Post on 30-May-2018
transcript
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Well-posedness in Philosophy and the Sorites problem
I. M. R. Pinheiro1
Abstract: In this piece of work, we remind people of the well-
posedness theory for philosophical problems to then judge
whether the Sorites is a W.P.P. in Philosophy or not and fix it to
the demanded scientific standards in what is found currently
escaping them.
Key-words: Sorites, well-posedness, problem, Philosophy, Science.
1. Introduction:
One could easily think that there is no need to even think about what a
solution for a philosophical problem is. However, we could not find any
clear-cut, step-by-step recipe, on how to check on whether a
specific solution proposal to a philosophical problem is, in fact, an
actual solution to the problem or not. With this, we have decided to
write this recipe ourselves.
Well-posedness is an interesting term, usually found in the
Mathematics literature. In fact, it is probably the case that the vast
majority of people in Science simply make use of the expression
referring to problems that are not well formulated, in any regards,
without really having a paper or a book in their minds where the
1 PO Box 12396, ABeckett st, Melbourne, VIC, AU, 3000. E-mail address: mrpprofessional@yahoo.com.
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subject has been dealt with, simply for intuitively knowing they should
be better, or more objectively, written.
In this sense, well-posedness is about clarity of the data brought by
the problem, clarity of intentions, and objectivity. Anything which is
not stated in top objective sort of lingo should not be scientific enough
to be debated over.
In this little article, we endeavor to provide written guidelines for both
the writing up of philosophical problems and for judging the validity of
their proposed solutions, or efficacy power contained in them, in terms
of 'attacking' what is needed.
Not having found any other article on the subject, we have decided to
assume it is a novelty in Philosophy. As a consequence of that
assumption, our article may end up being a repetition of what has
already been stated by someone else, but with our own words.
The sequence of presentation follows:
a) Well-posedness for philosophical problems, theory;
b) The Sorites problem and why it is not found well-posed in the
literature so far;
c) The fixed Sorites problem, fixed to the demanded standards of
Science, so that the problem may be considered by a philosophical
audience of scientific value.
d) Conclusions;
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e) References.
2. Well-posedness for philosophical problems
Basically, before departing to facing solutions, one must make sure the
own proposed problem is clear enough as it would be necessary for it
to be well addressed.
The conditions for a problem to be acceptable as a problem in
Philosophy would have to be at least:
a) The problem must present, in a very clear way, all possible
enthymemes contained in it.
Therefore, in a well-posed philosophical problem (or of any other
scientific subject), no enthymemes should ever exist, unless they
are clearly irrelevant to the understanding of the problem, or the
needed addressing of it. Notice that no mistake may possibly be
found, in what regards this item, if even the enthymemes thought to
be irrelevant by the writer of the problem are spelled out. Why this is
necessary is a question which has got an easy answer: Basically,
enthymemes are non-declared, or silent, assumptions, all made by the
writer of the problem. However, nobody trying to solve the problem
will be able to enter the brains of the writer, and it is simply unfair not
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to provide the possible solver of the problem with the same tools
which are available for the writer of it when time to try to solve it has
come. Enthymemes are the same as silent talk, may easily differ from
individual to individual. Besides, true Science is not about puzzles, but
about very objective sort of proposal of problems, so that the largest
number of people as possible may try to solve them. Science is about
what those famous people, who worked on Classical Logic terms,
thought of: Most objective lingo ever, top effectiveness in
communication. Why? Because the objective of Science is not creating
problems, but solving problems. It is not that it does not end up
raising them, usually by accident, but its main objective has to be
solving existing problems, hopefully problems for a large number of
people on Earth, for Science also must worry about priority and
relevance: Nobody in it should be interested in solving first a problem
which is not that relevant if there is another one, more relevant, which
may be solved by them, quite trivially;
b) The language-terms, used to describe the problem, should be
as objective as they can possibly be.
Any extra non-objective complication is going to easily exclude free
thinkers to address the problem well. The intention of Science cannot,
ever, be preventing any possible public from proposing a solution. It is
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actually true that people who are brand-new to a field tend to present
many more innovative solutions than the others. This proves that a
new point of view, without paradigms, or with less paradigms, always
helps the solution to come quicker. Therefore, the language in which
the problem is described should be as objective and as simple as it can
possibly be. Several thinkers studied clarity in language; Russell and
Friege are just a few of those. Their theories may certainly be
considered in order to judge whether a very long standing problem is
well-posed before giving it international status;
c) The area of knowledge where the problem is located should
also be explicitly mentioned in the problem proposal, so that
people know what to study before trying to address it.
That saves time both of those addressing the problem and of those
proposing it, or even of those checking its proposed solutions, what is,
obviously, an intentional quality in Science: saving time, working
towards optimization in every possible way.
After guaranteeing the criteria for the problem to be considered well-
posed are satisfied, one may then check the possible solution for a
problem in Philosophy.
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3. On the Sorites and well-posedness:
It is very clear for us that the Sorites problem is generally
presented in a very poor manner, in terms of scientific
standards. Several improvements are necessary to make the problem
both understandable and easily addressable by a broad audience, or
by the broadest audience as possible, which should always be the aim
of Science: Making it simpler, if it can ever be.
In the Sorites problem, there are several enthymemes which should be
unveiled. All a scientific presenter should intend is being fully
understood in terms of what the problem, itself, actually is. Nobody is
able to address a problem that is not well understood. Yet, many will
try and will go wrong, as it has happened with the Sorites until we
have managed to see the problem from a perspective X, different from
the one from which people had been seeing it that far.
