"What is truth? said jesting Pilate; and would not stay for an answer."

Janus

That depends on whether you count it raining and not raining at different times at the same place or at different places at the same time as counterexamples to "it's raining or it's not raining". It's a matter of interpretation; is its both raining and not raining a counter-example under your interpretation? If not, then what do you take the formula to mean?

Banno

↪Janus

Meh. (p v ~p) is true for any proposition p regardless of spatiotemporal deportment.

Srap Tasmaner

↪Banno

All that's fine -- I think, I didn't check all that carefully -- but again look where you end up, contrasting

(1) Is P true?
(2) Is P possible?

Why are those constructions so similar, and why would it be so natural to contrast the truth of P with the possibility of P, the likelihood of P, and so on?

The intensional revolution in fact sweeps away truth along with possibility, necessity and the rest, and leaves a purely extensional model-theoretic semantics behind. ("True" turns out to be an incomplete symbol, completed as "true at W", which is in turn just defined as satisfaction, and everything is just shorthand for that.)

Which is just more evidence, in a screwy way, that this is the set of concepts truth belongs with -- which is a little surprising, since the stability of truth is nearly what defines the split between extensional and intensional contexts. If truth belongs with this stuff, something isn't what we thought it was.

(R v ~ R) is never untrue. time and place are irrelevant. — Banno

The way I was thinking about this: on each occasion when R v ~R is true, it's because R is true or because ~R is true. We additionally know that this covers all possible occasions, but what makes it true on each occasion is specifically one or specifically the other, not the additional fact that there are no occasions not covered by one disjunct or the other.

R v ~R doesn't need to know it's guaranteed to win in order to win; as far as it knows, it's just always lucky.

Banno

R v ~R doesn't need to know it's guaranteed to win in order to win; as far as it knows, it's just always lucky. — Srap Tasmaner

It can't be luck if whatever sentence we stick in (pv~p) gets us truth. It's structure, not correspondence.

Janus

↪Banno

Not if the "or" is thought of as exclusive, as in "it's either raining or it's not raining". Do you take the "or" to be exclusive, or do you think that if it is both raining and not raining, which it is probably doing most of the time on Earth, that that state of affairs satisfies the formula?

Banno

The intensional revolution in fact sweeps away truth along with possibility — Srap Tasmaner

I don't think so. Truth gets on quite satisfactorily in extensional circumstances.

Agent Smith

↪Janus

↪Banno

For "it is raining" (R) to be true, we have to go out and verify or, if you're Sherlock Holmes, you can infer it from wet shoes. The same goes for "it is not raining" (~R). [Correspondence check]

However, "it is raining or it is not raining" (R v ~ R) is true and doesn't require us to go out and verify anything at all. [No Correspondence check]

This has to mean something, oui?

Banno

Not if the "or" is thought of as exclusive — Janus

So you would have "it's raining or it's not raining" parsed as (r ≢~r).

That still get you a tautology,

+---+----+----------+
| R | ~R | R XOR ~R |
+---+----+----------+
| T | F  |     T    |
+---+----+----------+
| F | T  |     T    |
+---+----+----------+

and so it's true without regard to location. The contents of R are irrelevant. Hence what R coresponds to is irrelevant.

Banno

For "it is raining" (R) to be true, we have to go out and verify — Agent Smith

Nuh. It can rain without you noticing.

Agent Smith

Nuh. It can rain without you noticing. — Banno

:snicker: Think of a universe with only me in it.

Banno

↪Agent Smith

Don't fall to the idealist error of thinking truth is dependent on you. Down that path lies solipsism.

It could still rain without you noticing.

Perhaps in Spain, on the plain.

Janus

↪Banno

How can it be true (under my interpretation) regardless of location if it can be both raining and not raining at the same place at different times or at the same time at different places?

I agree with you that it's always true if the "or" is not considered as exclusive and as implying "either raining or not raining, but not both", but it should have been clear to you, if you were paying attention, that I already acknowledged that.

Also, why don't you save time by answering questions posed to you in plain English?

Banno

I agree with you that it's always true if the "or" is not considered as exclusive — Janus

It's just as true for XOR.

Agent Smith

Don't fall to the idealist error of thinking truth is dependent on you. Down that path lies solipsism.

It could still rain without you noticing.

Perhaps in Spain, on the plain. — Banno

Solid copy!

Janus

It's just as true for XOR. — Banno

What does that mean in English? If it means "raining or not raining, but not both" then it is not always true, but more likely always false, because it is mostly always both raining and not raining on Earth, depending on time and location. You'll need an argument to convince me otherwise; dogmatic pronouncements are not going to cut it, matey.

creativesoul

This seems to have the odd result that the sentence "it is raining or it is not raining" is true because it corresponds to anywhere. — Banno

Put that one in the schema...

