well posedness philosophy

8/14/2019 Well posedness Philosophy

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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: [email protected].


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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 à single grain of sand,

therefore, being added to the previous amount of sand does not make

any difference' is a correct deduction, but à 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

ènunciation' 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, À 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 à 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 à 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)


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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)


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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/

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