Seen from the most basic and objective point of view, the Sorites
problem is not even a paradox, or ever has been. Therefore, to
start cleaning it or making it scientific, the word paradox should never
be contained in its description (item b, section 2). Why?
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Basically, if the premise `adding one grain of sand does not make any
difference' may only be generalized for very small pieces of the
soritical sequence, what is obvious, only where there are no shocking
differences (something like a clear non-heap and a clear heap together
would be a shocking difference), we are left with three types of objects
contained in the same scope of definition (either a clear `heap, or a
clear `non-heap, or a clear `confusional area, blurred region, as
many would put it). If the short sequence of objects, which vary by
one grain, and are indiscernible for the eyes, is entirely contained in a
specific definition scope of some standard dictionary word (heap, for
instance), it is true that there is no contradiction between the starting
and the final object. Therefore, it could not ever be said to be a
paradox of sight. A paradox of sight would be what we have named,
after solved, the Parallax mistake, for instance. Such means that we
would see two things at once and would not be able to tell which one is
true. In the Sorites, there is a confusional area, which could be told to
correspond to seeing two things at once, conflicting things. But nobody
puts it that way! If they were seeing both a heap and a non-heap,
however, at the same time, then it would have been a paradox of sight
for the share of the sequence where that has happened. Notice that it
will never happen for its totality, therefore we are unable to state there
is a paradox of sight over the Sorites, such happening only, at most,
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over part of the soritical sequence instead. Notice, as well, that in a
paradox of sight, if the right referential is applied, we would be able to
work out which sight is correct, just like in the Parallax Mistake. Such
is definitely not the case in the Sorites
The reason why the Sorites problem has been presented wrongly so
many times is because it has been intended for general entertainment,
not for Science, but scientists of Language, or Philosophy, never
bothered fixing its presentation to the standards demanded by Science
so that it could be included in the list of scientific problems in a proper,
or ethical, way.
A paradox in communication would demand that one starts with
one piece of information but the audience understands it precisely the
opposite as to what has been originally intended by the presenter. It
cannot be a paradox in communication either then, because one may
assume that the audience always understands the problem the way it
is posed, not the opposite way.
It could be a logical system paradox of the sort `false and `true,
for instance, such as the Liar Paradox (If I told you I always lie, would
you believe me?), but there are no truth values involved. Even to
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make the presentation of the Sorites problem scientific, there is no
need to assign any truth values to each one of its parts; it is all about
language in its purest human part!
It cannot be a paradox in language either because it is precisely the
same as asking the audience how linguists work, in terms of deciding
on a certain scope of definition for a word, that is, the actual question
contained in the Sorites, or its scientific question (the simplest way to
propose the problem, already explained why this would be the
scientific way) is: What is the most precise definition for the word X
does it apply to this object, Y, as well as to that object, Z? The term
paradox demands a conflict of some sort, and such does not seem to
exist in language lingo inside of the Sorites.
The linguists, therefore, are the only people who would really be
entitled to address this question, or judge its addressing, in the best
scientific way, once that is what they live for.
But if that is what they usually do, how can that possibly be a
paradox? Do they really find it hard to decide about it, or a new
dictionary comes up updated every year, with not a single issue
directed to the general public about how `in doubt, or `confused,
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they were when deciding on the word `Xs scope?
Basically, it is widely known that if there is any doubt as to
whether a term (which is also a lexicon word) applies or not to
a situation then it does not!
Conclusion, which is obvious, is that if there are any doubts as to the
application of the word `heap to a certain amount of sand, in any
possible way (confused speech (not yes or no, exclusively)), then it
does not apply to that object ever, until there is no confusion anymore
for the vast majority of the people involved in such a decision!
Therefore, `heap means all situations in which the vast majority of
the people in the (possibly selected) audience has said exclusively
`Yes, it is a heap; `Non-heap then means everything else, until the
linguists accept another word called `non-heap in the dictionary, what
they have not done so far (that decision would be ridiculous and non-
scientific, and we did find at least one dictionary where the author has
included such, probably for willing to solve the Sorites and noticing
they were unable to do it. Notice that this is so absurd it would
demand every word in the dictionary to contain a dual in it: Red and
non-red, man and non-man, and etc. It is obvious the case that
whatever is not there, in the positive definition of the word, is a
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non-'that specific term', instead. Also, individual groups of linguists,
even groups, may diverge in their acceptance of terms, such as in this
case, 'non-heap'. Nonetheless, what counts is whether they keep on
printing the dictionary with that term or not, and they have not
continued printing 'non-heap' as a dictionary word, decision which is
simply logical). What gets defined is what a `heap is, the words `non-
heap not appearing in the dictionary at all. Therefore, if `non-heap
gets to be the opposition to `heap, `non-heap is everything that
could be a heap but is not, even a shirt Basically, if tomorrow the
whole World, or the majority of it, wishes to say that a `heap is not a
bunch of something anymore and it is, instead, the absence of
anything, that is what the linguists will take it to be, so that references
are not immutable, or even the referents, and one may easily find
several theories on that (Friege's, Russell's, Wittgenstein's, and etc.).
It is then not a paradox in language, not a paradox in sight, not
a paradox in communication, or a paradox of any other sort:
absolutely not a paradox!
