[EM] Richard's frontrunners example

[MIKE OSSIPOFF]

>MIKE OSSIPOFF wrote:
>
>>Wouldn't it
>>make much more sense to just say that, since water can't talk, then
>>the statement that you're a banana if water can talk isn't saying
>>you're a banana? Can it be true or false to not say that you're a
>>banana? The statement would be true if it said that you aren't a banana.
>>But it doesn't. It merely doesn't say that you are one.
>
>The statement "I am a banana or I am not" is true. The statement "1+1=2"
>is true. Such statements are tautologies, and tell us nothing we didn't
>already know. They are still true. They are probably the most
>
>We even use this in normal speech. "If he's a lawyer, then I'm the
>Pope's second cousin". "If Blackpool win, I'll eat my hat". Both true if
>he isn't a lawyer, and blackpool doesn't win. (both probably false if
>they do).

Now I accept that it does seem that (not A) implies (if A, then B).
When A isn't true, I've heard people say things like "If A, then
I'm a monkey's uncle!". I had no idea that it's literally true.

>
>
>>Now we're talking about conventions of logicians & mathematicians.
>>But conventions aren't the same as facts.
>
>If you say Pij, then you're using mathematical terminology.

Using terminology and accepting an assumption that (as I believed at
the time) is false seem very different things.

>
>If you say Pt|ij, as Richard did, then you're using mathematical
>terminology for conditional probabilities, and as such have to be using
>the mathematical definition of 'if'.
>
>If you use large numbers of such symbols, and then go on to talk about
>differentials and worse, the probability that you're talking in
>mathspeak is pretty darn close to one.

Adopting and believing a definition that says that something is true
that (as I believed at the time) is actually false, seems like more
than just using mathematical language. In that case, I'd rather make
an exception and not use that particular piece of mathematical language,
a definition of "if" that implies something that is (as I then believed)
false.

I still haven't heard anyone actually say what the mathematical
definiton of "if" is. Will it be in a definition of mathematics?
Won't someone tell me what it is?

Mike Ossipoff



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