Ayer on Frege and Russell: Section 2

[gorgolyt]

brb, apparently there's a video of a drunk bear on a tricycle

[TheDavid2222]

I really was never very good at mathematics. I love continental philosophy, but I might not be too talented when it comes to analytic philosophy, or any philosophy involving an exceptional amount of mathematics. I guess it will just be an arduous undertaking for me. All I can really do is try not to get too discouraged. Anybody else share my disposition?

[beethovensworld]

@TheDavid2222 That would depend on what you define as "not very good at mathematics". If you are referring to agility in mental calculations (which I think you are), then as with any technical skill, it can be improved via arduous practice. And if you are referring to grasping of mathematical notation and concepts, then that too, through good explanation of concepts and practice, can be improved. One insight that made it easier for me to understand mathematical concepts (including those...

[beethovensworld]

of logic) is that mathematics is a symbolic based system that makes use of linguistic statements and transforms them into a sort of short hand, if you will. Logic is an indispensable tool or system of analysis that makes it easy to distinguish valid and invalid arguments from its constituent premises. And nowadays, it is more necessary than it has ever been! Best of luck in conquering your mathematical demons.

[philokvetch65]

Why is there a conspicuous cut/gap omission at a crucial point in this video at 5:25 , when Ayer seems about to state that "Frege's answer...(to Russell's challenge) also...." (and I assume he was to about to say), "....also was flawed" ??? Why was this crucial point omitted!!! These things happen so consistently in web media when it comes to any formidable challenge to math based logic!!! Russell finally admitted Hume's great argument against math based logic was never convincingly refuted.

[xpaderom]

Hi flame0430. Thanks so much for posting all of these! I thought you'd like to know that there are several gaps--I mean, places where the text is cut off and/or garbled--in this part 2. At least, that's what I get when I view it. If others are having the same problem, perhaps you could repost it?

[German1184]

5:20

Ayer: …Russell’s objection. However, it was show soon after Frege’s death by a Polish logician, Lesniewski, that Frege’s answer was untenable, a fact which may have been suspected by Frege himself, since he never recovered from Russell’s blow. After publication of Grundgesetze, as you said yourself earlier, he never wrote the third volume.

Magge: It must have seemed to him that his life’s work had been demolished.

[dekekyo]

please do not adjust your (infinite) set!

[supertoouber]

Interesting however the Ayer's position regarding Frege is no longer very popular.

[shack0001]

fascinating, thanks for posting

[theinternetscholar]

haha that always happens to me . . . i think i've thought up some novel idea, and then i research it and i realize that some famous guy or gal thought it up years ago :P

[deanshotokan]

At 4:29 I want to know what Frege's paradox was, but Ayer is mumbling like crazy. Can anyone clarify this for me?

[TheConsumption]

It's known as Russell's paradox and it's mean to show that the fifth axiom of Frege's set theory is inconsistent.

Axiom V states (roughly) that for every concept you can think up, there is an extension of that concept (a set). So if you have a concept fish, there will be an extension of that concept (the set of all fish) of which all and only fish are members.

[TheConsumption]

. Similarly there is a set of all non-fish containing all and only the things which are not fish (note that the set of all non-fish itself will be a member of this set since it is not a fish). Frege thinks that this works for all concepts. Russell shows this axiom to be inconsistent by taking the example of the set of all sets which are not members of themselves (say we call this set X). If something is to be a member of X, it must not be a member of itself.

[TheConsumption]

. If we ask of X if it is a member of itself, then it turns out that, if X is a member of itself, then it is not a member of itself and, if X is not a member of itself, then X is a member of itself. That is, X is a member of itself if and only if it is not a member of itself; which is a contradiction. Thus it looks like Frege is buggered.

Hope that helps. If not, you'll find loads of info by searching for "Russell's paradox".

[Pforstaffer]

it seems pretty easy

[bucles2000]

@TheConsumption what about the concept the set of all set...is it a set?...if it is...has an extension or a new set?

[ReduxRex]

@bucles2000

No.  The set of all set doesn't exist. The best formulation you can achieve is: All that exists stands in some reference to all else that exists.

Every set negation MUST imply some object.

[ExMachine]

Actually its not that Ayer was mumbling, the recording skips at that point (although he does seem less sprightly than his appearance discussing logical positivism).

[siddhaam]

He says something like: "Epimenides the Cretan who says that all Cretans are liars"; this is something like the form of Russell's paradox, which is well explained by theconsumption.

[AreYouKiddinMelol]

A drunk bear on a tricycle gets 1 million views and this gets 300.

[ORAKAR]

Haha! Quite!