ELEPHANT TO FUZZY-WUZZIES: Eeeevening All. Oot fora Strrrroll are we?
Let me take you by the hand and walk you through the streets of binary
logic.
> HORSE WROTE:
> If you adhere exclusively to classical logic then your choices are limited to
> one of two positions - True or False.
>
>> ELEPHANT HAD WRITTEN:
>> I don't think so, because classical logic is perfectly consistent with the
>> "I don't know" point of veiw, and I have argued that it is in fact the only
>> logic which can be consistent with the "I don't know" point of veiw, since
>> fuzzy logic will take the uncertain either/or question and construe it as a
>> both/and answer: turning an epistemological state into a logical one.
>
> HORSE WROTE:
> A third state is an option with classical logic but this is really a non-state
> (Pirsig refers to this state as Mu) which is declaring that classical logic
> has broken down and it is not capable of making a rational analysis.
ELEPHANT:
Precisely what I mean by the "I don't know" state. Mu is spoken of by
Phaedrus in ZAMM as a pointer to our having come at the whole problem from
the wrong angle, and as motivating some serious thought. This couldn't be
so if Mu were a proper answer, a third value in logic. In that case Mu
would be closure, which is the exact opposite of what it is.
And it isn't classical logic which is incapable of anything here, because
logic is no kind of agent: it's us that have failed to produce a rational
analysis, not some impersonal 'logic'. We have failed while using a certain
tool. Well, a bad workman always blames his tools.
ELEPHANT HAD WRITTEN:
>> Further, the operation of classical logic can sit perfectly well besides the
>> mystical intuition that the world beyond language cannot be correctly
>> described in logical terms. The reason it cannot be perfectly captured is
>> that it does not contain objects, and not, as fuzzy-logicians pretend, that
>> it does contain objects, but that those objects are "fuzzy" ones. Oddly,
>> this connects with what I say about Wagner in another posting (mysticism).
>> Wagner's objects are pretty fuzzy alright - but I don't think that this
>> makes them a better decription of the mystical reality beyond words than,
>> say, Bach's.
>
HORSE WROTE:
> You seem to be making erroneous connections here. Fuzzy logicians do not
> pretend anything of the sort. Classical logic takes the mistaken view that if
> something is not True or False then there is a problem with the world.
ELEPHANT:
That's just where you are going wrong: 'classical logic' or 'binary logic'
or what have you takes no such view. Whoever heard of a universal
quantifier with an opinion? Anyone got into arguments with an integer, I
mean lately? Has anybody, while sober, had a meaningful conversation about
epistemology with the cast of thousands in Wilfred Hodges Symbolic Logic
textbook? Well have you? Er, no. Own up: we are the ones with the views.
OK now, there are some *logicians* and physicists who have had this "there
must be a problem with the world" approach - well so much the worse for
them. A logic is not the logicians. Nor is it the theories expressed in
that logic. In a theory expressed in binary logic, when we come accross a
proposition that we cannot answer true or false, but which actually involves
a self-contradiction both ways, this is a sure-fire proof that the whole
damm theory is wrong. It is what's called a reductio ad absurdum, and it is
the most important and valuable tool in the whole kitbag. So, reject the
theory. You want to keep the theory and reject the logic!
>> HORSE HAD WRITTEN: If you've read Chris' post on Fuzzyness then you'll see
that
>> what you've said creates unnecessary complication. Using classical logic a
>> statement such as: "I am typing an email at a computer keyboard" is Either
>> True OR False and in a particular context this is fine. But the same
>> statement considered from a multivalent logic perspective shows that it is
>> BOTH True AND False - False in this sense meaning that it is not exclusively
>> True. This does not mean that there is a contradiction involved, only that
>> True and False are complementary not contradictory.
>>
>> ELEPHANT HAD WRITTEN: I'm at a loss to understand what "contradictory" means,
if "True
>> and False are complementary not contradictory". Perhaps you can explain
>> this? Perhaps you can also explain how having two logics in place of one is
>> not an "unnecessary complication"?
>
> HORSE WROTE:
> In classical logic there is A or ~A (i.e. True or False) and to say that (for
> example) a statement is BOTH True AND False within classical logic assumes a
> contradiction. Within Fuzzy logic it is not the case that something is
> necessarily True or False. It is True that at the moment I am typing this
> email but I am also thinking about what to type, listen to music, breating,
> digesting my food, replicating my body cells etc. The truth value of my typing
> this email is complemetary to the other activities mentioned (or they are
> complementary - take your pick).