It is more of an allurement to show how interesting the work of the
linguist actually is.
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Because Science is not there to `trick' people, as a commoner would
be doing when presenting something in a very similar situation to a
`busker', in Australia, to attract attention, the problem must be well-
posed. One may easily notice that just by clearing it from any possible
distraction that is not scientific, it gets as simple as to coincide with a
very well-known and old professional area: Linguistics.
In this case, unfortunately, there was never a `new striking problem,
just an unskilled writing, of a `buskers' presentation, of something
that could not ever be seen as scientific, or skilled.
This way, one could be stating that `adding one grain of sand to the
previous amount of sand does not make a difference' but one would
also have to state that `adding thisxamounts of grains of sand to the
first bunch of sand does make a difference' (when the area of no clear
distinction named as blurred is over, one may pick the next
element already, to compare with the first one, or any of the others in
the blurred area, where it all seems to fit in the same scope of
language wording/eye sight) at some stage, because we see clearly a
`heap and a `non-heap there, in those two randomly chosen
elements. The two previously mentioned premises are our
enthymemes that should be clearly stated in the problem description
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so that nobody will ever get confused. It is not a novelty we mention
them, other people have done such. Notwithstanding, we actually have
made it clear that the solution can only be (and proved it) in the scope
of the purest Philosophy of Language, if in anywhere logical, that there
is, in terms of it being totally human, and may only be addressed from
a linguistic point of view (the experts in writing dictionaries then being
the most adequate people to do it). The issue on whether the
application of the term starts here, or there, is then addressed with
the linguists solution (so far their decision, which, if changed, may go
against any possible common sense and logic): If there is confusion,
for the vast majority of the people in the audience, in terms of uttering
either `it is or `it is not, with no mistake, or they does not know
(considering an audience of suitable people for the term under
observation, like do not include blind people when we need to judge
colors), then it does not apply! This is precisely how we described our
solution in the precursor paper with `Semiotica. However, here, we
actually exhibit more developed argumentation as to defend its
standing as a full solution, much harder to be objected to or, hopefully,
impossible. We then state that the solution would be passive of
updating to fit the linguists latest decision theory on semantics.
Consequently, the Sorites problem, if ever presented correctly, is
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neither a new problem, nor a paradox (Note 11): It is the same
problem, faced by centuries now, that the linguists writing our lexicons
deal with, all holding very solid theories about its solution.
Linguists theories on lexicon sigmatoids will not relate to computers
logic, or Mathematics, and the question is always a much more generic
one: How can we define a word, in a dictionary, so that the vast
majority of the people on Earth accepts that word to be what we
declare it is?
With this, the problem created, or raised, if any, because it would be
no novelty as well, would be a standard problem, related to a very
specific and old profession, so that the Sorites could never be seen as
a scientific problem at all, in an isolated manner: It is at most an
example, an allurement, as we have already stated. Or, if the linguists
wish, a very nice name for what they must do, in their work, when
writing lexicons, each and everyday.
4. Proposed step-by-step guide to judging a possible solution
to a philosophical problem:
1) Is the problem well posed in the rigors of Science?
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If the answer is yes, go to number 2. If the answer is No, re-write it
first, following our previously proposed guidelines for scientific
problems (no enthymemes, most objective language terms as
possible, naming of the precise area of knowledge to which the
problem belongs), to then proceed to step 2.
2) What is the most refined area of human scholarship to which
the problem belongs to, and into which generic group of sub-
areas does it fall?
2.1) if it does not belong to Philosophy, forget it! If it is inside of
Philosophy, the entire problem should now hold very logical and simple
description/sequence of steps.
2.2) if the group is, indeed, Philosophy, and the problem has not been
dropped at item 2.1, what part of Philosophy does it belong to?
First, one tries the top possible reduction, the most objective way of
describing it, once that should be the objective of Science. In the case
of Philosophy, the top possible reduction would be into Classical Logic
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terms.
Next step is checking on the possibility of another logical system, more
complex - a Non-Classical Logic system - being able to describe the
whole problem in scientific terms; still Computer `Science. Why?
Because any logic has got a system of reasoning assigned to it, and
any system of reasoning, fully described in natural language, in precise
rules of inference, may be fed into a machine.
If decided that the problem cannot, ever, be totally reduced to the
Computer `Science level then it might belong to some specific area of
Philosophy: Language, Science, and etc. It is necessary that we
determine precisely which one.
3) If it belongs to Philosophy of Language, for instance, and it
cannot be reduced to the most objective lingo of language, to
any computer-friendly logical system, then it must be in the
purest scope of Philosophy of Language, the Philosophy
properly stated, purest: Totally human.
In this case, the problem may only be well-addressed if referring
purely to theories in that particular area, so that a solution must be,
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first of all, checked against this criterion: Is the solution using tools
from inside of the most reduced area to which the problem belongs to
in Philosophy?
If it is not, the solution is discarded immediately; if it is, number 4
applies.
4) In being inside of the right area, is the solution something
based on accepted theories, or the theories being applied in the
proposed solution have suffered many objections in their trials
of acceptance by the targeted scientific audience?
If there were many objections to any of the theories involved, the
same objections are going to be objections to the proposed solution.
The solver must then have explicitly addressed those for their solution
to be passive of consideration for refereeing.
