Freethought & Rationalism Archive

Witt · 06-04-2003, 01:20 PM

John:

How about :

A statement is deemed to TRUE if it is considered to accurately convey a state of affairs.

A statement is deemed to FALSE if it is considered to completely contrary to a state of affairs.

Rather than the Boolean 1 and 0, this could be represented by 1 and -1 with 0 as a neutral value (maybe caused by irrelevance or uncertainty). This is not to say that truth has to be binary!

A & B = 2
~A & ~B = -2
-----------------

Some interesting three valued logics have been developed eg: Lukasiewicz (1920), Kleene (1952), but they deny the validity of p v ~p and ~(p & ~p) etc.

Reichenbach(1944) suggested that a three valued logic would provide a solution to some problems raised in quantum mechanics.

The 'middle' value might represent Godels' undecidable !?

IMO, your proposal also denies the law of excluded middle.

p v ~p
1 1 -1
0 0 0
-1 1 1

I think odd-numered logics are more awkward than those with 2^n values, but, perhaps there are suitable interpretations.

Witt

Witt · 06-04-2003, 02:03 PM

quote:
--------------------------------------------------------------------------------
Consider the statement, 'My car is blue' and let's assume that it is in fact true.
--------------------------------------------------------------------------------

SlateGreySky:
But what you point to here as a "logical truth" (i.e. that the car is either blue or not blue) just seems to be the law of non-contradiction, which would be true regardless of any factual truth or falsehood.

Yes, (p v ~p) is the law of excluded middle and ~(p & ~p) is the law of non-contradiction, and they are equivalent.

(i.e. that the car is either blue or not blue), is an instance of the law of excluded middle.

Witt: My car is blue or My car is not blue, is logically true but not factually true, i.e. there cannot be a situation that confirms 'My car is blue or My car is not blue'.

SlateGreySky:
I disagree. I would say (especially if you agree to phrase the above as "it is either the case that my car is blue or it is not the case that my car is blue") that every logically possible state of affairs confirms "it is either the case that my car is blue or it is not the case that my car is blue." That is just to say that the law of non-contradiction applies universally, right?

Right. (and your phrasing is better)

quote:
--------------------------------------------------------------------------------
We cannot 'see' that, My car is not red.
--------------------------------------------------------------------------------

SlateGreySky:
Of course we can! If it's blue, we see that it's not red.

Not so. We can only see, ie. sense, what is presented by the existent state of affairs.
Its blueness is shown and its non-redness is inferred.

We realize that it is not red by reasoning and assuming other premises, eg. no object can be two different colors at the same time, etc.

quote:
--------------------------------------------------------------------------------
There are no factual necessities at all.
--------------------------------------------------------------------------------

What about 1=1? That seems to me to be a factual necessity, in that it is factually true in all possible worlds that 1=1.

That it is true in, all possible domains or true in all possible worlds, is what makes it a logical truth.

There is no empirical situation that contains the number 1.
There is no place in the world where the number 1 could be found.

quote:
--------------------------------------------------------------------------------
If p is factually true or factually false, []p is contradictory. I.e. material truths are not theorems, rather, they happen to be the case.
--------------------------------------------------------------------------------

SlateGreySky:
Is this just the assertion that there are no such things as necessary truths?

No. It is the assertion that there are no such things as necessary facts.

SlateGreySky:
Sorry to try and open so many threads here . . . I just find your "multivalent logic" very worthy of discussion. Hopefully somebody has the time to talk about at least one of these issues . . .

Philosophy demands many.. questions, threads, etc., imo.

Witt

SlateGreySky · 06-04-2003, 02:38 PM

Quote:

Its blueness is shown and its non-redness is inferred.

It seems to me that one property (albeit a Cambridge property) of blueness is non-redness. That being the case, we don't infer (or even deduce) that blueness is non-red; we see, in seeing blueness, non-redness (one type of it, anyway).

Quote:

That it is true in, all possible domains or true in all possible worlds, is what makes it a logical truth.

So "logical truth" just means "necessary truth," it seems: necessary truths are just truths that are true in all possible worlds. Once again, I don't see the distinction between your "logical truth" and what most contemporary metaphysicians would call "necessary truth."

