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Re: [ontolog-forum] {Disarmed} Reality and Truth

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Kathryn Blackmond Laskey <klaskey@xxxxxxx>
Date: Thu, 17 May 2007 11:41:56 -0400
Message-id: <p0611044dc27216f3bc00@[]>
>[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?    (01)

[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."    (02)

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.    (03)

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.    (04)

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.    (05)

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.    (06)

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.    (07)

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.    (08)

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.    (09)

Kathy    (010)

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