If there never has been any strong objection to the theories of the
solution, or the theories have been popularly applied for many years in
practice (for instance, lexicon theories), then it will be a definite
solution in case it addresses the issues of the problem with perfection.
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5. Further considerations and re inforcement of what has been
stated so far by us :
1. Apparently, the presenter of a Sorites problem has never
deserved to be listened to by a scientifically educated
audience at all: Blame those who have not identified a confused
speaker and have accepted the Sorites as a paradox, creating
problems for us to think of!!!!
If one takes it to be a paradox for the eyes, it is not suitable, once
Parallax ( Note 12 ) is a paradox for the eyes but we can actually
prove it is such with our own good eyes. Same will never happen with
the Sorites: It is not our observation that is faulty at all, or our
judgment. If one takes it to be a paradox in language, it is again not
suitable, once, in language, there is no confusion: It is not the case
that we then start doubting the concept of `heap and `non-heap at
all, taking the original proposal into consideration.
What could then be taken into account, in language, as paradox, in the
sense of implying contradictory conclusions, would be the if..then. We
could easily start doubting the if...then from Mathematics, and
challenge the whole World of Mathematics/Classical Logic that way. But
we then understand that the reduced scope of meaning, attached to
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the Maths lingo, is not all that if...then may mean in language by just
visiting the simplest dictionary, or book, on writing. Therefore, where
could a paradox in language possibly lie?
Is it actually possible to find a single paradox in language? We
actually challenge you to think about this. The so-called Liar Paradox,
for instance, seems to be a logical paradox, not a language paradox. It
is also the case that, if re-written properly, it will generate the same
sort of reasoning that we expose here, or very similar one for its
solution. And we shall endeavor to try such, as possible extension of
our results for the Sorites. Basically, there is one possible
enthymeme involved in the Liar Paradox: `but in this previous
assertion, I did not (lie)'. If that is correct then everything uttered by
that speaker should always be false, apart from the particular time
they have uttered that they always lied. Therefore, there is absolutely
no problem involved in believing them at all. The issue about believing,
however, is, once more, a personal issue, and depends on reasoning
which is fully detached from whatever happens in reality. This way,
there is no point in even analyzing that logically, unless we know the
mental attitude, as for a recipe, for that particular person who is the
object of the speech of the first one. If they also lie when they say
they always lie, then they do say the truth sometimes. In this case,
whatever follows is useless for any logical purposes, or inferences,
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unless we know all enthymemes involved, and they may reassure us of
when they lie or not. Basically, in dropping the logical acceptance of
the assertion, we are still following the `lexicon reasoning', that of not
accepting whatever is contradictory, in the positive way, in the
definition. Interesting enough, the lexicon reasoning, as we have
decided to name it, seems to be the recipe, or underlying reasoning, to
make every possible language paradox solved in Logic, when they do
not belong to the most objective scope of it (logic, Computer
`Science).
Well, if the paradox is not in language, is not in our observation, or
judgment, or even in logic, where would it possibly be? Perhaps in the
own ontology of the object, or in the conflict between a premise, which
states that adding a single grain does not make any difference, and
the conclusion. All we can say is that the premise does vary, but there
are enthymemes because, by the time of the third step, it is already
two grains, and not one anymore, if you regard the first step.
Therefore, the premise is always being rebuilt, in what regards the first
step, but remains the same in what regards the previous one, so that
there is no paradox at all: as much as in Physics, it is all about the
referential. It is all true and fine. If one thinks it is the ontology of the
object which is paradoxical, it is then missing pointing out why. Is it
the ontology of `heap, or the ontology of `non-heap? Do you actually
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have doubts about those? It actually seems true that nobody doubts
the first and the last step in the Sorites so that nobody, in the whole
Universe, has ever challenged what a `heap and a `non-heap is, in
the most astonishing conclusion of all: We do have a universal concept
of what both ends mean in a Universe where even blind people
inhabit!!! Thus, the paradox could, perhaps, regard the objects
splitting one end from the other. However, is it really plausible that we
assert the own object of observation bears inconsistencies or it is all
about the relationship between our minds and the object? Quite
trivially, the object does not bear inconsistencies and if we think it
does, it is all due to our ontology, not the objects ontology.
When the inconsistencies are found inside of the human mind, all we
usually need is a decision theory, that is, philosophical foundations in
which to base ourselves to make non-regrettable decisions.
Via the simplest observation of human->machine communication
differences, we get to understand what is what. Learning that a
computer and a normal human being cannot, ever, be thought to be
the same, or a normal human being be thought as something which is
reducible to a machine [2, Turing contest], makes us understand
why there is much more than what is contained in a logical
system in the world of consistent theories, which may be
expressed by us somehow. And that extra is certainly contained in
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Philosophy, but not in what could possibly be encompassed in any
logical system rules. If mental processes were fully, and accurately,
transmitted to others, that is, Communication/Language could ever be
machine-friendly, why would couples ever divorce? Where there is full
understanding and will to be married, why would people ever fail, once
they know precisely what the other wants, or expects, and how to do it
right? We are sorry to think that there are a lot of superficial thinkers
out there doing Philosophy, and publishing, to keep people occupied
with this sort of thing for so many years now. It is certainly true that
Psychiatry and Psychology will explain it all: The need that the whole
World gets presented in a way it may fit logic. Why? Well...drugs,
detachment from others and reality, shortage of interest in things that
are purely human, too much wrong Army oriented formation (war,
strategy, more strategy )...shortage of being charged on being socially
useful...Thus, the Sorites may become a paradox for those who see
the World, or the human kind phenomenon, as passive of confinement
in a box, contained inside, or equal to, the logical universe.
