Fuzzy Logic

[Fool]

First, a quick primer on 'Fuzzy Logic'

Lets say you have an apple. It is what it is ('A' is 'A').

Now take a bite out of it.

Is it still an apple? Yes.

Now continue eating it until it there is nothing left but the core.

is it still an apple? No, its just a core.

So here is the crux of how 'Fuzzy Logic' differs from traditional western logic. In traditional logic, the apple began as 'A', and at the end became 'not A'.

Some indeterminable bite of the apple made it pass precipitously from one absolute, to another.

In 'Fuzzy Logic' the statement 'this object is an apple' would have a degree of truth to it, as opposed to a binary truth value. In practice, this means that as each bite is taken out of the apple, the truth value is a continuous variable.

Proponents of Fuzzy Logic cast it as a challenge to western logic. They point out that while traditional formal logic systems declare, at an axiomatic level, that the essence of contradition is to say "A and not A". Whereas in fuzzy logic, a value can in essence, be both true and not true. In the example above, once you've eaten roughly half the apple, it is, by degrees, both true and not true that the object is an apple.

For those familiar with logic formalism, it defies the law of the 'excluded middle', in a rather seductive way.

And so, I was curious what the objectivist position on Fuzzy Logic might be.

[Thoyd Loki]

Here is what I think of fuzzy logic...

[stephen_speicher]

In the example above, once you've eaten roughly half the apple, it is, by degrees, both true and not true that the object is an apple.

No. It remains an apple which, to varying degrees, has been eaten through. Change does not contradict identity.

And so, I was curious what the objectivist position on Fuzzy Logic might be.

I do not recall Ayn Rand specifically addressing this, but my own view is that fuzzy logic is a misnomer. You attempt to imply that it is some other form of logic; that is not so. Fuzzy logic is a method completely based on standard principles of logic, a mathematical concept of method which is very useful in a certain class of problems.

[AndrewSternberg]

First, a quick primer on 'Fuzzy Logic'

Lets say you have an apple. It is what it is ('A' is 'A').

Now take a bite out of it.

Is it still an apple?  Yes.

Now continue eating it until it there is nothing left but the core.

is it still an apple?  No, its just a core.

So here is the crux of how 'Fuzzy Logic' differs from traditional western logic.  In traditional logic, the apple began as 'A', and at the end became 'not A'.

The Law of non-contradiction states that a thing can not be both A and non-A at the same time and in the same respect.

1) "Lets say you have an apple. It is what it is ('A' is 'A')". Here is one set of conditions in which the Apple is an Apple. No problems so far.

2) "Now take a bite out of it. Is it still an apple?". Under this new set of conditions, the entity in question still qualifies as an apple.

3) "Now continue eating it until there is nothing left but the core. Is it still an apple? No, its just a core." Under this new set of conditions, the entity no longer qualifies as an apple, it is the core of an apple.

Your attack against the Law of Contradiction does not hold. An apple is an apple, a partially eaten apple is a partially eaten apple, and an apple core is an apple core. Yes the apple changed, but not in contradiction to its identity. If 'Fuzzy Logic' claims that change neccesitates contradiction, then 'Fuzzy Logic' is not logic at all, its just plain fuzzy.

[msb]

The ancient Greeks were able to answer the objections about the apple being eaten violating the law of identity.

Fuzzy logic is a certain (valid) method that has a specific uses in computer science. Sometimes it is useful to treat a small number of objects as able to transition into one another without definine extra objects. So, to use your example, you could treat an "apple sprite" as part apple, part eaten-thing, without having to define a new, separate "half-eaten apple sprite".

[argive99]

Fuzzy Logic is an assault on the law of non-contradiction. If you want a clear example of this, check out Robert Anton Wilson's latest at his website. It's called 'Maybe Logic' and it is specifcally designed to do away with Aristotelian either/or. For those of you who know of Wilson, no further introduction is necessary. I am sure Stephen Speischer knows about him and his 'theories' on physics.

I read his books 'Prometheus Rising' and "Quantum Psychology' on the reccommendation of someone I know and I quickly learned that Wilson was in hostile disagreement with every principle of Objectivist metaphysics and epistemology. But his greatest disdain is for Aristotelian logic. (He feels that quantum physics has disproved it along with the view of an independent universe.) Thus his advocacy of 'Maybee Logic' and something called "E-prime" which is language with the "is" removed out of it (Bill Clinton anyone). Its a language where nothing is definitely anything but are rather probabilities of something; ie 'more likely than not an apple.'

That was my first introduction to "fuzzy logic.' After I read it, I needed to take a shower.

