WJ

snatch!

"Yes, but these two came to mind because, I believe, they invested a large proportion of thier energies to "products of mind". Thier efforts had few practicle applications."

Can you think of or offer any specifics relative to those applications/products of the mind?

walrus

snatchbalance

WJ,

Well, I'm pretty sure that Aquinas came up with a number of logical proofs for the existance of god. I'd have to do some research to get more specific.

Augustine, I believe, tried to reconcile faith and reason.

SB

James Still

I think that philosophy falls flat when it seeks to produce anything practical. We shouldn't expect it to solve real-world problems (that is the domain of science) but rather we should use it to clarify our thoughts and to dissolve pseudo-problems.

ohwilleke

A few thoughts.

First: An example of 1/3+2/3 not equal to 1 is as follows:

You are doing math in modulus 2/3. Thus, the number line goes 0/3, 1/3, 2/3, 0/3, 1/3, 2/3, etc. In this system 1/3+2/3=0. Addition with moduli is useful in various situations. For example, this kind of math might be useful in using a computer with trinary circits (i.e. on, off, and half-on, instead of on and off only) or doing traffic light modelling (since traffic lights have three sequential stages that loop). I am trying to remember what kind of mathematical system this is from my Abstract Algebra class many years ago, and believe that this is called a "group" and is part of "group theory". There are other neat versions of mathematics in which the normal rules of algebra don't apply.

Second, mathematics is useful because the axioms have been chosen to corrospond to real world laws of nature. Two apples plus two apples does produce 4 apples in the real world. If you keep consistent units, math will take you a long way. Different axioms work in different contexts. If you are dealing with designing a machine, Euclidian geometric assumptions do just fine. If you want to navigate from Spain to Hispanolia, you do better with non-Euclidian geometric assumptions.

Math is often done with assumptions that have nothing to do with the real world, before applications are found. For example, abstract algebra was developed as an intellectual exercise in seeing what would happen is you changed the ordinary rules of algebra, just for the fun of it, long before applications for abstract algebra (e.g. in tensor theory in physics, and communcation coding) were developed. Math is an area where invention often preceeds necessity.

A more fruitful way of approaching the subjective/objective truth dichotomy, is to ask: "What assumptions must two people share to subjectively reach the same conclusion about the truth of a statement?" In the case of 1/3 + 2/3 =1 example, they must share: A common understanding of 1/3 and 2/3 as referring to rational numbers as commonly defined, a common understanding of "+" as referring to an ordinary algebraic addition operator, a common understanding of what "=" means, and an implicit understanding that 1/3, 2/3 and 1 involve the same units of measurement. People who share all of these relatively commonplace assumptions will find that the statement is true, people who do not share one or more of these assumptions may disagree on the truth of the statement.

[Incidentally: 0.333... and 0.666... equals exactly 1 and not 0.999..., or to put the statement differently, 1 and 0.999... are different expressions of the same number].

This isn't all that profound really.

snatchbalance

Well, I wish I could keep up my end of this discussion, but I have to leave town for a few days.

SB

James,



No, I woudn't neccesarily expect any solutions from philiosophy; but, some philosophising seems to have immediate application; Machiaveli, Paine, Locke, come to mind.

SB

[ June 03, 2002: Message edited by: snatchbalance ]</p>

WJ

oh!

re: "What assumptions must two people share to subjectively reach the same conclusion about the truth of a statement?"

Monday's are typically not too good for me so forgive my ingnorance here. Shouldn't that read 'objectively' instead of 'subjectively'? The reason I ask is that in my mind, if only one person 'internally' agree's with a percieved truth, then it is subjective. If two people agree to a subjective truth, how many more people does it require for it to become objective? Perhaps it is indeed apples and oranges. In a similar manner, perhaps no matter how hard you try, one cannot derive say a synthetic proposition from an analytical one.

Starting with a clean slate though, can a subjective truth become objective one? Logically, it seems induction is the closest synthesis to these dichotomous ways of thinking. Otherwise, I guess 'assumptions' have to made for any process of thought to take place in search of an objective/universal truth about certain things... .

As far as universal truths (math, etc.), verifying someone's assumptions has been the problem with deductive reasoning... . I wonder how truth had its beginning? Who invented objective truth...just thinking aloud.

Pehaps it is simply unknown as to whether math exists independently of the observer. Do you think it does? Or is it completely a 'human construct'?

What is your take on mathematics and reality? (Sorry for all the questions.)

walrus

ohwilleke

I am saying that even a statement such as 1/3+2/3=1 is too ambiguious, in the abstract to have a universal and objective meaning. It is a simple statement that has meaning only in the contexts of assumptions about what that statement means.

There is an objective reality that if you make certain assumptions about what the amibiguous statement 1/3+2/3=1 means, that it is true. But, until you make those assupmtions, it is just so many black dots on a computer screen.