Nevertheless, it is clearly not a paradox for those beings who are able
to accept and deal with the complexity of human existence, certainly
extrapolating, in much, the machine complexity.
2. We have then managed to provide people with the desired
output: `Yes, it is a heap/I agree' or `No, it is not a heap/I
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disagree'. This is the outcome for each observer, once if it ever
happens that they state both or neither, or something with the
same effect, we choose the second option, a `No, it is not',
decision provided by the best dictionary writers reasoning, that
is, linguists': People working on the scope of the Philosophy of
Language, once we have decided the problem belongs there.
3. `One grain of sand does not make any difference' is/is not a
fixed premise valid for all propositions: We have decided that
this is not the case.
This sentence may only be regarded as a premise if the other
premises involved are neighbor utterances (face neighborhood
as that in Mathematics). Otherwise, we have to be re-building
the premise to account for as many intermediary grains as the
ones added to go from the initial premise to the last considered,
taking into consideration the presenter always works with only
three basic premises in their inferences. Easy to see that, this
way, there is absolutely no paradox in what regards the truth-
values of two of the premises, once the grain step is always true.
It is just a natural thing to judge and see, not a paradox
anymore, that is, presented correctly, with no enthymemes, it is
really not a shock.
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4. `I am also confused at the end of the presentation as much as
you, presenter, seems to be/I am not, you are an idiot'. Sorry to
state we have decided to state that the presenter was an
actual idiot, that is, a very - and intolerable - confused speaker.
6. YES, WE DO HOLD A DEFINITE SOLUTION FOR THE SORITES
PARADOX. AND WE ALSO DARE PROVING THAT IT WAS NEVER
A PARADOX IN ANY POSSIBLE SENSE!
We seem to hold an actual solution to the problem in every possible
sense: There is a definite line where the term should stop being
applied, or start, there is no doubt as to where the line lies for each
person being submitted to the Sorites, and there is allowance for each
person to have their own solution for each predicate, and each object,
that is, each soritical sequence presentation, so that it is not an
imposition to the general public and even people with problems in the
judgment (meaning unusual thinking) could express themselves
correctly in logical entries. There are also no gluts or gaps of truth-
values, once it is either the case that a soritical sentence is TRUE, or it
is FALSE, that is, the truth-values accepted, and always possible to be
assigned, by both the 'utterer' and our translation system, are the
classical ones and, in Classical Logic, there are no gaps or gluts.
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We also do not commit the same mistakes made by Epistemicists, or
Epistemologists, because we never say there is a universal line, and
we actually believe this can only be the most serious mistake of all.
First of all, there is no way a person can believe they are, ever,
receiving what any 'utterer' has intended were to be received by the
listener. It is no surprise that there is so much available in the
literature about communication not being effective and, just by luck,
someone speaking to their own race, closest person, same language,
as well as cultural background, that is, with top similarities and things
in common, will ever know, for sure, and with certainty, that they have
got the idea intended by the 'utterer', just like in the kids' game:
Cordless telephone!!! - You think it is not good enough to make use of
kids' games to explain? Talk about that with the greatest philosophers
of all, and also our best logician ever: Jesus Christ, son of God, That
who knows it all...even what you think nobody else knows, or sees!!! -
Apart from that, some people might write that another account
actually states that the object itself has got an ontology and,
therefore, a very precise color, for instance. We do not ever deny
something like that, that is probably totally true. However, it is never
accessible to human beings at all, once Language is not enough, and
this is the broadest thing we have nowadays, in terms of describing
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objects. A picture is also not good enough because of us - who are
humans - and, therefore, not able to agree in our judgments over the
World objects. This just means that the ontology of the object is
something such as God: Totally perfect but inaccessible to human
beings apart from transcendance. To divert a bit further, even the
name of God is doubted until nowadays. God Himself, in the own Bible,
states that we should refer to Him as `God of Abraham, Isaac, and
Jacob (Matthew 22:32), that is, God, Himself, feels the need of
presenting Himself as someone attached to other people. One must
understand, then, that it is only possible to refer to the ontology of an
object, even humans considered as such (for a quick thing such as
beauty contests, for example), by associating that object to
something else - a reference - just like in Physics. What is actually
meant is that Abraham, Isaac, and Jacob, actually knew who God is,
and what He is precisely like, but we are just going to dream about it,
and always state that that is the `God of Abraham, Isaac, and Jacob'.
With colors, or predicates in language, there is only a dream we can
actually express the ontology of the object perfectly well, and in
agreement with our educated observation. But we can easily say that
that object is of the `red' stated by `Carla, Marcia, and Pedro, for
instance, with no possible logical inaccuracy. Therefore, we deny the
universal line, usually defended by both epistemicists and
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epistemologists, and simply present a way of speaking about a
relativistic, or democratic, line, in place.
The color has to be attached to an observer, then, just like our God
from the Bible. With this development, all we meant is that the
solution must be personal, and attached to the observer. We could also
come up with an argumentation on the lines of Semantics, another
part of Philosophy of Language (but we actually did, only without
mentioning it...). In face, here we have a sort of walked through
Wittgenstein, Russell, and all the best researchers in the field, skipping
their technical lingo. We are basically writing about referent and object
of reference, or designation and designated, and etc. In our own
terms, about sigmatoids and World references.
