Comments for Der Philosophstein

Comment on That’s just semantics! by imatfaal

imatfaal — Thu, 03 Jan 2013 17:56:03 +0000

I understand it may be necessary to avoid certain words, that shouldn’t be impossible; I’ll ensure I use none of them at all… bugger!

Silliness aside – I struggled to be precise in the initial comment and was back and forth deleting and amending, trying to get my meaning across; at this point I realised the benefit of the language you were explaining

Comment on That’s just semantics! by ydoaPs

ydoaPs — Wed, 02 Jan 2013 17:05:39 +0000

The only time the conditional is false is when the antecedent is true and the consequent is false, yes. When the antecedent is true in a true conditional, then the consequent must be true. The consequent, however, can be true for reasons completely unrelated to the antecedent, so it can be true with the antecedent being false and the conditional will still be true. I’ll talk about this more in the second post on semantics.

Now, you keep using the word (or variants of it) “necessary”. You should avoid that. It means something very specific and we won’t get to that for a long time. Other words you may want to avoid are “impossible”, “all”, and “none”.

Comment on That’s just semantics! by imatfaal

imatfaal — Wed, 02 Jan 2013 15:35:49 +0000

The conditional is false only if alpha is true and beta is false?

Can I long-windedly think of alpha ⊃ beta as – the truth of alpha necessarily implies truth of beta, but truth of beta implies nothing to the truth of alpha?

the biconditional however works in both directions alpha ≡ beta – truth of alpha implies beta, and truth of beta implies truth of alpha.

Is that right?

I realise that the whole point is to avoid the necessary ambiguities of everyday language – but I do want to get it straight in my head

Comment on There and Back Again: The long LONG road to Gödel by ydoaPs

ydoaPs — Tue, 04 Dec 2012 16:53:25 +0000

That was a good question.

Comment on There and Back Again: The long LONG road to Gödel by ydoaPs

ydoaPs — Tue, 04 Dec 2012 16:53:14 +0000

α~ is indeed not well formed. That is a complete list of well formed formula. They are, however, not just non-compound formulas. ‘α’ and ‘β’ can be ANY wffs. So, things like ‘~(α⊃β)’ are well-formed.

Comment on There and Back Again: The long LONG road to Gödel by imatfaal

imatfaal — Tue, 04 Dec 2012 15:42:58 +0000

Excellent – understood so far. Can I take it that α~ by itself is meaningless (or should that be badly-formed)? ie that the list of six formations of simple (ie non-compound) wffs is complete.

Comment on Assessing Interest by imatfaal

imatfaal — Fri, 30 Nov 2012 13:21:54 +0000

yes – my knowledge of godel (like a lot of neteratti) is limited to Hofstadter’s GEB so would love to see a more formal academic approach.

Comment on Assessing Interest by ydoaPs

ydoaPs — Wed, 28 Nov 2012 14:28:02 +0000

Yeah, the idea is a long series of short-ish posts.

Comment on Assessing Interest by ajb

ajb — Wed, 28 Nov 2012 09:55:33 +0000

I say yes, though try to break everything down so that each post is not too long.

Comment on Assessing Interest by ydoaPs

ydoaPs — Wed, 28 Nov 2012 02:41:26 +0000

It will be a very long series, but the end result should be worth the read.