of Non-Contradiction is... the Law od Non-Contradiction. Try it out: If the Law isn't true, then there is some proposition that is true and false at the same time; but no proposition can be true and false at the same time, as per the Law; therefore, the Law must be true.

It can seem like a lot to get your head around at first, but look at it another way. The alternative to accepting the Law (if you are really deperate to avoid any type of circularity) is to accept the position that e.g. 2+2=4 and 2+2 doesn't equal 4, basically undermining all of [wester/analytic] philosophy. And since the aim of avoiding circularity is a philosophical one, you would have basically rejected rational though in an effort to preserve rational thought. Which is, in a perverse way, a consistent philosophical position.

This last concept, the one of consistency, is the crux of the issue. Non-fallicious circularity is found in every good philosophical position, and that property is called 'consistency'. Admitting you just have to take on faith, as it were, that 1 is a number is no crime if it allows you to produce a system of arithmetic that precludes a proof that 1=2; in the same way, accepting the Law as a given is just needed and beneficial, and not to be counted as a strike against.

Thus, all sound mathematical systems like logic and aritmetic are closed systems; they have the necessary detriment of relying on basic principles within them, but the advantage of no internal corruption. To take it a step further, do some reasearch on meta-logic or on goedel's theorem which demonstrates the inclmpleteness of mathematic (the idea that some additional axiom will always have to be added on the outside as a presupposition to accept the truth of the system as a whole). A great lay discussion to this can be cfound in the final chapters of "What Is the Name of This Book?" by Raymond Smullyan, a former MIT professor.

Fallacious cirilarity, however, does abound. An example would be:

Jennifer is a hippie. All hippies wear outlandish clothes. And Jennifer wears outlandish clothes. Therefore, Jennifer is a hippie.

In a philosophy classrom, this would be correctly labelled as a circular argument because none of the statements in it have the esteemed status of the Law of Non-Cotradiction. Decartes' "Cotigo", or "I think therefore I am," breaks down (after a lot of rich analysis and the most faithful and charitable reading of his whole view) to, 'I exist and think, therefore I exist." That is also an example of circular reasoning.

Another guise circular reasoning can take is is an argument that commits the fallacy of 'begging the question'. This is where a premise in an argument that appeals to circular reasoning is implicit instead of explicit:

All hippies wear outlandish clothes. And Jennifer wears outlandish clothes. Therefore, Jennifer is a hippie.

Jennifer could just be an interesting dresser. The only way you could conclude from the premises what the argument concludes is if the arguer assumes the conclusion without telling us; and assuming the conclusion as an implicit premise to prove the conclusion is begginf the question.

The interesting thing about all of this is that the laws of reason, including the Law of Non-Contradiction, cannot be founded completely on themselves. Of course the Law isn't circular in a fllacious way, but it is non-fallaciously circular. And reason insists that circularity is a bad thing when it comes to reason; so part of our acceptance in the laws of reason adn reason itself must be an additional source. It may be that faith is indeed an essential part of being human at the most basic level... But faith in what?

I've seen some other fundamental laws of logic, that didn't have the law of non-contradiction in them - though I think which are the fundamental laws of logic depends on exactly which laws of logic you use (however, they all end up with the same results unless you're in some weird nonstandard logic). Anyway, non-contradiction is pretty basic yes, and yes its impossible to prove without assuming it in the first place. As a mathematician, I'm inclined to take it as an axiom and get on with life... there's a sense in which we dig back further and further into what we can try and prove, and at some point we really do hit the bedrock of rationality, and its simply not possible to get further back (at least it seems that way, but its probably impossible to prove a statement like that). A fair amount of the philosophy of mathematics I've seen seems to be trying to dig below the bedrock.

Incidentally, consistency isn't (as far as I'm aware) written into the axioms of arithmetic etc. Godel's 2nd incompleteness theorem essentially tells us that you cannot do that - you end up with an inconsistent system if you try. So we don't know that there is no internal corruption at all. It is an article of faith. To my knowledge, all of the consistency proofs of mathematics are about relative consistency - i.e. 'if the arithmetic of the natural numbers is consistent, then so is this thing'.

About what you had to say about Goedel:

Fisrt of all, I have to give a disclaimer that I am only a very amarute mathematician, and I only have a relatively cursory understanding of Goedel.

But what I meant to say was not that cosistency is axiomatically written into mathematics, but merely that mathematics were in point of fact consistent in virtue of the axioms it has.

"...but merely that mathematics were in point of fact consistent in virtue of the axioms it has."

Well, we don't really properly know that do we? There is no proof as far as I'm aware, and it doesn't seem that obvious that there cannot be some contradiction lurking out there amongst the infinite number of statements you could make about natural numbers.

Fair enough. If you can help with your knowledge of mathematics, please edit my entry appropriately so that the illustrations about math are accurate but still help as illustrations about the two types of logical circularity. I would appreciate the input in the math statementsa from a math buff. But I primarily wanted an entry that was accesible to veryone, so if you can try and balance that in...

I don't think I can edit your entry - as far as I'm aware only the author is allowed to. You're welcome to use any of what I've said in the forum if you want.

Natch. Thanks; if su gets ahold of it and cares, I'll work your stuff in an credit you.

There's a distinction you are missing between fallacy and circular logic. The example about Jennifer's clothes is not a circular argument, it's faulty logic. Correct usage of logic would state either:

"All Hippies wear outlandish clothes. Jennifer is a hippy. Therefore Jennifer's clothes are outlandish." or

"Only hippies wear outlandish clothes. Jennifer's clothes are outlandish. Therefor, Jennifer must be a hippie."

In proper logic, it's accepted that you must assume something to serve as a basis for proving something else. It's not possible to prove everything without assuming something - like the law of non-contradiction. That is not a case of circular logic, it's an assumption. Circular logic would be, in Jennifer's case:

"Jennifer wears outlandish clothes. Because Jennifer wears outlandish clothes, she must be a hippie. Since Jennifer, with her outlandish clothes, is a hippie, all hippies must dress outlandishly. Since hippies always dress outlandishly, and (as I have already shown), Jennifer is a hippie, whatever she is wearing today must be outlandish."

In any case, the hippie example has too many badly documented assumptions in it to fly, but the main point of circular logic is that you wind up claiming you have proved something when you're really just assuming it. If you state at the beginning that something is an assumption, and then use it to prove something else, that is not circular reasoning. It's just that you have proved your point is true in situations where your assumption is true.