Regarding the Sorites Problem, the issue that makes philosophers
think the most is the higher-order vagueness issue. Basically, the best
criticism that could be made, in what regards that and our solution, is
that the reduction of our choices to No and Yes would bear some lack
of naturality, or precise definition/scope. However, we believe to have
already addressed these two possible items to perfection.
Therefore, because we have addressed every single issue with
previously proposed solutions to the Sorites Problem we have solve it
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for good.
7. IS THE SOLUTION TO THE SORITES PARADOX SOMETHING
LOGICALLY USEFUL? IF SO, IN WHAT SENSE?
The solution to the Sorites paradox is something logically useful in
the sense that any progress in human reasoning, or
understanding, may be told to be of broad scientific future use.
However, there is absolutely nothing extra gained in Logic with the
specific solution to the Sorites paradox besides progression in
reasoning. The simple fact that we tell people the problem has
emerged because people understood things wrong helps Logic
progressing, once it helps logicians and researchers to observe things
better next time. Notwithstanding, our solution does not bring a new
logic: It simply explains all the different logical systems involved and
explores one of them, which must be of purely philosophical nature,
the logical share of the human reasoning, which may not be found
ever entirely confined to any formal logical system.
Pure Human Reasoning (P.H.R.) is that part of reasoning in which
there are feelings, emotions, or any sort of unreasonable (for
instantaneous observers) individualized deductions, inferences,
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premises that, of course, cannot, ever, be translated into
computational logical systems (so far, up to our current knowledge on
how the mind works in conjunction with what is deduced/felt/observed
by an individual). The rest is also human reasoning, but may be told to
be computable, or machine-friendly, like Classical Logic is.
It is annoying to understand that, at the end of the day, there is
absolutely no language paradox at all, it all derives from wrong
observation and wrong premises-understanding, that is, actual
premises in language, but faulty logical premises due to the
overlooking of the fact that language is far more than the logical
systems in place, and not all of it may be translated into logical lingo.
That is obvious, once a word in English, one of the most objective
languages in the World, bears several meanings, even in an English-
English dictionary. Furthermore, different linguists may hold different
interpretations for any dictionary word (from an individuals
perspective). That just means that we can only hope communication is
successful, and this is obviously why people tend to have extensive
courses on how to write, read, spell: To have more chances of
communicating what they actually want to the broadest audience as
possible. It is obvious then that, even if one has two native English
speakers speaking, there is still the need of understanding their
feelings, when they speak, to grasp the whole meaning behind it, so
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that even English-English communication is almost impossible, in
terms of full effectiveness.
One may state they are communicating with others, but all a
Logician, or a Science person, would be able to state is that
they are making efforts to.
There are even books, and books, written on the subject on how
effective communication happens. This way, it is very easy to
understand that language is also symbols, and so is a logical system,
just a far more reduced scope of symbols. If a logical system has got
less symbols available than the natural language, it is just scientific
that it is impossible to even think of translating language into a logical
system, as a whole, because the only possible way would be an
overlapping of ideas converging into the same symbol. Furthermore,
there are the enthymemes, sentences usually omitted in
communication when it happens between people who know each other.
The enthymemes make effective translation impossible, even if it is in
writing. And it is obviously the case that there lies the beauty of
cinema, or plays: The much variety of interpretation a single action of
an actor, a single word, generates. Everyone knows that `To be or not
to be' has been giving way to an infinite number of texts around the
World and it is just six words...
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opposite to the 'utterer''s understanding of the problem.
Conflict between receptor and transmitter, paradox, once
communication is supposed to occur the way it was intended by
the transmitter.
Paradox, in Human Communication, to the side of interpretation which
is passive of writing, still belongs to the Philosophy of Language, so
that we are still correct. And it is again not possible to label it as
`Sorites paradox' because if it belongs to the scope of Communication
then it should be the `problem proposer's paradox' (in
Communication) to which an example is the Sorites problem. The
obvious mistake is then having logicians, who are not from
Philosophy of Language, thinking they have a say there: They don't.
Unless they are keen on writing in terms of the Philosophy of
Language, that is, with all the specific lingo and scholarship it
demands, logicians really have no say in the Sorites problem.
The Sorites paradox, as our conclusion tells, is basically a
motivation for the listener to think of the beauty of the work
developed by the linguists. The basic question is: How hard is it to
translate thoughts, as well as their expression, into something
accepted by most of the people on Earth as a lexicon? How to do it?
Subtracting the Sorites from Logic, and Mathematics, leads us to a full
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understanding of its beauty. It is as interesting as `to be or not to be'.
One could write a whole library of books with just that inspirational
thought: That is basically it.
We believe the solution to the Sorites paradox is there to make
logicians, and mathematicians, see the limitation of their work, and
accept that Language is far more than Logic and Mathematics, not the
other way around. One could easily say that Mathematics is the most
reduced scope of Logic, and logic is the most reduced scope of
Language. Mathematics applies Russell and Friege's logic, the most
objective way of communicating, which has ever existed. So much so,
there are several mathematicians who are well understood if they give
a talk in, for instance, Romanian, but write good self-explanatory
Mathematics lingo on the board, or print it. That is a clear example to
show that Mathematics is the Universal Language, that Language
in which communication is always possible and effective. Logic is the
third choice, following logical systems, or computer-friendly systems.