ELEPHANT:
Sure, fine. But this goes back to my very first posting in this thread. If
the manner in which something is symultaneously true and false is through a
specification of different objects that it is true and false of, thn this
is precisely the course of contradiction-avoidance which binary logic
recommends. True: I am typing this email. False: I am typing this email
with the totality of my being. No contradiction here whatsoever. This is
by no means a case of "True and False" in answer to one question, because
the two questions "are you typing?" and "are you typing with your whole
being?" are transparently different from each other. Your argument that
this could be a case of a fuzzy True/False, therefore, depends on the
oldest mistake in the book: a fallacy of equivocation. If this is what you
are about then there is absolutely no call for fuzzy logic here, quite the
reverse! You already seem to have quite a surfit of fuzzy logic, and what
you need is a tiny bit of classical precision.
ELEPHANT HAD WRITTEN:
>> There's more to life than logic. And isn't that just what we are saying,
>> when we say that "the world consists of a multitude of colours in between
>> black and white"?
> HORSE:
> Correction - logic systems can only say what there rules allow them to say.
> Classical logic says that there are two states. People recognise that there
> are more.
ELEPHANT:
I'm going to talk myself hoarse saying this (pause for applause), but
Classical logic says nothing of the sort. What it does say is that there
are only two *logical* states. People recognise that there are more states,
but you have an odd circle of friends if, amoughst them, it is common sense
that there are more than two *logical* states. We can talk about a state of
suspicion or of being in love. All kinds of attitudes - not all kinds of
logical states. The discussion of logical states isn't dinner-table
conversation. How many people do you know who, of an evening, are to be
found recounting to their sprogs "this little attitude went to a logical
state, this little attitude went to market, and THIS little attitude ran
aaaaalllllll the way home!".
ELEPHANT HAD WRITTEN:
>> Now look, what you're trying to do is to take away this
>> world-outside-of-logic from me and everyone else, and then give it back to
>> us nicely formulated in a three value logic (True/False/True and False).
>> Well, Hell, I don't want it back that way - it certainly isn't what I
>> started with. What I started was was something unformulable, not for the
>> lack of a magic third value in logic, but for the lack of object-hood in
>> that wonderful rainbow between black and white. In this way, fuzzy logic
>> can't possibly be fuzzy enough for what it's claiming to do. The addition
>> of the third value replaces a two sided plane with a triangular figure - but
>> the geometric angularity is still there, now with the added insult of
>> calling to us proudly, "come, look at my lovely triangle, everything
>> important about our lives is here!". I don't find this appraoch very
>> appealling.
>
> HORSE WROTE:
> Again the 3 values!!!!!! Fuzzy logic is multivalent or, if you prefer
> polyvalent.
ELEPHANT:
Please excuse me if I have continued to talk about fuzzy logic as having
three logical values. This is purely for my conveiniance, as I think that
if I can show that it couldn't successfully have even one extra value over
binary logic, and still be a logic, then I willl have shown that it won't
get to having the millions of values that you want for it. All my arguments
against three value logics apply against four, five, twelve or twenty value
logics. In fact, I think further considerations apply against a trully
multivalent logic: viz that with the infinity of values you are implicitly
allowing this 'logic' (HORSE: "What you refer to as the third value is (the
in-between) is in fact a spectrum of values/possibilities/states not a
single value.") would be entirely uncomputeable, and so not a logic. (don't
lets go confusing computability and completeness, please! - I've had quite
enough of Godel).
> HORSE WROTE:
> What you refer to as the third value is (the in-between) is in fact a spectrum
> of values/possibilities/states not a single value.
>
>
>> ELEPHANT HAD WRITTEN: Do you mean that *your* 'fuzzy logic' has nothing at
all to do with logical
>> reasoning, syllogisms, truth tables, symbolic formulation etc? Ok. I can
>> dig it. Now, could you please tell me what you are talking about?
>
> HORSE WROTE:
> As I have said Fuzzy logic is also a logical system that deals in reasoning
> etc. but it uses degrees and probabilities rather than absolutes - although
> absolutes are permissible but generally relegated to the realm of definition
> or truisms or mathematical models. Could I suggest that you get hold of a copy
> of Fuzzy Thinking by Bart Kosko and have a read of it. It's a great book and
> an excellent introduction to Fuzzy systems in general.
ELEPHANT:
You kind of didn't answer my question there. But Re getting that book:
Sure. Even better if there is a text floating on the net. I have to say
though, that the world is full of great books with nothing of any substance
to say, and as a rule the less the substance the better the sales. Prisig
is a remarkable (and lucky) exception to this otherwise universal law of
modern publishing.
