Is logic faith?

Originally posted by Palynka
If you don't even know what X is, how can you say it's true, partly true or untrue? Moreover, what does ~X mean if you can't define X?

There is no conjunction until you define the sets.

Of course I know what X is. I can recognise when something is blue or tall. But I can never get a precise numerical definition of what blue or tall means. In fact it would be ridiculous and counter-intuitive were I to say "A tall person is defined as exactly 1.8 meters. A person 1 millimeter shorter than that is not tall." X still has meaning even if I cannot defined every member of the set of X.

Originally posted by Conrau K
Of course I know what X is. I can recognise when something is blue or tall.

And yet you claim this is false for some elements, that aren't clearly blue or tall.

So you don't know what X is.

Originally posted by Conrau K
Of course I know what X is. I can recognise when something is blue or tall. But I can never get a precise numerical definition of what blue or tall means. In fact it would be ridiculous and counter-intuitive were I to say "A tall person is defined as exactly 1.8 meters. A person 1 millimeter shorter than that is not tall." X still has meaning even if I cannot defined every member of the set of X.

This is more or less a repeat of what Palynka is saying: You previously claimed that something could exist which was both blue and not blue. That means you you have a definition for blue which however imprecise includes the item in question. You also have another definition called 'not blue' that also includes the item in question. Sadly you have not followed the traditional use of 'not' in your second definition so your argument does not apply to the statement X & ~X.

Originally posted by Palynka
And yet you claim this is false for some elements, that aren't clearly blue or tall.

So you don't know what X is.

I think there must be some misunderstanding here. Of course I know what blue and tall mean. But that does not mean these are defined. In a colour spectum which moves imperceptibly from red to blue, I cannot decisively say that pixel P is definitely blue and P+1 definitely not blue. Blue is a vague property. The set of things which are blue is not definite. Of course physicists will approximate blue to a specific wave-length, but even they would admit that such a cut-off point between blue and not-blue is arbitrary and could be placed at many places on a spectum.

Originally posted by twhitehead
This is more or less a repeat of what Palynka is saying: You previously claimed that something could exist which was both blue and not blue. That means you you have a definition for blue which however imprecise includes the item in question. You also have another definition called 'not blue' that also includes the item in question. Sadly you have not foll ...[text shortened]... of 'not' in your second definition so your argument does not apply to the statement X & ~X.

This is more or less a repeat of what Palynka is saying: You previously claimed that something could exist which was both blue and not blue. That means you you have a definition for blue which however imprecise includes the item in question. You also have another definition called 'not blue' that also includes the item in question. Sadly you have not followed the traditional use of 'not' in your second definition so your argument does not apply to the statement X & ~X.

Fuzzy logic is a perfectly respectable philosophical position in logic circles. I don't see why people here have such a problem with it. Probably you did not bother to read the links I suggested.

To restate the argument for such a fuzzy logic. Say I have a pile of 10^8 grains. Obviously since 10^8 grains is a pile, then so is 10^8 -1 grains. A single grain cannot make any perceptible difference. So if 10^m grains is a pile, then so is 10^m -1, and so, if 10^m -1 is a pile, then so is 10^m - 2, etc. So 10^m -n is also a pile. This is a perfectly logical use of modus ponens and the principle of transitivity. But the fact is that there will come a certain time when there are no grains left and no longer any pile (when 10^m = n). This is called the sorites paradox. The premises are true, the reasoning is perfectly valid, yet the conclusion obviously false.

Now if you and Palynka believe that for X to be meaningful, every member of X must be defined so that it cannot be a member of ~X, then you both are committed to the position that there is a precise number of grains in the above example in which, should I take one more grain, I no longer have a pile. So n is a pile, but n-1 is not a pile. I can only say that such a use of language is both bizarre and unnatural. I cannot see how one grain makes a difference nor can I imagine any sane person counting the number of grains to confirm whether those grains constitute a pile. The fact is that many people will naturally say "He is borderline tall -- tall and yet not tall"; That vase is a kind of blue, but kind of not". Such expressions are coherent.