When I bite into an apple, I am not biting into a pear, an orange, a bannana, or a steel pipe. Its a god damn apple.

http://www.rawilson.com/main.shtml

[Charles]

When the apple is eaten to the core it doesn't change its identity - essentially it doesn't have an identity beyond that which we give it in making a statement about it. It was still there, it was still what we call an apple. All that need change is the way in which you identify it: 'it is an apple core' would be a more accurate/useful way of describing the apple now it is eaten. It, however, always was an apple at that point in time before you ate it. The process of identification is that of attempting to describe/relate something in the most accurate way known to you. To argue the apple now eaten to the core is still an apple is your failure in logic, like you say it is 'fuzzy' logic and amounts to evasion.

[Betsy]

To argue the apple now eaten to the core is still an apple is your failure in logic, like you say it is 'fuzzy' logic and amounts to evasion.

Why is this "evasion" and what do you mean when you use that term?

[dougclayton]

So here is the crux of how 'Fuzzy Logic' differs from traditional western logic.  In traditional logic, the apple began as 'A', and at the end became 'not A'.

Some indeterminable bite of the apple made it pass precipitously from one absolute, to another.

This is a mistaken understanding of the law of identity. It does not say that something can be only A or B but nothing else: it says that something is A or not-A. So in the case you gave, it does not say that something is either 100% an uneaten apple, or it is not an apple at all. It says that whatever the entity is, that's what it is.

If it is a brand-new uneaten apple, then that is what it is (and it is therefore not an eaten apple). If it is a half-gnawed apple, then that is what it is (and it is therefore not an uneaten apple nor yet an apple core).

I've heard the argument also given like this: "Aristotle says that you are either/or, like you're either drunk or sober. But clearly you can be slightly buzzed, which is neither drunk nor sober, so I have proved Aristotle was wrong! Damn Western logic."

Aristotle, of course, never said that something cannot exhibit partial characteristics (as, for instance, an adolescent may have some properties of an adult, and some of a child, without having the least bit less identity because of it).

Doug

PS: First post! I found this forum about a week ago and have been very impressed with the level of rationality on it. Don't know if I will ever get to 1000 like some of the regulars.

[dougclayton]

By the way, on the subject of fuzzy logic: from what I understand of it, it can be useful in certain engineering applications, to deal with something changing state or value. To continue the apple analogy, it is perfectly logical to quantify the "eaten-ness" of the apple and say that is transitions in jumps from 0% eaten to 100% eaten. (This, as I gather, can be useful in certain feedback-control applications.) But at every point along the way, it is still what it is at that instance: an x% eaten apple. It doesn't pass through any "vague" or "fuzzy" states and it certainly never loses its identity.

[Charles]

QUOTE (Charles @ Aug 5 2004, 03:55 AM)

To argue the apple now eaten to the core is still an apple is your failure in logic, like you say it is 'fuzzy' logic and amounts to evasion. 

Betsy:

Why is this "evasion" and what do you mean when you use that term?

'The process of identification is that of attempting to describe/relate something in the most accurate way known to you.' To ask the question he has asked is fail to understand our position as observers, as namers, and that the quality he is questioned is the word 'apple' and at what point that word became un-useable in describing the core. This is indulging in a linguistic fallacy - its question of judgement - if you have a better word: use it. Use 'core'.

I called it evasion as I felt in confusing the actual apple with the labelling/identification of the apple the personal responsibility of making an accurate judgement is evaded. This is what was originally said:

Fool"Some indeterminable bite of the apple made it pass precipitously from one absolute, to another."

An apple is not an absolute, and neither is a core. The words 'apple' & 'core' are absolute in so much as they are tautologies:

Fool"So here is the crux of how 'Fuzzy Logic' differs from traditional western logic. In traditional logic, the apple began as 'A', and at the end became 'not A'."

What true logic would say is 'A' was then, and always will be 'A' then. It is no longer 'A', it would be more accurate to describe our core as 'B', but that doesn't change the irrefutable fact that it was 'A'.

So 'A' is always 'A', the concept of an apple is what it is, but that to which we ascribe the value 'A' needn't remain 'A' under forces of change in reality - apple are eaten, Ive decided to call whats left 'B' - what I concieve 'B' to be more closely resembles reality now im done eating!

Ive never been so pedantic about an apple! And incidently, though my tone may read curt - it is the spirit of demonstration, so no-one take it personally.

[Betsy]

I called it evasion as I felt in confusing the actual apple with the labelling/identification of the apple the personal responsibility of making an accurate judgement is evaded.

