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Re: Is logic "purely" formal?

Hi Smith.

David Stove’s contention that “almost every logical truth which anyone knows, or could know, is either not purely formal, or is singular or of low generality” is itself a claim to formality and generality, and therefore self-contradictory and surely false – for a start. Behind that is a mass of misrepresentations of logic and fake examples.

Let us consider the example, given by Bill Briggs: “in which formal transposition fails, let p = “Baby cries” and q = “we beat him”, thus “If p then q” = “If Baby cries then we beat him”. But then by transposition, not-q = “We do not beat Baby”, not-p = “he does not cry”, thus “If not-q then not-p” = “If we do not beat Baby then he does not cry,” which is obviously false.”

Well, the conclusion is false here because the premise is false, not because the inference process is false. “If Baby cries then we beat him”? 1) Is this a generality? Who is “we”, the whole world or a certain family or some families? 2) Is this a real if-then statement? It cannot be, because “we beat him” is a volitional act, so logically it cannot be an inevitable consequence of “baby cries” but at best a probable consequence. That is, at best, “If Baby cries then we are likely to beat him”. So, this is not a true example of a formal and general if-then statement, nor therefore a correct example of if-then contraposition. The example given is, thus, fallacious nonsense.

Furthermore, the contraposite there presented is misleading. The real contraposite of “If Baby cries then we beat him” is not “If we do not beat Baby then he does not cry,” but “If we did not beat Baby it can be assumed that he did not cry,” i.e. “if we did not beat him it is because he did not cry.” In cases like this, when dealing with human actions and reactions, I would recommend use of the form “when-then” rather than “if-then”, i.e. with natural (de re) conditionals rather than logical (de dicta) conditionals (see my book Future Logic (part 4) for a study of de re conditioning: http://www.thelogician.net/FUTURE-LOGIC/De-Re-Conditioning-IV.htm.

It is fashionable to attack logic, but such attacks are all illogical bunk.

Re: Is logic "purely" formal?

Hi Avi, thanks. I had a feeling there was something fishy about it, but couldn't put my finger on where the error was.

Avi Sion
Hi Smith.
Furthermore, the contraposite there presented is misleading. The real contraposite of “If Baby cries then we beat him” is not “If we do not beat Baby then he does not cry,” but “If we did not beat Baby it can be assumed that he did not cry,” i.e. “if we did not beat him it is because he did not cry.”

Right. In this case the 'if then' is being used in the sense of causality, so the proposition could be expressed as 'baby crying causes us to beat him' in which case the contrapositive would be 'not beating baby "causes" him to not cry'. It doesn't mean that he may not be crying for other reasons, only insofar as 'we are not beating him'.

To be fair to Stove, I don't think he was attacking logic, at least, I assume he wasn't if he's written a book called 'The Rationality of Induction' (although I haven't read it). But then I wonder what his point is. It seems trivial to say that there are restrictions on the value a variable can take, but that doesn't make logic any less formal, any more than the need to restrict values in some mathematical formula makes maths 'informal'.

Anyway, I'm happy to have found your site.

Re: Is logic "purely" formal?

Hi Smith, thanks.

I haven't read Stove's'The Rationality of Induction', so I do not know what he advocates in it. I ought to read it, but I have a pile of books I still want to read waiting for me.

If you're interested in Induction, I strongly recommend my book 'Hume's Problems with Induction', which should inoculate anyone against fallacious claims regarding this subject.

You can read it online here: http://www.thelogician.net/LOGICAL-and-SPIRITUAL-REFLECTIONS/Hume/Hume-Problems-with-Induction-A.htm. Or you can buy it at amazon.com or at lulu.com in softcover or e-book form.

If you leave your e-mail address at www.thelogician.net, I will add you on to my mailing list for future announcements.