I think the best solution to this paradox is to posit that while the initial 10^8 grains is a pile and the final 0 not a pile, there is an intermediary set of number of grains which can equally belong to both sets. This way the conditional 'If 10^m is a pile, then so is 10^m -1' is only partly true and the paradox is circumvented.

Originally posted by Conrau K
I think there must be some misunderstanding here. Of course I know what blue and tall mean. But that does not mean these are defined. In a colour spectum which moves imperceptibly from red to blue, I cannot decisively say that pixel P is definitely blue and P+1 definitely not blue. Blue is a vague property. The set of things which are blue is not def ...[text shortened]... ff point between blue and not-blue is arbitrary and could be placed at many places on a spectum.

I see fuzzy logic as a poor man's approximation. It doesn't solve the problem of arbitrariness, just replaces it with an arbitrary, but smoother, approximation.

Defining such "imprecise" concepts in terms of fuzzy truth, requires a well-defined measure (wavelength, cms, kgs, etc), used to construct truth values, which can be directly used as the basis for standard Boolean logic. The results would be in terms of the measure and well-defined. Subjective considerations about what the measure means would be left to the reader.

Of course, under the rules of fuzzy logic, what you're saying is true. After all, I am a formalist. I just don't see the applicability.

Originally posted by Conrau K
The fact is that many people will naturally say "He is borderline tall -- tall and yet not tall"; That vase is a kind of blue, but kind of not". Such expressions are coherent.

But it is essential to realize that:
Borderline tall is not equivalent to tall. So X & ~X does not hold.
Kind of blue is not equivalent to blue. So again X & ~X does not hold.

Even in fuzzy logic it must be recognized that once something is 'bluish' it cannot be 'not bluish'. Further even though once can say the statement "It is blue" has the same 'truth value' in fuzzy logic as "It is not blue" that is not equivalent to saying "It is blue and not blue" is true. Two half truths do not make the truth.

Originally posted by Palynka
I see fuzzy logic as a poor man's approximation. It doesn't solve the problem of arbitrariness, just replaces it with an arbitrary, but smoother, approximation.

Defining such "imprecise" concepts in terms of fuzzy truth, requires a well-defined measure (wavelength, cms, kgs, etc), used to construct truth values, which can be directly used as the basis for ...[text shortened]... at you're saying is true. After all, I am a formalist. I just don't see the applicability.

Defining such "imprecise" concepts in terms of fuzzy truth, requires a well-defined measure (wavelength, cms, kgs, etc), used to construct truth values, which can be directly used as the basis for standard Boolean logic. The results would be in terms of the measure and well-defined. Subjective considerations about what the measure means would be left to the reader.

I cannot have any objection to that, but that it is bizarre. It means that there is a precise measurement (down to the nanometer) at which a person stops being tall; a precise number of grains which ceases to be a pile; an exact wavelength which divides blue from non-blue. That does solve the sorites paradox, of course. I simply do not think that solution reflects our natural usage of vague terms and were you to ask someone for a precise measurement at which a person ceases to be tall, they could not answer. No doubt if one answered 1.8m, they would also include 1.79, 1.795 as well. They simply could not be precise.

After all, I am a formalist. I just don't see the applicability.

Fuzzy logic is all the rage in engineering.

Originally posted by twhitehead
But it is essential to realize that:
Borderline tall is not equivalent to tall. So X & ~X does not hold.
Kind of blue is not equivalent to blue. So again X & ~X does not hold.

Even in fuzzy logic it must be recognized that once something is 'bluish' it cannot be 'not bluish'. Further even though once can say the statement "It is blue" has the same 't to saying "It is blue and not blue" is true. Two half truths do not make the truth.

Borderline tall is not equivalent to tall. So X & ~X does not hold.Kind of blue is not equivalent to blue. So again X & ~X does not hold.

