unforum

[dusty2229]

Sorry Brevity my bad. You do in fact have a 67th card. That'll teach me not to jump in till i've checked me facts

[SteveC]

[oliverkeers13]

No, i disagree. As with Elucidate, if the area in discussion is your speciality, then it is easy, we happen to have people who know about philosophy, but not about the grey blobs.

[SteveC]

It took me no more than a minute to trace it to Wittgenstein using Google. I'm no philsopher. I'm at a loss as to how to search for the contour diagram, my only suggestion for that is to wander from department to department in a big university and hope someone recognises the diagram (I'd personally go from engineering to astrophysics, then onto microbiology and then possibly geography for good measure. Failing that i'd just put it on the Union bar wall and hope someone noticed it

[tanner]

now ive rechecked

looks like ((not p) and q) -- ie p is false and q is true

but what the answer to the card is -- i dont know

[Leeravitz]

Just to 'elucidate' a bit further (not that this gives an answer...still...):

When Wittgenstein was discussing the 'Law of Contradiction', as far as I understand it, he was making a mathematical and logical point relative to the traditional Aristotelian syllogism, which ordinarily is held to state if 'A and B are true, then Z is true.' The immortal Aristotelian rendering of the theory is, of course,: All men are mortal; Socrates is a man; Socrates is mortal (or variation thereof). This, simply put, produces a so - called 'Middle Term' ('All men') which establishes a connection to a Predicate ('are mortal'). In the second part of the syllogism, the subject ('Socrates') is established as belonging to the category of the 'middle term'. Therefore, we can deduce whether, by the law of logical necessity, it makes sense to claim the subject further as (literally) being subject to the predicate. If it does, then this is a well - formed, or truthful, syllogism, but there are examples of false logic as well, which Aristotle faithfully codified.

What Wittengenstein was interested in was pointing out that the 'logical necessity' of such an operation was not exactly *logical* at all - it was, in his opinion, entirely arbitrary, depending upon the conventionalities of symbolisation that were taken as being valid by auditors in a given situation. He gives an interesting (if slighly bizarre) example to illustrate this (not in the Tractatus) whereby a student is asked by a teacher to complete the numerical progression '2, 4, 6, 8...etc' up to '1000' and then continue on. At the '1000' point, the student starts to relate the progression '1004, 1008, 1012,' and the teacher is baffled. But all that is happening is that the student is applying a different rule of progression to that of the teacher - once the '1000' mark is reached, he adds four every time rather than two. This is not 'logical' only if we assert that, for some reason, 2 must be added every time for the progression to make sense. As Wittgenstein did not hold that such a progression was ineluctable in any way, then the student's progression can be held to be just as logical as the teacher's!

This is why Wittengenstein was interested in the 'Law of Contradiction'. The Law suggests that, if A and B are true, Z *must* be true, and if they aren't, then it won't be. But Wittgenstein saw tautology in this - which is to say that the syllogism only serves to confirm itself within its own system of reference. Because it establishes A and B as necessary givens (axioms, if you like) and it establishes a given principle of logical progression, then the syllogism cannot fail to be proven. But asking why any of these usages are accepted as being 'true' in the first place is an entirely different question.

Wittgenstein dicusses 'the Law of Contradiction', syllogistic tatutology etc. most heavily in Section 6 of the Tractatus - To take a brief look at his notation (which, I have to confess, more mathematically inclined peeps than me, should really set to work on):

'In order to recognize an expression as a tautology, in cases where no generality-sign occurs in it, one can employ the following intuitive method: instead of 'p', 'q', 'r', etc. I write 'TpF', 'TqF', 'TrF', etc. Truth-combinations I express by means of brackets, e.g. and I use lines to express the correlation of the truth or falsity of the whole proposition with the truth-combinations of its truth-arguments...'

'p', 'q', 'r' is Wittgensteinian standard notation, relating back to syllogistic principles. It's just another variation on 'Middle Term', 'Subject', 'Predicate' relations i.e. if P and q are true, then R is also true. What Wittgenstein talks about above is the problem of tautology to which I've just alluded. 'TpF', 'Tqf' etc. is, therefore, the form used when Wittengenstein is trying to demonstrate the tautological (self - referential) qualities of a syllogistic system. 'Truth - combinations' means reference to how a certain conclusion follows from initial axioms ('if P and q are true, then R is also true'), and the 'truth and falsity of the whole proposition' is whether or not that conclusion syllogistically 'makes sense' in relation to the earlier parameters established for the syllogism.

What Wittgenstein is demonstrating graphically is how our logical thinking applies this reasoning.

But I'll have to give some more thought to the actual puzzle!

[Leeravitz]

I have to admit that I'm not really certain how to apply the notation exactly (which'd help, surely!), but it does look like something tautological is being got it - something like a graphical representation of the theory that if proposition 'Tpf' is either false or true, and proposition 'Tqf' is either false or true, then, in all scenarios, an equivalence will be set up whereby what is true must also be false, therefore, tautological. In truth, that sounds pretty illogical even to me, but that may be the point of the exercise: Wittgenstein was trying to make points about the illogicality of our thinking processes. So, it's a diagram of an anti - syllogism.

[erekose]

Just thinking, if this diagram actually represents an argument in formal logic, as seems to be the case, is there anything stopping it from being a fallacy (eg. an undistributed middle term).
Not that I have anything but the most basic understanding of formal logic.

[oliverkeers13]

Just another Leeravitz essay!

[Leeravitz]

I take the point, but when you're dealing with Wittgenstein, it's not that easy to boil it all down to a quick soundbite

[tanner]

never did like Wittgenstein -- why did he invent such an ugly notation instead of using the propositional calculus?

[firefox]

i wonder how many more cards will pop up. And just exactly how this pre-wave wave system will work.

edit: its late now, will check this obscure notation later, so do we have a solve?

[BrianEnigma]

Forgive me if this is a little off-topic. For those of us who are digital engineers and not philosophers, does anyone have pointers to online resources that will help us understand the notation on this card. It looks like a really pretty diagram, but people are somehow extracting boolean algebra from it? I understand the latter, perhaps a little too well, but not the former.

[tanner]

[madam o'brien]

The card just asks for a proposition, I don't think it is looking for a logical rule or principle, just simple proposition i.e. p and ~q

My way of reading the diagram is, for example, if p is True and q is False follow the lines starting from the T for p and the F for q i.e. from TpF and TqF in this diagram this leads first to T then to F. The truth tables for this are