[FOM] The unbearable ghastliness of EFQ, and sundry other matters arising from Harvey's last post

[Dennis E. Hamilton]

Applying baby logic here, I think there is something important missing in this conversation.  It has to do, in my case at least, with a temptation to make assertion or deduction of P -> Q signify anything in itself about Q (other than it be a proposition).

In particular, ~P |- P -> Q 

  says nothing about Q whatsoever under truth-value propositional semantics.

>From what I have seen here, the difficulty is with 

  P |- P v Q

which can be found disturbing for philosophical and other reasons.  Yet if truth-value semantics hold  (and excluded middle too) this is on safe ground and is used heavily in some renowned introductions to symbolic logic.  That it might not always be safe under particular tensions around what are accepted as propositions (and higher-order situations) seems to be at the heart of this, just as is ~~P |- P for some.

It seems to me the statement "from a contradiction follows anything" is a kind of sleight-of-hand that is a popular meme, yet at "contradiction" and "follows" I think the fingers have left the hand.  It is certainly the case that if a system is inconsistent, anything may be deduced.  If the contradiction is asserted by clever means, it is not the system that has failed.

 - Dennis

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Timothy Y. Chow
Sent: Friday, September 4, 2015 08:52
To: Foundations of Mathematics <fom at cs.nyu.edu>
Subject: Re: [FOM] The unbearable ghastliness of EFQ, and sundry other matters arising from Harvey's last post

A private email from an FOM member helped me understand this debate a bit 
better.

Consider:

A. From a contradiction follows anything.
B. The material conditional P => Q is true if P is false.

Does the disagreement boil down to whether there is any distinction 
between A and B?  As I understand it, Neil Tennant sees a distinction and 
says that Core Logic utilizes B but not A.  Harvey, perhaps, sees no 
important distinction between the two, or at least claims that actual 
mathematical practice does not observe a distinction?

Tim
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