ELEPHANT HAD WRITTEN:
>It is not naivety
> about how the world is constructed to suppose that it conforms to binary
> logic, because it is precisely with language operating according to binary
> logic that the "constructed" world is constructed. If you are talking of
> the world beyond language and logic, then there is no "how the world is
> constructed" for you to be talking about. There is only flux. Do you, much
> to my astonishment, turn out to be a Kantian noumenalist after all,
> beleiving in a (if fuzzy) 'structure of the world' which fuzzy logic is an
> attempt to pin down? If so, I don't think your ideas sit well with the
> pragmatist outlook of MOQ.
HORSE WROTE:
> [I'M] Definitely not a Kantian (noumenalist or otherwise) - well not to any
damaging
> extent anyway.
ELEPHANT:
I pressed the wrong key when I read this, and sent outlook to the back of a
huge pile of windows, so astounded was I by your turn of phrase. "not to
any damaging extent"? Pardon? What? Excuse me? Turn me over and giggle
me about a bit until the penny goes down the slot again. Er, I'm sorry,
but being a noumenalist is like having the plague. You've either got it or
you haven't, and if you've got it then your whole metaphysics is going to
weaken and die of it, sure as rotten eggs is rotten eggs.
>
>> ELEPHANT HAD WRITTEN : What lies beyond electrons and quarks and all the
>> rest isn't some ever more "complex" world, but Quality. I am very far from
>> holding a simplistic either/or view, because I certainly do not believe that
>> a perfect description of the world in terms of classical logic is or could
>> be possible. I simply maintain that this is the only logic we have worthy
>> of the name. The failure of language coexists with it's indispensability.
>>
>> HORSE WROTE: The irony here is that language is a fuzzy system of enormous
>> complexity (words have multiple meanings without contextual reference) and
>> that classical logic was designed to simplify and particularize language. It
>> works fine with mathematics and some areas of science but elsewhere it fails
>> miserably.
>>
>> ELEPHANT: Yes. But why is that? Is it because we are all perfect
>> reasoners, who happen to reason logically with fuzzy logic, or is it because
>> we are lots of us fuzzy reasoners, who often have fluid, murky kinds of
>> 'thought', with no sucessful logic in them at all? (Even though language
>> is an attempt in that direction - if it weren't there would be no point in
>> it). I know which veiw I prefer. Look, I'm not trying to capture the whole
>> of human experience in logic: it's you who is trying to do that. I'm not
>> failing miserably, because I'm not so hasty as to make the attempt.
>
> HORSE WROTE:
> Classical Logic tries to stuff the world into one of two compartments, fuzzy
> logic expands the number of compartments but in the end this also breaks down
> because what they are both trying to classify is only one part of reality.
ELEPHANT:
Great: I accept your admission of defeat. You accept that fuzzy logic is no
advance over binary logic. Closure.
ELEPHANT HAD WRITTEN:
>> Don't assume a necessary connection between the manifestos of the logicians
>> and the logic they hold. Aristotle had a manifesto and it wasn't Plato's.
>> But it would be hard to think of them as holding to different logics. If
>> they did, it would seem that any real argument between the two views would
>> be impossible. Your conception of classical logic is bound up with Prisig's
>> (justified) criticism of Aristotle. But, I think, what Prisig has to say
>> about Aristotle fits very well with the Platonic manifesto: subjects and
>> objects have a dependant being, and that being depends on Quality.
>
> HORSE WROTE:
> Subjects and objects continue to exist within the MoQ but they are just part
> of one toolkit created by Quality. Reality will understand itself but not by
> relying solely on inadequate intellectual classification systems.
>
ELEPHANT:
I think that's what I just said. It's also what I'm saying about fuzzy
logic: that it is an inadequate intellectual classification system.
Considered as allowing for an infinity of logical values it isn't any kind
of classificatory system at all, and considered as allowing for three
logical values is is a classificatory system which turns questions into
answers. Not really what we want in an effective thinking tool.
>>
>>
>> Finally, a quote from Prisig (lila p113, ch 8):
>>
>> "The tests of truth are logical consistency, agreement with experience, and
>> economy of explanation."
>>
>> If you are allowed your "True and False" answer, it seems to me that the
>> first test will be completely done away with. How can a statement or theory
>> ever be logically inconsistent, when inconsistency itself is elevated to the
>> status of a logical value? Any statement whatsoever is "consistent" with
>> fuzzy logic. I really think that settles the matter.
>
> HORSE:
> Somehow I doubt it.
ELEPHANT:
Indeed.
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