[snip]
[KBL wrote] So then, should we follow Waclaw's suggestion and say that the
number
0.73 reflects our uncertainty about whether he is tall? I would
argue against this. It is too easily confused with subjective
probability. Assigning a subjective probability of 73% to the
statement that Waclaw is tall is very different from assigning a
fuzzy degree of truth of 73%. In the former case, I am asserting
that: (1) there IS a fact of the matter, in the clarity test sense,
of whether or not Waclaw is tall; but (2) I am uncertain about the
facts; and (3) the odds at which I would bet that he is tall are
73:27; and (4) in principle, I could find out the truth of the matter
and settle the bet. But whether Waclaw is tall does not satisfy the
clarity test, because I have not provided a precise definition of
what it means for him to be tall, that could in principle be verified
by anyone with access to the facts of the matter. Therefore, it is
not appropriate to assign a probability to the statement that he is
tall.
[snip] (01)
I think that in these words about Waclaw, and the fuzzy logic discussed in
earlier paragraphs, at least IMHO, the probabilities we are discussing measure
the certainty/uncertainty with which WE KNOW the actual height of Waclaw. That
is NOT the SAME as Waclaw's probability of actually being xx.xx cm tall. (02)
Jack (03)
Kathryn Blackmond Laskey wrote:
>> [SB]...I feel impelled to hurl an insult at this point -
>> > Platonist!
>>
>>> More seriously, it depends on your understanding of language - does
>>> language model the world? or does it talk about the world? (Plato v.
>>> Aristotle, or Tractatus v. Philosophical Investigations if you're in to
>>> Wittgenstein)
>>>
>> [WK] Not sure what you read. What I mean is that even if mvl or fuzzy logics
>> explicitly involve truth-degrees, it may be a misnomer: these degrees
>> reflect the degree of our certainty about the truth of a statement, not
>> the degree of truth of the statement.
>>
>> Suppose that we have the linguistic variable 'tall'. Suppose you assign
>> to it a fuzzy set with a membership function f such that f(x) = 0 if x <
>> 160, f(x) = 1 if x > 180, and f(x) is linearly increasing from 0 at 160
>> to 1 at 180. Suppose my height h is 170. Thus, f(h) = 0.5. Would you
>> say that it is 50% true that I am tall? That the truth of 'wk is tall'
>> is a 50% truth?
>>
>
> [KBL] There are some statements to which one can assign definite
> truth-values. We may not KNOW the truth-values, but the statements
> HAVE truth-values. An example is "The infinite sum 1 + 1/2 + 1/4 +
> 1/8 + 1/16 + 1/32 + ... converges to the value 2." This statement is
> true. An example of an empirical statement with a definite
> truth-value is: "At midnight EDT on 16 May, 2007, Kathryn Laskey's
> university phone number is +1-703-993-1644."
>
> Statements with a definite truth-value are those which pass the
> clarity test. You may recall my statement some time ago during this
> thread that a proposition passes the clarity test if it can be stated
> sufficiently clearly that it is possible in principle to verify
> whether or not it is true in Reality. Of course, for future events,
> such verification must be postponed until the date of occurrence or
> non-occurrence. Thus, the statement, "At midnight EDT on 16 May,
> 2011, Kathryn Laskey's university phone number is +1-703-993-1644,"
> does have a definite truth-value, but no one yet knows it. Depending
> on one's metaphysical leanings, the truth-value may as yet be
> undetermined, but it will be fixed as of 16 May, 2011.
>
> An example from this thread that some would say has a definite
> truth-value is "Waclaw's height is between 169 and 171 centimeters."
> However, there is a bit of a problem with this. A person's height
> can change by as much as a centimeter during a day. A person's
> measured height depends on how he or she is standing -- whether
> slumped over a bit or with square shoulders and extended spine. If
> we are talking EXACT height all the way down to the Planck level, it
> isn't even well-defined. For many practical purposes we can act as
> if this statement has a definite truth-value (time-qualified, of
> course -- Waclaw was at one time much shorter than 169 centimeters).
> If we specify a definite procedure for measuring Waclaw's height at a
> particular time, and then apply this procedure, we will obtain a
> definite answer. We can then assign a definite truth-value to his
> measured height for that particular measurement event.
>
> This brings me to Waclaw's "degree of tallness". Fuzzy logic enables
> us to attach a number "degree of tallness" to Waclaw's height, and to
> relate Waclaw's degree of tallness to his degree of heaviness, to his
> father and mother's degrees of tallness, etc. Fuzzy logic provides a
> calculus for manipulating these "degrees of set membership"
> (equivalently, "degrees of truth" or "degrees of having a property")
> consistently. Actually, there isn't one single calculus -- there are
> several, depending on what combination operators one chooses to
> employ. There is an enormous literature on fuzzy logic, a number of
> implemented fuzzy reasoning systems, and a proliferation of
> applications of fuzzy logic. Many people find fuzzy logic
> interesting and useful, and it has a passionate community of
> adherents.
>
> The fuzzy logic community has agreed to use the terminology "degree
> of membership", "degree of truth", etc. for the numbers fuzzy systems
> manipulate. The fuzzy community has agreed to use this terminology
> because things that have 100% "degree of truth" correspond to things
> that satisfy the clarity-test definition of true statements, and the
> terminology has intuitive resonance for many people.
>
> Suppose we say that Waclaw's degree of tallness is 0.73. Does this
> mean Waclaw "really" has membership level 0.73 in the set of tall
> people, or that it "really is" 73% true that he is tall? I don't know
> what that means. Waclaw's "degree of tallness" doesn't satisfy the
> clarity test.
>
> So then, should we follow Waclaw's suggestion and say that the number
> 0.73 reflects our uncertainty about whether he is tall? I would
> argue against this. It is too easily confused with subjective
> probability. Assigning a subjective probability of 73% to the
> statement that Waclaw is tall is very different from assigning a
> fuzzy degree of truth of 73%. In the former case, I am asserting
> that: (1) there IS a fact of the matter, in the clarity test sense,
> of whether or not Waclaw is tall; but (2) I am uncertain about the
> facts; and (3) the odds at which I would bet that he is tall are
> 73:27; and (4) in principle, I could find out the truth of the matter
> and settle the bet. But whether Waclaw is tall does not satisfy the
> clarity test, because I have not provided a precise definition of
> what it means for him to be tall, that could in principle be verified
> by anyone with access to the facts of the matter. Therefore, it is
> not appropriate to assign a probability to the statement that he is
> tall.
>
> I personally think, therefore, that it is misleading to say I am
> uncertain about whether Waclaw is tall. I think it is less
> misleading to say that (according to a given system of assigning
> fuzzy memberships) he has membership degree 0.73 in the set of tall
> people. The consumer of such statements must, of course, bear in
> mind the rules by which fuzzy memberships are assigned and
> manipulated, and think carefully about whether the resulting
> mathematics applies to the problem at hand. But this is the case
> with any application of any theory.
>
> Kathy
>
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