Quote:

There is no empirical situation that contains the number 1.

Anytime someone uses arithmetic involving the number 1, that's an empirical situation that contains the number 1.

Quote:

There is no place in the world where the number 1 could be found.

If you mean that the number 1 does not present itself for sensory perception, then of course that's right; numbers are abstract objects, but that doesn't mean they don't exist, just like sets.

What do you think?

Witt · 06-04-2003, 03:14 PM

quote:
--------------------------------------------------------------------------------
Its blueness is shown and its non-redness is inferred.
--------------------------------------------------------------------------------

SlateGreySky:
It seems to me that one property (albeit a Cambridge property) of blueness is non-redness. That being the case, we don't infer (or even deduce) that blueness is non-red; we see, in seeing blueness, non-redness (one type of it, anyway).

What is a 'Cambridge property'?
Surely non-redness is concieved and it is not percieved.
There is no sense perception that identifies non-red things, is there?

quote:
--------------------------------------------------------------------------------
That it is true in, all possible domains or true in all possible worlds, is what makes it a logical truth.
--------------------------------------------------------------------------------

SlateGreySky:
So "logical truth" just means "necessary truth," it seems: necessary truths are just truths that are true in all possible worlds. Once again, I don't see the distinction between your "logical truth" and what most contemporary metaphysicians would call "necessary truth."

Nor do I see a difference, (analytic, necessary, apriori, etc.) all mean the same thing...tautologous truth.

quote:
--------------------------------------------------------------------------------
There is no empirical situation that contains the number 1.
--------------------------------------------------------------------------------

SlateGreySky:
Anytime someone uses arithmetic involving the number 1, that's an empirical situation that contains the number 1.

No, it is not!
Numbers are concoctions of mind, and they have no physical presence.

That there is 1 object on my table, means that there is 'an' object on my table...it's oneness is a philosophical rendering of the situation.

quote:
--------------------------------------------------------------------------------
There is no place in the world where the number 1 could be found.
--------------------------------------------------------------------------------

SlateGreySky:
If you mean that the number 1 does not present itself for sensory perception, then of course that's right;

Yes, that is indeed what I mean.

SlateGreySky: ..numbers are abstract objects, but that doesn't mean they don't exist, just like sets.

Of course-- abstract objects, eg. numbers, sets, exists.
But, their abstractness denies their physicallity (if there is such a word).

Existence, like identity, applies to all objects concrete or abstract.

Witt

SlateGreySky · 06-04-2003, 06:32 PM

Quote:

What is a 'Cambridge property'?

"Cambridge property" is the name given to any sort of negative property that applies by virtue of its absence; e. g. one property of the blue car is that it is non-red. The property of the blue car's not being red is a Cambridge property.

Quote:

There is no sense perception that identifies non-red things, is there?

Just as the sense of sight identifies positive properties such as the blueness of the car, it also identifies negative (Cambridge) properties such as the non-redness (and non-greenness, non-yellowness, etc., all negations of the positive blueness) of the car.

It could be argued that non-redness is only a function of language and not identifiable by sense-perception, but as we know from Wittgenstein and Husserl, so is blueness - our mind wouldn't distinguish a property like blueness unless our language already did so.

Quote:

Numbers are concoctions of mind, and they have no physical presence

Even if it were the case that numbers are "concoctions of the mind" (and I'm not entirely sure that they are), certainly it doesn't follow from the fact that they have no physical presence that they are not facts (and so can compose propositions that are factual necessities, e. g. 1=1), unless you want to argue that the only facts are physical facts (and it seems that you do not, given that you admit the existence, nonphysical though it may be, of numbers and sets).

What's your verdict?

John Page · 06-04-2003, 07:05 PM

Keep going, guys, facts are facts but the truth, well, thats another thing...

Quote:

Originally posted by SlateGreySky
"Cambridge property" is the name given to any sort of negative property that applies by virtue of its absence; e. g. one property of the blue car is that it is non-red. The property of the blue car's not being red is a Cambridge property.

Oh my Cambridge god!!

