Re: Curry's paradox - (Google=Google?)

From: Sam Hill (dontwrite_at_never.com)
Date: 11/19/04 

Date: Fri, 19 Nov 2004 12:10:15 GMT

Immortalist,

As they say back home, "That don't make no sense."
Please define the antecedent of 3.

For all conditionals we assume the number of conditions, which is a grave
mistake.

3. False , then what? Open sesson?

As I have said, "Logic is a wretched thing."
Sam Hill

"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:SMWdnXCXr7SlHwDcRVn-jg@comcast.com...
> Curry's paradox is negation-free; it may be generated irrespective of
> one's
> theory of negation. An intuitive version of the paradox runs as follows.
>
> Consider the following list of sentences, named 'The List':
>
> 1. Tasmanian devils have strong jaws.
>
> 2. The second sentence on The List is circular.
>
> 3. If the third sentence on The List is true, then every sentence is
> true.
>
> 4. The List comprises exactly four sentences.
>
> Although The List itself is not paradoxical, the third sentence (a
> conditional)
> is. Is it true? Well, suppose, for conditional proof, that its antecedent
> is
> true. Then
>
> the third sentence of The List is true
>
> is true. By substitution, it follows that
>
> If the third sentence of The List is true, then every sentence is true
>
> is true. But, then, Modus Ponens on the above two sentences yields that
>
> every sentence is true
>
> is true. So, by conditional proof, we conclude that
>
> If the third sentence of The List is true, then every sentence is true
>
> is true. By substitution, it follows that
>
> the third sentence of The List is true
>
> is true. But, now, by Modus Ponens on the above two sentences we get that
>
> every sentence is true
>
> is true. By naive truth theory we disquote (or, in this case, dis-display,
> as it
> were) to conclude: Every sentence is true! So goes (one version of)
> Curry's
> paradox.
>
> http://plato.stanford.edu/entries/curry-paradox/
> http://plato.stanford.edu/entries/russell-paradox/
>
>

Relevant Pages

  • Re: Currys paradox - (Google=Google?)
    ... > For all conditionals we assume the number of conditions, ... Well, suppose, for conditional proof, that its antecedent ... >> If the third sentence of The List is true, ... But, now, by Modus Ponens on the above two sentences we get that ...
    (sci.logic)
  • Re: When does p imply q (redux)?
    ... "Sextus Empiricus refers three times to debate on ... four views which had been held about the nature of conditionals. ... For he maintains it will always begin with the false antecedent ... "Atomic elements of things do not exist" and end with the true ...
    (sci.logic)