All you know from the evidence available to you is that he made a confused identification.

It could have been an honest, innocent error due to lack of information or not knowing the meaning or usage of certain terms. It could have been evasion -- the most evil, vicious, vice a human being can commit -- a DELIBERATE refusal to acknowledge facts. You don't know HOW he made that error.

In all justice, when you don't know why someone else did something, the proper principle is "Innocent until proved guilty." Words should be used precisely and crucial moral identifications like "evasion" should not be used indiscriminately.

[Charles]

Oh im sure it was an honest mistake, so many are.

[Fool]

Thanks for the informed and rational responses. I'd like to tip my own hand now, and say that after studying fuzzy logic a bit on my own, the useful aspects are easily integrated within formal logic systems, by allowing the systems to identify intermediate values with precision. In the example above, all that is really entailed is to recognize that an apple with a bite out of it can be accurately described as 95% of an apple, and that an apple core is perhaps 10% of an apple. (Specifically, it depends on the context of what the logical representational system needs in order to define an apple. In other contexts, an apple core could be considered an apple with 10% the mass of full apple. Or in another system, an apple core could be measured as 10% likely to be classified as an apple for a given purpose. Or in another scenario, an apple core could be considered a full 'apple' if the purpose of usage is for using the apple seeds, etc.)

Proponents of fuzzy logic sometimes argue that this approach misses the point. That this sort of system merely defines precise 'shades of gray' instead of accepting the world as a set of continuous values which are all subjectively interpreted.

When proponents go that far, they've begun to overstep the bounds of rational classification and reason that have proved so useful over the centuries. What's worse, is they imply that we should not attempt to use our minds to classify and interpret.

And some do. What's interesting about fuzzy logic to me, is that fundamentally it is a useful concept, that some people wish to attempt to use to undermine all of western logic. I am a software engineer, and find fuzzy logic a useful tool in modelling aspects of the world, especially in artificial neural networks.

One of the reasons I wrote the original post, was to understand to what degree any vague challenge to something that sounds like 'A is not A' would be received by objectivists. I'm heartened to see that there was very little in the way of knee-jerk reaction. I was afraid more people would try claiming that apple cores should be considered apples. Or that any attempt to add granularity to a logic system should be met with immediate contempt, just by using the word 'fuzzy'.

As a side note, 'Fuzzy Logic' is actually used much more often in Asian engineering, where it is called something that sounds much more like 'Adaptive Logic'. "Fuzzy" sounds derogatory and inferior, when in reality, arguably, fuzzy logic is an attempt to model the world much more precisely than more traditional logic approaches.

[AndrewSternberg]

It seems like 'Fuzzy Logic' just identifies a relationship between one entity and other causally possible version of it; The core is a causally possible consequence of an apple, once eaten.

Furthermore, based on what others have said about it, 'Fuzzy Logic' seems like a very useful tool that attempts to quantify the causal chain by 'locking' onto a specific attribute and 'tracking' what happens to that attribute over time. Thus I am willing to embrace 'Fuzzy Logic' with perhaps a name change that gets rid of its connotative opposition to formal western logic.

[y_feldblum]

dougclayton nailed it.

A thing is what it is. The object you are holding in your hand is what it is. Its identity is the totality of its properties.

Observe the object, figure out what other things it is fundamentally similar to and how it is different from them, etc. Abstract and form concepts, assign words to them, etc.

But the thing does not have the identity consisting of the word or concept "apple". It is what it is, and it is not a mental construct.

Am I not I when I wiggle my little finger? (Ha! - you try to use "I" three times in six words!)

[xobject]

Correct form of using I:

Am I not "me" when I wiggle my little finger?

Correct form of using you:

Are you not you when you wiggle your liile finger ?

Don't trick I

oh i mean: Don't trick me

[dougclayton]

Correct form of using I:

Am I not "me" when I wiggle my little finger?

Actually, as long as we're being pedantic, y_feldblum said it correctly. In the sentence "I am I", the second "I" should be the nominative form because "to be" is a linking verb. Thus you have "Am I not I when...." (http://webster.commnet.edu/grammar/verbs.htm#linking)

In your sign off, however, it should be "don't trick me" because "trick" in this context is a transitive verb (it takes an object), which means the "me" should therefore be in objective form.

And, of course, by some unwritten law of the internet, now that I have corrected someone else's grammar, I must have made at least one mistake in the above post.

/former grammar nazi

[Capitalism Forever]

(Moved from another thread/topic. This (link) is the post that originated this part of the discussion. - softwareNerd)

How on earth is non Aristotlean logic an 'inherently dishonest idea'?