Quote:

Originally posted by SlateGreySky
Just as the sense of sight identifies positive properties such as the blueness of the car, it also identifies negative (Cambridge) properties such as the non-redness (and non-greenness, non-yellowness, etc., all negations of the positive blueness) of the car.

But you have to perceive there to be something that the property is mutually exclusive to in the fist place. How about Oxford properties - would Cambridge acknowledge the existence of those?

Quote:

Originally posted by SlateGreySky
Even if it were the case that numbers are "concoctions of the mind" (and I'm not entirely sure that they are), certainly it doesn't follow from the fact that they have no physical presence that they are not facts (and so can compose propositions that are factual necessities, e. g. 1=1), unless you want to argue that the only facts are physical facts (and it seems that you do not, given that you admit the existence, nonphysical though it may be, of numbers and sets).

I don't mind

that the mind is a property of physical substance such that it interprets numbers as one physical substance's quantification of similar characteristics in other parts of physical existence. It's all in the mind, really.

Cheers, John

Dominus Paradoxum · 06-04-2003, 07:28 PM

Quote:

Nor do I see a difference, (analytic, necessary, apriori, etc.) all mean the same thing...tautologous truth.

No, it does't. Just how is it that you suppose tautologies to be true? And how, for example, can p v ~p be tautolgously true if it is possible to formulate logics without it?

John Page · 06-04-2003, 08:18 PM

Quote:

Originally posted by Dominus Paradoxum
Just how is it that you suppose tautologies to be true?

By (self) definition.

Quote:

Originally posted by Dominus Paradoxum
And how, for example, can p v ~p be tautolgously true if it is possible to formulate logics without it?

Irrespective of the formulation, one needs a substrate to implement it.

(This) p is not (that) p. Realite, ces't Vraiment. Toujours (this) p is (this) p. Realite, ces't Vraiment. Ou est realite? C'est ca!

Cheers, John

Dominus Paradoxum · 06-04-2003, 09:00 PM

Quote:

By (self) definition.

The notion of truth by stipulation is not as clear as some would take it to be.

Intuitionists in logic reject the the principle of the excluded middle. If it were true 'by definition' then it would be impossible to create a logic that does without it.

Witt · 06-07-2003, 03:35 AM

Dominus Paradoxum:
Intuitionists in logic reject the the principle of the excluded middle. If it were true 'by definition' then it would be impossible to create a logic that does without it.

The intuitionis's not is different from the not of classical logic.

I is not provable that, is not the same as, it is not the case that.

Witt

06-04-2003, 01:20 PM	#11
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	Three valued logics John: How about : A statement is deemed to TRUE if it is considered to accurately convey a state of affairs. A statement is deemed to FALSE if it is considered to completely contrary to a state of affairs. Rather than the Boolean 1 and 0, this could be represented by 1 and -1 with 0 as a neutral value (maybe caused by irrelevance or uncertainty). This is not to say that truth has to be binary! A & B = 2 ~A & ~B = -2 ----------------- Some interesting three valued logics have been developed eg: Lukasiewicz (1920), Kleene (1952), but they deny the validity of p v ~p and ~(p & ~p) etc. Reichenbach(1944) suggested that a three valued logic would provide a solution to some problems raised in quantum mechanics. The 'middle' value might represent Godels' undecidable !? IMO, your proposal also denies the law of excluded middle. p v ~p 1 1 -1 0 0 0 -1 1 1 I think odd-numered logics are more awkward than those with 2^n values, but, perhaps there are suitable interpretations. Witt