Objective reality is inherently pre-lingual. Things that are "out there" don't come with lables attached. I have no doubt that there is an objective reality out there. There are real atoms and real objects in real places, whose existence is not dependent upon who is observing them. The tree makes a noise in the forest even when no one is there to hear it.

My assumption that there is an objective reality is a metaphysical axiom, which is plausible in light of overwhelming evidence in my life that it is true. But, it is only an axiom not contradicted in experience, rather than a rigorously proven logical truth. I doubt that such a fundamental axiom can be proven logically. It is an observation, much like the observation that the digits of pi are comprised of numbers in all known number systems that appear with approximately equal frequency, even though there is no known proof that this is a logically necessary fact at this point.

Mathematics is a set of concepts which are well defined, and can lead to certain conclusions within a conceptual model. I believe that it is possible to construct mathematical models that accurately (even 100% accurately) describe natural phenomena. But, mathematics itself is a set of concepts only. Concepts are not themselves, in a sense that makes an objective-subjective distinction meaningful, "real" (i.e. there are not corporally existing things). The difference between objective and subjective is not well defined with regard to concepts.

I am inclined to limit "objective" truth, to things that exist corporally (i.e. physically), and to view intangible concepts upon which many people agree to be a subjective true for a large group of people who share certain characteristics.

Of course, definitions should always be fit to the purpose of the definition. What constitutes objective truth in the concept of determining liabiility in a commercial lawsuit, is something different than determining objective truth when trying to decide which painting is most beautiful.

tergiversant

Could you give a clear cut example of a wholly objective truth and a subjective one?

I would think that truths about languages, e.g. 1+1=2 or "A bachelor is an unmarried man" are neither strictly subjective nor objective. They express truths about the common usage and subjective meaning of symbols, that is, intersubjective truths.

Alternatively, one could say that such statements may be interpreted either as subjective statements about the relationships between subjectively held meanings, or as objective statements reflecting reportive definitions.

Ierrellus

Walrus,

I was not trying to be irreverent or humorous in my post about the match, gas tank and explosion. I was suggesting that anything we consider abstract refers to some experienced activity. It make no sense without reference in the same way that my thread on bars and spaces presents an object that makes no sense. Attempts to make sense of abtractions do more to define the observer than the abstaction.

IMO, mathematics is a skeletal form of logic, or at least precedes logic. Experience precedes mathematics. Adaptation to environment by a creature with a very large cerebral cortex tends to indicate that such a creature needs math and logic in order to deal with experentials such as motion, space, energy, gravity in their effects on bodies.


Ierrellus

WJ

As usual, there's much to consider with regard to mathematics and reality. I still have a belief that says certain assertions made about a some thing, in its essence, is either an objective or subjective truth. Meaning that... fish have fins, bachleors are men, 1+1, etc. is an objective statement of truth as it does not depend on how one feels about it. Statements that refer to taste, emotion, likes/dislikes, and so forth depend on perceptual experience to impart their truth. Thus, I'm still back to the limitations of apriori logic (math) as the direct metaphor in the usefullness of knowing the nature of reality.

Ok, we beat that dead horse I know, but there are many philospher's (particularly viz. the existence of deity and metaphysics) that expect this pure form of objectivity to be the tell-tale savior. I believe, as the ontological argument demonstrates, that that approach is out of context from the meaning and nature of human existence. Irrellus makes such a point clear(I think):

"Attempts to make sense of abtractions do more to define the observer than the abstraction."

Fabulous point. Again, I know I can peform a mathematical/logical/objective calculation to get the correct size of a structural beam for a building, but it doesn't completely answer the nature of its physical existence. So anyone who asserts that apriori statements about a certain physical objective truth about such existence (whew) as being absolute and universal, would require the burden to 'qualify' how that is so. And, in doing so, the subjective elements rear their ugly heads.

Unavoidable I know. This I think speaks to the synthesis that say subjectivity provides in thinking or arriving at how and why one believes that a some thing comprises an absolute. In an epistemic sense, if the nature of reality then is unknown thru logic, and that all there exists is a subjective 'belief', do any of you believe that knowledge about reality exists? In a general sense, I suppose the answer is yes to some degree. But, what is reality? Objectivity? subjectivity? Or, is there another concept that captures or describes reality?

Maybe the deeper question pertains to the mystery at the end of the universe. If math can someday solve the origins and nature of conscious existence (anthropic), there will still remain the wonder about whether math is completely a human construct or whether math has its own independent, timeless existence (ie, is a deity's existence and essence math?).

So, is it objective or subjective to believe that in effect, *we* are deity or that we can know the nature of reality? It seems there is no truth to our existence, but what follows? A belief? What does it mean to hold a belief? In that regard, Irrellus' point is a good one indeed!

...just some more thoughts...

Walrus