What do you mean by "non-Aristotelian logic" ?

(I know what Dr. Peikoff means by it. You apparently think you know it too, but I am not sure you do.)

Edited August 2, 2005 by softwareNerd

[Hal]

What do you mean by "non-Aristotelian logic" ?

Any logic with 3 or more truth values (ie without bivalence).

Edited August 1, 2005 by Hal

[JMeganSnow]

Any logic with 3 or more truth values (ie without bivalence).

In other words any logic which is inherently self-contradictory. True and False in regards to logic are absolutes. Any statement which could be ascribed to another category would be neither true nor false and thus have no identity; it would be arbitrary and not subject to a process of cognition.

[DavidOdden]

True and False in regards to logic are absolutes.  Any statement which could be ascribed to another category would be neither true nor false and thus have no identity; it would be arbitrary and not subject to a process of cognition.

Okay, work with me here, 'cuz I think this has to be refined a bit. An arbitrary statement such as Peikoff's convention of gremlins studying Hegel's Logic on Venus does have an identity (the statement, if made, does exist, and no existents are lacking in identity). What's important is that the statement is not the product of grasping the nature of reality. An arbitrary statement is subject to cognition: you can understand what it states, and you can cognitively evaluate it (a prelude to rejecting the statement). But an arbitrary statement is necessarily excluded from logic, i.e. it is not proper fodder for reasoning.

[Hal]

In other words any logic which is inherently self-contradictory.  True and False in regards to logic are absolutes.  Any statement which could be ascribed to another category would be neither true nor false and thus have no identity; it would be arbitrary and not subject to a process of cognition.

Are you familiar with, for instance, fuzzy logic?

But an arbitrary statement is necessarily excluded from logic, i.e. it is not proper fodder for reasoning.

But theres no reason to exclude non-arbitrary statements without an absolute truth value from logic. Its silly to claim that the a question like "Is the water hot?" has to be answered with a definite yes/no reply, rather than with 'a bit', 'not really' or 'exceptionally so'. Some non-classical logics (eg fuzzy logic) were introduced precisely to deal with inherently vague statements which arent necessarily either 100% true or 100% false - for instance "that man is fat" or "it is cold outside". There's nothing mystical or irrational about this.

Edited August 2, 2005 by Hal

[DavidOdden]

Are you familiar with, for instance, fuzzy logic?

Of course

But theres no reason to exclude non-arbitrary statements without an absolute truth value from logic. Its silly to claim that the a question like "Is the water hot?" has to be answered with a definite yes/no reply, rather than with  'a bit', 'not really' or 'exceptionally so'.

I think it's silly to hold that "a bit" isn't a species of "yes". Scalar values simply amplify the answer. On the other hand, if you answer the question "is a million degrees hot" with "No", slyly thinking "at least by the standards of the core of the sun", then you're just playing with words -- dropping context. Fuzzy logic is nothing more that classical binary logic with some concept of context glued on.

[ed: I see your first comment wasn't aimed at me]

Edited August 2, 2005 by DavidOdden

[Hal]

Of courseI think it's silly to hold that "a bit" isn't a species of "yes".

Its a lesser degree of commitment than 'absolutely'. If you admit that some categories have blurred boundaries ('fat', 'warm', 'beautiful' etc), then fuzzy logic is going to be needed to evaluate propositions containing them.

Scalar values simply amplify the answer. On the other hand, if you answer the question "is a million degrees hot" with "No", slyly thinking "at least by the standards of the core of the sun", then you're just playing with words -- dropping context. Fuzzy logic is nothing more that classical binary logic with some concept of context glued on.

But its not about context. Theres no definite right or wrong answer to 'is that man fat?' when looking at someone who is maybe 14 stone, 21% body fat. Some people might say hes fat while others say he isnt - noone is incorrect here, its just that the concept of 'fatness' isnt precisely delimited. We can all agree that someone weighing 40 stone is fat whereas someone weighing 6 stone isnt, but theres a significant grey area around maybe the 12-16 stone mark. Classical logic forces these statements to be definitely resolved one way or the other, but this isnt really natural. Fuzzy logic allows us to say "that man is 90% fat whereas that person is only 68%" (or whatever).

The same applies to 'hot'. As you say, you can drop the context and play with words. But even when we keep context, 'hot' can be quite vague. Was it a hot day today? Well, I guess it was a bit warmer than usual, but not enough to make a trip to the beach worthwhile.

Edited August 2, 2005 by Hal