06-04-2003, 02:03 PM	#12
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	Re: Multivalent Logics quote: -------------------------------------------------------------------------------- Consider the statement, 'My car is blue' and let's assume that it is in fact true. -------------------------------------------------------------------------------- SlateGreySky: But what you point to here as a "logical truth" (i.e. that the car is either blue or not blue) just seems to be the law of non-contradiction, which would be true regardless of any factual truth or falsehood. Yes, (p v ~p) is the law of excluded middle and ~(p & ~p) is the law of non-contradiction, and they are equivalent. (i.e. that the car is either blue or not blue), is an instance of the law of excluded middle. Witt: My car is blue or My car is not blue, is logically true but not factually true, i.e. there cannot be a situation that confirms 'My car is blue or My car is not blue'. SlateGreySky: I disagree. I would say (especially if you agree to phrase the above as "it is either the case that my car is blue or it is not the case that my car is blue") that every logically possible state of affairs confirms "it is either the case that my car is blue or it is not the case that my car is blue." That is just to say that the law of non-contradiction applies universally, right? Right. (and your phrasing is better) quote: -------------------------------------------------------------------------------- We cannot 'see' that, My car is not red. -------------------------------------------------------------------------------- SlateGreySky: Of course we can! If it's blue, we see that it's not red. Not so. We can only see, ie. sense, what is presented by the existent state of affairs. Its blueness is shown and its non-redness is inferred. We realize that it is not red by reasoning and assuming other premises, eg. no object can be two different colors at the same time, etc. quote: -------------------------------------------------------------------------------- There are no factual necessities at all. -------------------------------------------------------------------------------- What about 1=1? That seems to me to be a factual necessity, in that it is factually true in all possible worlds that 1=1. That it is true in, all possible domains or true in all possible worlds, is what makes it a logical truth. There is no empirical situation that contains the number 1. There is no place in the world where the number 1 could be found. quote: -------------------------------------------------------------------------------- If p is factually true or factually false, []p is contradictory. I.e. material truths are not theorems, rather, they happen to be the case. -------------------------------------------------------------------------------- SlateGreySky: Is this just the assertion that there are no such things as necessary truths? No. It is the assertion that there are no such things as necessary facts. SlateGreySky: Sorry to try and open so many threads here . . . I just find your "multivalent logic" very worthy of discussion. Hopefully somebody has the time to talk about at least one of these issues . . . Philosophy demands many.. questions, threads, etc., imo. Witt

Thread Tools	Search this Thread
Show Printable Version	Search this Thread: Advanced Search

06-04-2003, 03:14 PM	#14
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	quote: -------------------------------------------------------------------------------- Its blueness is shown and its non-redness is inferred. -------------------------------------------------------------------------------- SlateGreySky: It seems to me that one property (albeit a Cambridge property) of blueness is non-redness. That being the case, we don't infer (or even deduce) that blueness is non-red; we see, in seeing blueness, non-redness (one type of it, anyway). What is a 'Cambridge property'? Surely non-redness is concieved and it is not percieved. There is no sense perception that identifies non-red things, is there? quote: -------------------------------------------------------------------------------- That it is true in, all possible domains or true in all possible worlds, is what makes it a logical truth. -------------------------------------------------------------------------------- SlateGreySky: So "logical truth" just means "necessary truth," it seems: necessary truths are just truths that are true in all possible worlds. Once again, I don't see the distinction between your "logical truth" and what most contemporary metaphysicians would call "necessary truth." Nor do I see a difference, (analytic, necessary, apriori, etc.) all mean the same thing...tautologous truth. quote: -------------------------------------------------------------------------------- There is no empirical situation that contains the number 1. -------------------------------------------------------------------------------- SlateGreySky: Anytime someone uses arithmetic involving the number 1, that's an empirical situation that contains the number 1. No, it is not! Numbers are concoctions of mind, and they have no physical presence. That there is 1 object on my table, means that there is 'an' object on my table...it's oneness is a philosophical rendering of the situation. quote: -------------------------------------------------------------------------------- There is no place in the world where the number 1 could be found. -------------------------------------------------------------------------------- SlateGreySky: If you mean that the number 1 does not present itself for sensory perception, then of course that's right; Yes, that is indeed what I mean. SlateGreySky: ..numbers are abstract objects, but that doesn't mean they don't exist, just like sets. Of course-- abstract objects, eg. numbers, sets, exists. But, their abstractness denies their physicallity (if there is such a word). Existence, like identity, applies to all objects concrete or abstract. Witt

06-07-2003, 03:35 AM	#20
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	Dominus Paradoxum: Intuitionists in logic reject the the principle of the excluded middle. If it were true 'by definition' then it would be impossible to create a logic that does without it. The intuitionis's not is different from the not of classical logic. I is not provable that, is not the same as, it is not the case that. Witt

Freethought & Rationalism Archive

The archives are read only.