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Comments on: Brave New Logic http://sharpener.johnband.org/2006/10/brave-new-logic/ Trying to make a point Fri, 25 Jan 2008 12:21:35 +0000 hourly 1 By: John Brissenden http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57734 Tue, 31 Oct 2006 20:40:43 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57734 Yes, well Larry this is all very clever, but does it take us any nearer solving the conundrum of your mum?

]]> By: Larry Teabag http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57729 Tue, 31 Oct 2006 11:22:08 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57729 NS – my fault, didn’t express myself at all clearly. Imagine this – a bottle of liquid called something medicinal and/or “natural” – sounding. It’s on sale in a chemist’s shop, and isn’t cheap. Somewhere on the bottle is an official (state-sanctioned) label which reads: “This product can be used in the treatment of lung-cancer.” Elsewhere on the packaging, in far smaller print, is written “Contents: 100% water.”

I’m sure water is used in the treatment of lung cancer

This is why the statement is true. However the intended implication, and the one which most people are likely to understand – that the product has some medicinal property in regard to lung-cancer – is false.

]]> By: Not Saussure http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57725 Mon, 30 Oct 2006 19:58:53 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57725 “Contents: 100% water. This product can be used in the treatment of lung-cancer”. Which of course it can, despite all the evidence saying that it can’t.

I may be missing the point, but I don’t see there’s a problem with that unless the label also tries to suggest that the treatment’s likely to have any effect. And, of course, I’m sure water is used in the treatment of lung cancer — washing down pills and so forth:

GLENDOWER

I can call spirits from the vasty deep.

HOTSPUR

Why, so can I, or so can any man;
But will they come when you do call for them?

]]> By: Larry Teabag http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57722 Mon, 30 Oct 2006 17:19:06 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57722 G. Tingey

Just to be clear, decidability is a separate issue, having to do with whether you could (in theory) program a computer to decide on the truth/falsity of a given statement.

And your two-sides of the card thing is a variation of the liar paradox (“this statement is false”) which I mentioned in the post.

]]> By: G. Tingey http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57720 Mon, 30 Oct 2006 16:59:11 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57720 And statement 2 should have finished “false” – careless with the cut-&-paste there.
Oops.

True / false / undecidable / undecided (?)
True If and Flase If – with differing values for If also as in ..If and only if, or if plus other comstraint – a bit like the diferences between necessary and sufficient conditions.
etc.
As I said, it can make your head hurt.

]]> By: Larry Teabag http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57711 Mon, 30 Oct 2006 09:02:23 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57711 Duff – are you suggesting that mathematical logic can develop without human endeavour?

G Tingey – What they are trying to say (I think) is a restatement of something like Godel’s theorem

Erm, no. It has been suggested that paraconsistent logic might be used to in relation to Gödel’s theorems, I don’t know how far anyone’s got with that. But the two are essentially different.

]]> By: G. Tingey http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57706 Mon, 30 Oct 2006 08:38:04 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57706 Erm, no.

Side 1 – 1: “The statement on the other side of this card is true”
Side 2 – 2: “The statement on the other side of this card is true”

Err …

Answer: The stements on this card are not dterminable (or decidable).

What they are trying to say (I think) is a restatement of something like Godel’s theorem (should be an umlaut in there, I know) …

Ther are undecidable propositions.
There are cases where a certain outcome cannot be arrived at.

It is important, oddly enough, but it CAN make your brain hurt.

]]> By: Doormat http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57705 Sun, 29 Oct 2006 23:01:52 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57705 For those who still have even a spark of curiosity in them (so, not Duff then) I can recommend Wikipedia for more info on paraconsistent logics. Although Larry’s link to New Labour political philosophy (possible a contradiction in terms) holds, I think, much promise of further study…

]]> By: David Duff http://sharpener.johnband.org/2006/10/brave-new-logic/#comment-57703 Sun, 29 Oct 2006 21:10:17 +0000 http://www.thesharpener.net/2006/10/29/brave-new-logic/#comment-57703 And there, in a Teabag, one might say, you have the difference between mathematical logic and human endeavours.

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