I think you are confused. It is borderline precisely because X & ~X holds. It is kind of blue because X & ~X holds. Since I cannot sort this colour categorically into either set, I can assign it a fuzzy status as a member of both sets, as a sort of case of both.

Originally posted by Conrau K
Fuzzy logic is all the rage in engineering.

All applications I've seen could be reduced to standard operations.

In those examples, anytime there is a IF THEN operated on a truth value dependent on a quantifiable measure, I could constructed a reduced form of the same operation directly on the measure that would not require fuzzy logic.

Can you give me an example where the operation would not be reducible?

Originally posted by Palynka
All applications I've seen could be reduced to standard operations.

In those examples, anytime there is a IF THEN operated on a truth value dependent on a quantifiable measure, I could constructed a reduced form of the same operation directly on the measure that would not require fuzzy logic.

Can you give me an example where the operation would not be reducible?

Can you give me an example where the operation would not be reducible?

No. It is not a subject I have any knowledge of. My argument is more on the linguistic side: that fuzzy logic better corresponds to natural language. But given that the claim under dispute is whether a contradiction can ever be coherent, I think the linguistic side more important.

Originally posted by Conrau K
[b]Borderline tall is not equivalent to tall. So X & ~X does not hold.Kind of blue is not equivalent to blue. So again X & ~X does not hold.

I think you are confused. It is borderline precisely because X & ~X holds. It is kind of blue because X & ~X holds. Since I cannot sort this colour categorically into either set, I can assign it a fuzzy status as a member of both sets, as a sort of case of both.[/b]

Fuzzy logic assigns a degree of truth (yes I have gone and read one of your links). Therefore you cannot correctly claim that "He is tall" or "It is blue" are true. Nor can you claim that "He is not tall" or "It is not blue" are true. They are all only partially true. Therefore you cannot claim that "He is tall and not tall" is true. At best it might be partially true but I am not certain how you combine truths in fuzzy logic.

Originally posted by twhitehead
Fuzzy logic assigns a degree of truth (yes I have gone and read one of your links). Therefore you cannot correctly claim that "He is tall" or "It is blue" are true. Nor can you claim that "He is not tall" or "It is not blue" are true. They are all only partially true. Therefore you cannot claim that "He is tall and not tall" is true. At best it might be partially true but I am not certain how you combine truths in fuzzy logic.

Yes, I know they are partial truths. That is the point of the word 'fuzzy'.

Originally posted by Conrau K
Yes, I know they are partial truths. That is the point of the word 'fuzzy'.

Have you found out enough about fuzzy logic to find out how it deals with truth tables? I find it unlikely that you can take two half true statement and claim that the combination is fully true. I wonder if the combination can necessarily be said to be even partially true. The part that is true about "it is blue" is the very part that is false about "It is not blue" and vice versa so one would expect the statement "It is blue and not blue" to be totally false as the two truth values have no overlap and the "and" operation cancels them out. Its rather like doing a bitwise "and" operation in binary were 1100 & 0011 = 0000

Originally posted by Scriabin
here it is again:

When you refer to God, what do you mean by the word "God."

There, I have used and mentioned the word in the same sentence. While answering the question, please also think about whether you know the difference.

When I refer to God:
I refer to the Creator of everything, by the power of His Word all things are held together.
I refer to the Almighty One that lives forever, Who was, is, and always will be the same for He changes not.
I refer to the One that puts up, and takes down, Who gives and takes away.
I refer to the Savior of my soul.
I refer to the One that does not lie.
I refer to the Father, Son, and Holy Spirit Who are One.
I refer to the One that never gets tired, who watches over us.
I refer to the One that watches over His Word to perform it.
There is no other god beside Him, He is Lord.
The Holy of One of Israel Who gave us Jesus Christ to save us from our sins.
I refer to the God that calls us out of sin into His Kingdom through Jesus Christ.
I refer to Jesus Christ through Whom we are saved, the Word of God made flesh and died for our sins and rose again.
I can go on, but hopefully this is specific enough for you. My words are inadequate when it comes to describing Him.
Kelly