'When Are Relations Neither True Nor False? [Logic]

Prev: geometry precisely defining ellipsis and how infinity is in the midsection #427 Correcting Math
Next: Accounting for Governmental and Nonprofit Entities, 15th Edition Earl Wilson McGraw Hill Test bank is available at affordable prices. Email me at allsolutionmanuals11[at]gmail.com if you need to buy this. All emails will be answered ASAP.

From: Daryl McCullough on 25 Mar 2010 06:35

Newberry says...

>The sentence "if it rains then some roads are wet" describes a
>possible state of affairs. I can picture to myself what it means. I
>can even picture "if it rains then no roads are wet." It is still
>conceivable although very unlikely. "If it rains and does not rain
>then the roads are wet" does not describe any possible state of
>affairs. I cannot picture to myself what it expresses.

Well, this is something you need to work on. The "state of affairs"
associated with an implication A -> B is any situation in which A
is false or B is true. If A is always false, then A -> B describes
every state of affairs.

--
Daryl McCullough
Ithaca, NY

From: Daryl McCullough on 25 Mar 2010 06:37

Newberry says...

>In my logic the Liar paradox can be expressed as follows.
>
> ~(Ex)(Ey)(Pxy & Qy) (L)
>
>where Pxy means that x is a proof of y, Q is satisfied by only one y =
>m, and m is Goedel number of (L).

That's not the Liar sentence.

--
Daryl McCullough
Ithaca, NY

From: Daryl McCullough on 25 Mar 2010 06:38

Newberry says...

>If you take the position that there are truth value gaps then the Liar
>papradox is solvable in English.

What does it mean to be "solvable" and why do you want it to be solvable?

--
Daryl McCullough
Ithaca, NY

From: Daryl McCullough on 25 Mar 2010 06:49

Newberry says...

>Tarski's theorem does not apply to formal systems with gaps. I think
>it is preferable.

If you the way you express Tarski's theorem is like this, then truth
gaps don't change anything:

There is no formula T(x) such that if x is a Godel code of a true
sentence, then T(x) is true, and otherwise, ~T(x) is true.

Anyway, *why* is it preferable to have a formal system for which Tarki's
theorem does not apply? Preferable for what purpose?

--
Daryl McCullough
Ithaca, NY

From: Jesse F. Hughes on 25 Mar 2010 13:26

Newberry <newberryxy(a)gmail.com> writes:

> On Mar 24, 3:32 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
>> Newberry <newberr...(a)gmail.com> writes:
>> > Plus
>>
>> > (x)((x = x + 1) -> (x = x + 2))
>>
>> > does not look particularly meaningful to me.
>>
>> I don't believe you.
>
> Trust me.
>
>> You know what it means. It's perfectly clear
>> what it means. It means that whenever x = x + 1, then x = x + 2.[1]
>
> The sentence "if it rains then some roads are wet" describes a
> possible state of affairs. I can picture to myself what it means. I
> can even picture "if it rains then no roads are wet." It is still
> conceivable although very unlikely. "If it rains and does not rain
> then the roads are wet" does not describe any possible state of
> affairs. I cannot picture to myself what it expresses.

Is the statement "Honesty is a virtue" meaningful? What do you
picture when you think about that statement?

As usual, your claim that meaning involves picturing various states of
affairs is silliness. I can understand various theorems about, say,
infinite dimensional spaces. I daresay that I know those theorems are
meaningful, even though I cannot picture a space with more than three
dimensions.

Of course, as Daryl points out, it is very easy to "picture" what the
above sentence means. It means the same thing as

(Ax)( ~(x = x + 1) or (x = x + 2) ).

I see no problem understanding that sentence at all.

> The analytic sentences are rather odd. But even then given "all
> bachelors are unmarried" if you examine every bachelor you will find
> that he is umarried. Given "all married bachelors are unmarried
> bachelors" is just like "when it rains and does not rain ..." I cannot
> picture anything.
>
> Similaly I cannot picture (x)(x = x+1) -> (x = x+2) any better than I
> can picture anything being attributing to married bachelors.

As I said previously, I understand the meaning of that sentence and
can even immediately see that it is true, through the following
perfectly simple reasoning.

>> [1] In fact, this statement seems obviously true! Suppose
>> x = x + 1. Then we may substitute x + 1 for x in the right hand side
>> of the equation x = x + 1, thus:
>>
>> x = x + 1
>> = (x + 1) + 1
>> = x + 2.
>>
>> I see nothing the least bit fishy about this reasoning.

--
Jesse F. Hughes

"As you can see, I am unanimous in my opinion."
-- Anthony A. Aiya-Oba (Poeter/Philosopher)