Infinity…… Infinite? Or Finite?

Although I also believe that any valid reasoning process must be a combination of inductive and deductive logic, which one is the primary tool is in my opinion debatable. I have heard good arguments on both sides. Personally, I favor the inductive as the first step, both chronologically and logically. I'ts the way a child learns. He first observes the world around him, and then he gradually learns to be consistant--to make deductions. But there may be innate or instictual factors involved also, concerning the way humans conceptualize. At any rate, it's a difficult subject. Philosophers have been debating the issue for a long time. And will continue to do so.

Sorry, Makis. Didn't mean to accuse anyone of anything.

With regards to undermining the usefulness of this forum, I was referring to the usefulness of multi-form inductive processes within science, which nderosa has touched on above.

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scientists use a mix of inductive and deductive reasoning, which is indeed a violation of Meno's paradox, i.e. they are simply in a total vaccum as to what they are looking for.
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The inductive and deductive processes should not be fissioned, but considered as part of the single entity called "scientific process.

Meno's paradox is an illusion.

I pointed to "languages" as an example.

Language, or more precisely, the ascribing of "meaning" is a purely inductive process. It has never ceased to be an indispensible part of human science. And yet, it will never be defined, because the definition will use language itself. (Therefore it is inevitable that one should be constantly maintaining an inductive process in one's own thinking at all times.)

We each have knowledge, pure and perfect within its limits, without deduction. We use terms such as "intense," "purpose," "real;" and each item is learned in a purely inductive way. But in the human lexicon, there is no separation between the inductive and deductively derived lexical items. Therefore, we should call them two aspects of one and the same thing.

How about the other sciences?

Philosophical relativists pounce on this fissioning of the deductive and inductive as an opportunity to blanket any area of scientific process that they choose with a ubiquitous "skepticism," simply because it lacks a deductive element, forgetting that the word "deductive" is itself, in fact, maintained by the inductive language process. And, Makis, I did not want to suggest that this is what you were doing.

The point is that knowledge is not merely cognitive; and that there are undesirable logical conlusions to abandoning any use of inductive reasoning altogether.

That's all. Pax.

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Meno's paradox is an illusion.

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I couldn't agree more with all the statements you've made except the one above. Meno's paradox is so real that it's avoided systematically. A solution to Meno's paradox will indicate the correct route we must take in searching for the causes. We have no clue of doing that so we deal only the the effects using a mixture of inductive-deductive methodologies that often lead to tautological conclusions, i.e., we get confused at some point as to what are our premises and what our conclusions.

Again, Meno's paradox deals with those that want to get the cause of things, like for instance, what creates Gravity. In the Principia, Newton used a mixture of inductive-deductive reasoning to explain the effects. He admitted that he never explained the cause simple because he didi not have a clue what the cause was but could only speculate (ether). That's Meno's paradox: How can we know something that we do not know what it is? Tha't not an illusion or linguistic fallacy. It is a problem scientist face every day in their searching for truth.

We must go beyong the inductive-deductive processes if we would like a chance of surving any longer. Do not get me wrong here and think I am implying anything religious or Metaphysical. Just a new scientific methodology.

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We must go beyong the inductive-deductive processes if we would like a chance of surving any longer.
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Yes. I agree entirely. But the process functions on distincions that are temporal (time-bound).

So, here's how I understand Meno's Paradox:

1. If you know what youfre looking for, inquiry is unnecessary.
2. If you donft know what youfre looking for, inquiry is impossible.
3. Therefore, inquiry is either unnecessary or impossible.

Effects must have cause, but the effects are only distinct in that time exists. Exclude the temporal element, and there is no paradox. The assumption is that all manifestations of "intellect" are temporally-bound.

I would suggest that they are not, in that the operations of the universe all exhibit intelligence, of which our own intelligence is a limited (but valid) reflection.

Your understanding of Meno's paradox coincides with mine. No dispute there. The dispute comes in your suggested way to resolve or dismiss. Your suggestions resembles a lot that of Socrates, Meno's teacher and the one he was faced with the paradox. Socrates insisted, in a desperate attempt to resolve this paradox, that we are reflections of universal truth and he proposed the mechanism for transfering knowledge to be the "soul". Time plays no role into this.

However, a fellow named Aristotle came along and disagreed, claiming that our minds are clean of any knoweledge when born and therefore we must devise means of getting to the truth. He developed the four Axioms of Logic in that pursuit.

I claim that your view, if carefully analyzed leads right into the existence of a Superior Being and Creator of All (Man was created to be a reflection of God the Bible claims). However, I am not in a position to dispute your thinking at this point. My view is that a mechanism for discovering causes is completely unknown to Scientists and most discoveries are made by chance. If we were a reflection of God we should have done much better... than wondering about the cause of gravity for the last 3,000 years. Yes, you may take the temporal element out and claim that at some point we will know but, this reminds me of little kids making fun of an older man trying to park in a tight space: "Heh, Grandpa, the first 100 years of driving are tough. Then you get used to it!"<img src=icon_smile.gif border=0 align=middle>

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Socrates insisted, in a desperate attempt to resolve this paradox, that we are reflections of universal truth and he proposed the mechanism for transfering knowledge to be the "soul". Time plays no role into this.
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Aristotle's temporal objection may have a contemporary parallel. He identified "logic" as the operation of verbal reasoning.

I proposed that the basis of verbal reasoning is an interaction of indissoluble units of meaning. Meaning deals with the further phenomena of space, matter, time, and scale -all of which harmonize in a way that appears fractal.

I suggest we look at it from the perspective of the fractal character exhibited by the universe. Fractal geometry (eg. the Mandelbrot set Z=Z^2+C) reveals infinite permutations of the original set. And yet, they all appear to have a resemblance, or a cartesian reflection of the whole set, and this exists in relation to the actual set.

On our computer, this kind of reflection bears itself only in our temporal calculation of the infinite iterations. The set never ceased to be itself, unchanging and permanent; and yet, we as individual intellects, will only ever experience it in a temoral "discovery" process through infinite calculations, and the use of our computers.

The "set" does not exist in our temporal world until we view it on our computer. Yet, the mathematical predisposition for the set to exist has always been there. Therefore, we may call the Mandelbrot set a complete, yet infinite "thing," even though it doesn't exist yet. That is merely a temporal limitation. it exists in the equation Z=Z^2+C.

The items of the above set "Z" and "C" would be Aristotle's items of meaning, which are the basis of the "verbal reasoning" that makes up "logic." The universe would be the cartesian plane on which they are projected -infinite, yet complete.

Aristotle would say that we must acquire the knowledge of the operations within the "Universal" set by observing the permutations -an unending process.

Socrates would say that it may be revealed to us in the form of a function (Z=Z^2+C).

Do you agree?