Hi there
Platt - many thanks for the reminder of the whereabouts of the (mis-)quote I used in my last
post. Much appreciated.
Puzz - I have assumed your references to "classical" logic are an alternative term for binary
logic and this is also my usage of the term.
On 13 Dec 2000, at 19:36, PzEph wrote:
> ELEPHANT TO HORSE:
>
> This discussion about fuzzy logic is turning out more interesting than it
> ought to be.
HORSE:
Yeah, I agree. It's been some time since I had any detailed discussion about Fuzzy Logic or
a general fuzzy view. In fact it's been a while since I continued a discussion like this.
> I think I'll pick out just one or two points to save time and
> refocus the discussion.
HORSE:
Fair enough. I'll probably do that as well as my time at the moment is fairly limited with Xmas
coming up.
> I want particulary to think about whether adhering
> to classical logic means that you have to have what Horse calls a 'black and
> white' veiw of the world.
HORSE:
If you adhere exclusively to classical logic then your choices are limited to one of two
positions - True or False.
>
> 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:
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.
> 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:
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. When classical logic (or fuzzy logic or any other
form of categorising system [i.e. static intellectual pattern of values]) breaks down there is a
problem with classical logic (or whichever system) and how it tries to compartmentalize the
world into X states. I'm not pretending for one moment that Fuzzy Logic is a universal
panacea and can provide all the answers - it has its limitations as does every other
intellectually inspired categorisation system, including metaphysical systems.
> HORSE WROTE: 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: 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:
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).
> HORSE HAD WRITTEN: But as I said above, Bivalent logic is not the whole of
> Logic only a part of it. Logic may pertain to all descriptions but it is
> certainly not the case that description are of necessity binary -
> additionally, it is not the case that logic (any or all) can provide a
> complete description of the world, far from it. You seem to be employing a
> circular logic here. :-)
>
> ELEPHANT: Look, binary classical logic does not imply a binary description.
> There is "I don't know". There is metaphor (whether we can or cannot have a
> literal translation of metaphor is an interesting question). There are all
> kinds of descriptive devices and states of mind. What's at issue here is
> not how many varieties of psychological state there are, or how many ways
> there are of expressing insights, but rather how many of these states and
> expressions we should regard as truth-values in logic. You want to take the
> "I don't know" or and turn it into a formal state in logic. In this, I
> maintain, you are taking the paradigm case of a question, and turning it
> into a paradigm case of an answer. This has to be wrong, because it takes
> away the whole motivation for inquiry. None of the James/Dewey stuff on
> value and the pattern of enquiry could possibly make sense if the "I don't
> know" of classical logic is turned into one of three "I know"s in fuzzy
> logic (True/ False/ True and False). If "true and false" was any kind of
> answer, what would be the point of, say, discussing which of us is right
> about logic?
HORSE:
Again you bring this mysterious third state into Fuzzy Logic. As I said above, your "I don't
know" (non)state is the sound of classical logic going tits up. Classical logic does not state "I
don't know" this is a recognition by the logician that the system has failed. Fuzzy logic
assumes that there are as many states between True and False as the are fractional
numbers between 0 and 1. But any (fuzzy or classical) logician worth his salt also realises
that there are aspects of the world that are not describable by intellectual systems - e.g.
religious experience.
>
> HORSE WROTE: If you choose to believe that classifying the world in Black
> and White terms is the best way then you go right ahead and do it. What you
> say above is fine for something like Logical Positivism - and again Logical
> Positivism has its uses - but for most people the world consists of a
> multitude of colours in between black and white. Intellectual systems that
> insist that everything can be forced into one of two boxes inevitably fail.
>
> ELEPHANT: So you think I'm a logical posititivist! (This falling of chairs
> business is getting tiresome). Accusing someone of that is almost as bad as
> shouting across a crowded conference room "Cartesian!". I think I seem to
> be a bit of a Platypus for you (my elephantness notwithstanding).
>
> I'll repeat what I said: binary logic does not imply a binary description of
> the world. What it implies is a binary description of the *logical* world.
> 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.
> 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:
Again the 3 values!!!!!! Fuzzy logic is multivalent or, if you prefer polyvalent.
>
> ELEPHANT HAD WRITTEN: ....it is the "I don't know" of classical logic that
> is paradigmatically the "realm of possibilities". The whole point of the
> third value in fuzzy logic is that it is a value, an answer to the question
> "what is the case", an affirmative cocksure "I know!", which puts it firmly
> in the realm of actualities, not possibilites. And, as I have already
> pointed out, this kind of answer is of great danger to the continued
> stimulation and development of enquiry: it precisely closes down all the
> really valuable intellectual possibilities.
>
> HORSE: What 3rd value in fuzzy logic??? Do you have any understanding of
> Fuzzy logic at all - I honestly don't mean to be rude of insulting here but
> it seems that you are disagreeing with a particular position without any
> knowledge of what you are disagreeing with.
>
> ELEPHANT: Well now, you might be right about that - my having no idea what
> it is I'm disagreeing with, I mean. You see, all along you and Chris have
> been talking about 'True' and 'False' not capturing the whole picture for
> logic, and about there being in fuzzy logic this other state or logical
> value: 'True and False'; or the "in-between" as you call it, in the passage
> below. Well now, if that's not a third truth-value, and if you aren't
> proposing a tri-value logic, then I really have no idea at all what it is
> you are saying. I don't mean to be rude either, but I have to say that I am
> very puzzled by your remark. It seems to me that as soon as I get you
> pinned down, as to where you are in this argument, you open some hatch in
> the roof and fly off in an escape capsule.
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.
> 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:
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.
> HORSE WROTE: Classical logic assumes that the world is or it is not a
> particular way - there is no in-between. This assumes a certain naivety in
> how the world is constructed and attempts to reduce the beauty and
> complexity of the world to one of two states whilst denying that it is not
> possible for any other state to exist - it has defined away anything other
> than the True or False state of the world and denied that anything more
> complex can exist.
>
> ELEPHANT: I think I've said something about this before. 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.
Definitely not a Kantian (noumenalist or otherwise) - well not to any damaging extent anyway.
Logical systems are useful tools that can illuminate certain static components of the world.
But the static components (patterns of value) are but one aspect of the world. Systems in
general (and these are nearly all classificationist - i.e. 4 levels of static patterns of value) do
not and cannot describe the dynamic component of reality - this is something that can only be
experienced.
> 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:
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. Within classical logic there are two and only two
compartments labelled True and False Within fuzzy logic there are two ends of a corridor
labelled True and False and a whole lot of space in between.
> 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:
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.
>
>
> 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.
Horse
PS I'm not around for a couple of days so don't expect a reply to any further points till
Saturday (assuming I'm not too hungover).
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