Agent Smith

What about scientific theories? We can never check for their correspondence to reality as n number of them are consistent with observation and this is dealt with by appealing to principles like the novacula occami (simplicity) & beauty & elegance. In some sense [@A Christian Philosophy] they're innocent (true) until proven guilty (false).

Srap Tasmaner

It can't be luck if whatever sentence we stick in (pv~p) gets us truth. It's structure, not correspondence. — Banno

In the back of my mind I'm thinking of the intuitionist's rejection of p v ~p as an unqualified introduction rule. To introduce p v ~p, you have to have p in hand, or ~p in hand, and use the usual rule for or introduction. I simply allowed the introduction but applied the idea to truthmakers: one or the other of those will be what makes the disjunction true when it's true. The disjunction itself is a freebie, vouched for by whichever of the disjuncts is true. You're right of course that one or the other will always turn up, but we still get to say, on each occasion, here's what makes R v ~R true this time.

(Snipping the rest the past-my-bedtime speculation about truth. Probably shoddy stuff anyway.)

Banno

If it means "raining or not raining, but not both" then it is not always true, — Janus

Yeah, it is:

+---+----+----------+
| R | ~R | R XOR ~R |
+---+----+----------+
| T | F  |     T    |
+---+----+----------+
| F | T  |     T    |
+---+----+----------+

Janus

↪Banno

You "forgot" to include a column for "raining and not raining". :roll:

Banno

In the back of my mind I'm thinking of the intuitionist's rejection of p v ~p as an unqualified introduction rule. — Srap Tasmaner

Interesting. So we again need a trivalent logic, with (p v ~p) being neither true nor false, but this time in order to defend the correspondence theory of truth.

A marriage of correspondence and anti-realism.

Oh, the time in which we live!

Banno

↪Janus

What?

R: it's raining.

~R: It's not raining

XOR: exclusive OR

R XOR ~R: It's either raining, or not, but not both

T: true

A bunch of T's down a column: this is true regardless of whether it is raining or not raining.

Therefore,

If it means "raining or not raining, but not both" then it is not always true, — Janus

IS false.

Janus

↪Banno

Could it be both raining and not raining on Earth at any given time? Place is relative and the same goes for time. It can't be both raining and not raining right here, right? But what does "right here" mean? What if I am standing on the edge of a rain front and it is raining on the right half of my body but not the left. You need to get your focus away from your precious formulas and truth tables and open your mind up to the actuality. You can do it; it's not hard to understand.

Banno

↪Janus

:roll:

Janus

↪Banno

:cool: I'll take that as an admission that you cannot come up with a counter-argument.

Banno

↪Janus

You are not doing argument.

It corresponds to the fact that it is never, at the same place and time, both raining and not raining. — Janus

Could it be both raining and not raining on Earth at any given time? — Janus

Cheers. Bye.

Janus

You are not doing argument.

It corresponds to the fact that it is never, at the same place and time, both raining and not raining. — Janus

Could it be both raining and not raining on Earth at any given time? — Janus — Banno

Further admissions?

Of course I am "doing argument"; I am examining the actual and interpretive possibilities. It seems you think I have contradicted myself, but the first statement should be read as 'if the formula is true, then it corresponds to the fact that it is never, at the same place and time, both raining and not raining". But then I go on to question the meaning of 'place'. If 'place' means 'Earth' then obviously the formula is not true. Then I offered the example of standing on the edge of a storm front. So the truth of the formula rests on the meaning and scope of 'place'.

In any case, if the proposition 'it is either raining or not raining' is true then it corresponds to the fact that it is always and everywhere either raining or not raining, leaving aside all other considerations of time and location as well as whether it is actually true or not.

Likewise if the proposition "it cannot be both raining and not raining:is true, then it corresponds to the fact that it cannot ever be both raining and not raining, regardless of considerations of time and location and whether it actually is true or not.

If you think none of this constitutes a valid argument then you should be able to say why it is not, but you have made no attempt to directly address anything I've said. All I'm getting from you, as usual, are pompous statements with no accompanying explanation. It's a poor showing.

Banno

↪Janus

You were all over the place, and I pushed you too hard. Not very helpful either way.

Janus

You were all over the place, and I pushed you too hard. Not very helpful either way. — Banno

:rofl:

creativesoul

↪Banno

You're either right or not about those sentences that assert nothing.

"What is truth? said jesting Pilate; and would not stay for an answer."

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