Pure Language is the messiest one, in which only by means of luck one
understands each other. And thought...don't even think about it! We
have proposed that logicians worry about things they can do and are
actually useful to human kind. For that end, we advise the reader to
check on [9].
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That is because there are several things in this World: It is obvious
that calculations would not be the only ones where Logic does apply.
The problem, of course, is finding out what, amongst all this universe,
is truly relevant, so that if person X, as a Logician, worries about it,
the whole World is going to be thankful, and willing to pay loads of
money for any result X ever gets. Basically, mental diseases seem a
wonderful way to go, even if to prove that, with some mental labels, it
is better that they only exist in theory and are never applied to a
subject (lexicon logical decision when there is doubt). Medicine should
be a logical thing. If it is not, there is no point. It is time to interfere,
yeah, but not with language, which is so well structured, as a piece of
Science, and so wonderfully explained, as well as founded. It is time to
interfere with what lacks perfection, as we write in [9]: Whatever is
perfect, like God, we should just bow for it, and respect Let go.
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8. Notes
Note 1 It is not that Dr Casti has declared that this is his intention,
literally. We simply infer that from the way he is able to deal with
higher-order mathematical concepts (popular way). See, for instance,
[2].
Note 2 Odd enough, we had this really well known Philosopher, whose
specialization is Logic, with more than one hundred published papers
nowadays, demanding we presented the problem in mathematical
terms. Sometimes, one must just do it, given that those who truly
matter, in terms of being convinced we hold a solution, seem to need
us to do it. In the world of Science, as we see it, there is very little
which is really scientific. Science seems to have regressed in its power
and scope, not to say understanding.
Note 3 The Mathematics used by us is not wrong, but it is simply the
case that the problem escapes its scope completely and any trial of
representation of it, in mathematical terms, is doomed to failure, as it
is easily proven by all objections presented to the solutions which have
made use of mathematical tools to describe the own problem so far. It
is easy to understand that a problem lying in a larger set, with
elements in the complementary set of the smaller one, cannot possibly
be fully described and should not be even partially described in terms
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of the symbols for the smaller set. The explanation is very easy to be
understood, but we must spend a few papers doing such in order to
convince those who could possibly doubt it, as our so illustrious
Philosopher/Logician, mentioned before, because, once more, that is
how modern scientific publications are achieved/settled.
Note 4 See www.geocities.com/trmsorfiap.
Note 5 The name of the person will remain confidential, might be
disclosed for prevention of suit over false statements, but it is a real
case, occurred in Brazil, Rio de Janeiro, more than 20 years ago.
Note 6 The first non-classical system ever created was created
apparently by Nicolai A. Vasiliev, in 1910. For more on Vasiliev, please
refer to [6].
Note 7 Zadeh's introduced his idea on Fuzzy Logic in 1965, as
mentioned in [7].
Note 8 Notice the difference, for us, between the set of all possible
logical events, Logic, and a particular reasoning that bears logical
structure, logic. For example, Fuzzy Logic is part of the Sub-
philosophical-science, Logic.
Note 9 Enthymemes involved in the previous utterances, always. The
Sorites does not state, but assumes that a proposition has been
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understood in the middle of each further progression: If I add one
grain of sand to the `previous amount of existing sand', that is, it is
not that it does not make any difference if added to another member
of the sequence, only in that particular step, when one result is next to
the other in the sequence (that is, uttering `a single grain of sand,
therefore, being added to the previous amount of sand does not make
any difference' is a correct deduction, but `a single grain of sand
added to any amount of sand does not make any difference' is a wrong
deduction from what has been stated or, at least, a wrong
`enunciation' of what has been stated). If we propose a problem the
wrong way, and that is basic scientific reasoning, the solution is not
achievable, once only very well defined, refined in all possibilities,
scientific problems, may be solved the way a lecturer, or proposer, or
presenter, ever intended to be solved. Otherwise, a new problem might
have been created, and it might not even be a well formulated
problem, so that it is just dropped from an exam, for instance. The
Sorites is proposed the same way lecturers would propose problems to
students, so that the same principles, which do include full clarity of
presentation, should apply. Otherwise, just drop it for another better
defined problem. If it is ever to have its solutions judged, or
appreciated, it is more than necessary that it is correctly stated. At
this stage, one could easily think of why we simply did not forget
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about the problem. So it is not a problem at all. However, if a small
group of members of the soritical sequence is considered, `A grain of
sand does not make any difference' would still be a possible
proposition. It is obvious, as well, that the Logic from language would
never allow us to encompass every stated proposition along the way,
stated as `a single grain of sand added will not make any difference if
it is added on the top of the previous amount', in the only, supposed to
be, resulting global assertion `a single grain of sand added will not
make any difference if it is added on the top of any amount of sand`.
If there is a language mistake, there is a logical mistake of some sort,
all encompassed in the Philosophy of Logic which is part of Philosophy.
Therefore, it cannot be accepted as a well proposed, or defined,
problem, this way.
Unfortunately, then, we are limited by the only two possible problem
formulations: It is either the case that we hold a small amount of
elements in the sequence to which the generalized proposition could
be added and, in this case, we would never face heap and non-heap in
the same sequence, or there is no problem worth thinking of. At this
stage, once more, all we, and others, did might sound useless.
However, if one forgets about the `heap' and `non-heap' situation,
and considers the only valid one, all the reasoning used by us is still
valid, so that we are still the only ones to hold an actual solution (it
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does not matter what) to the problem, if ever stated correctly.
In any hyp., in this note, all we needed to clarify is that there is no
chance the Sorites implication is mathematical, ever. And it
cannot be purely logical either (Machine Reasoning), simply
because it depends on human observation and judgment, which
falls inside of the scope ofpurely human reasoning (P.H.R.). It is,
therefore, a language implication only, in the complementary set
of Mathematics and Computer Science, never inside. As a
language implication, and being the whole problem proposed in the
scope of purely human reasoning (P.H.R.), only purely human
reasoning theories would address it well. We do believe that this
is what we do when we decide there must be a `translation
interface', just like there is with literary translation from one
language into another (purely human scope).
Note 10 it is more an evidence of possible proof, once, as
mathematicians, we would never accept any practical proof to be like
that, unless it were possible to guarantee that every possible case is
dealt with by that specific procedure.
Note 11 In [12], one will find the word paradox defined with the
wording below:
Main Entry: paradox javascript:popWin('/cgi-
http://popwin%28%27/cgi-bin/audio.pl?parado02.wav=paradox%27)http://popwin%28%27/cgi-bin/audio.pl?parado02.wav=paradox%27)8/14/2019 Well posedness Philosophy
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bin/audio.pl?parado02.wav=paradox')Pronunciation: \'per- - dks, 'pa-
r -\ Function: noun Etymology: Latin paradoxum, from Greek
paradoxon, from neuter ofparadoxos contrary to expectation, from
para- + dokein to think, seem more at decent Date: 1540.
1: a tenet contrary to received opinion2 a: a statement that is
seemingly contradictory or opposed to common sense and yet is
perhaps true b: a self-contradictory statement that at first seems true
c: an argument that apparently derives self-contradictory conclusions
by valid deduction from acceptable premises3: one (as a person,
situation, or action) having seemingly contradictory qualities or
phases.
Note 12 Parallax mistake, as mentioned in [12].
Main Entry: parallax javascript:popWin('/cgi-
bin/audio.pl?parall02.wav=parallax')Pronunciation: \'pa-r - laks\
Function: noun Etymology: Middle French parallaxe, from Greek
parallaxis, from parallassein to change, from para- + allassein to
change, from allos other Date: 1580: The apparent displacement or
the difference in apparent direction of an object as seen from two
different points not on a straight line with the object; especially: the
angular difference in direction of a celestial body as measured from
two points on the earth's orbit.
http://popwin%28%27/cgi-bin/audio.pl?parado02.wav=paradox%27)http://dictionary/decenthttp://popwin%28%27/cgi-bin/audio.pl?parall02.wav=parallax%27)http://popwin%28%27/cgi-bin/audio.pl?parall02.wav=parallax%27)http://popwin%28%27/cgi-bin/audio.pl?parado02.wav=paradox%27)http://dictionary/decenthttp://popwin%28%27/cgi-bin/audio.pl?parall02.wav=parallax%27)http://popwin%28%27/cgi-bin/audio.pl?parall02.wav=parallax%27)8/14/2019 Well posedness Philosophy
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9. References
[1] Pinheiro, M.R. A Solution to the Sorites. Semiotica, 160 (1/4),
2006.
[2] Casti, J. Five Golden Rules.John Wiley and Sons Ltd, 1997.
[3] Bloom, B.S. Ed. 1956. Taxonomy of Educational Objectives:
The Classification of Educational Goals. Handbook 1: Cognitive
Domain. Longman, White Plains, NY, 2006.
[4] Wolenski, J. Maccoll on modalities. Nordic Journal of
Philosophical Logic, 3(1): 133-140, 1998.
[5] Hippocrates. On Ancient Medicine.
http://classics.mit.edu/Hippocrates/ancimed.18.18.html, acc. Feb,
2007.
[6] Bazhanov, V.A. Ocerki sotsialnoj istorii logiki v Rossii
[Sketches of the Social History of Logic in Russia] Review
author[s]: Werner Stelzner The Bulletin of Symbolic Logic, Vol. 10, No.
3 (Sep., 2004), pp. 421-423.
[7] Priest, G. An introduction to non-Classical Logic. Cambridge
University Press, 2001.
[8] Blair, B. Interview with Lotfi Zadeh. Azerbaijan International,
Winter 1994 (2.4).
[9] Schmid, C. Course on Dynamics of multidisciplinary and
controlled systems. Die Ruhr-Universitt Bochum, http://www.ruhr-
uni-bochum.de/profil/index.htm, 2005.
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[10] Pinheiro, M.R. Exploring the concept of Non-Classical Logic,
preprint located at www.geocities.com/mrpprofessional, submitted,
2006.
[11] Read, S. Thinking about Logic: an introduction to the
philosophy of logic.Oxford University Press. 1995. Oxford.
[12] Merriam-Webster dictionary online, ` http://www.m-w.com/, as
accessed in Feb. 2007.
[13] Weisstein, Eric W. "Gdel's Incompleteness Theorem." From
MathWorld--A Wolfram Web Resource. Accessed on the 20th of
December of 2007.
http://www.m-w.com/http://mathworld.wolfram.com/about/author.htmlhttp://mathworld.wolfram.com/http://www.m-w.com/http://mathworld.wolfram.com/about/author.htmlhttp://mathworld.wolfram.com/