Thursday, September 22, 2005

Abstract Logic

Sasca D'Agostino a.k.a Just an Ordinary Girl a.k.a Calabrizella, You were going to write some treatise about your views on logic and why you always failed at it (not surprising, as you are still a Thomist-Catholic-Apologetic)! ;) Anyway, so still waiting to read it. In the meantime, I thought while the rest of this country is presumably occupied with Rita gearing up for a strike right behind Katrina, I can sit around in my cubicle and plot out some detached, anti-realist logical principles for fun (in a philo-sophic-geeky sort of way). This, ofcourse, is so unlike me. But I'm just waiting for a hurriance update meeting I'm supposed to attend in about 30mins, and can't do anything else until then... so why not this?! So here's a statement. -- note: by the sheer statement of a statement, I am making an assertion. Thus, every statement is an assertion, which is different from an affirmation. The affirmation or negation or neutrality of a statement is jugded by logic. Anyway, I digress. Here's a statement: The coffee in my mug is black and is not black. Is this a contradictio? If yes, why? If not, why not? Now, remember, we are dealing with abstract logical principles... right now, I'm not being an Objectivist and scrupulously applying logic to every referent in reality. So, the above statement can be broken down into two assertions. The coffee in my mug is black. The coffee in my mug is not black. The truth of these statements will decide whether their assertions are contradictory. Now, if the first statement is true, then the second statement is either false or not fully true. If the first statement is false, then the second statement is either true or not fully false. Since, in Aristotelian logical principles, typically things are taken as either fully true or fully false, the above statement might seem to contradict the law of non-contradiction. However, if we challege the assumption that things are always fully true or fully false, then we might be able to get away with saying that my statement "The coffee in my mug is black and is not black" is actually NOT a contradiction and does not violate that principle. O, I gotta go now. More later. Okay, I'm back to write more.... so where was I? Okay... so the statement "The coffee in my mug is black and is not black" is not a contradiction if I do not accept the premise that A is A in the same respect and in the same time. I could mount a challenge by saying that A could also be fully A in the same respect but at different times, or A could also be fully A at the same time but in different respects, or that A is sometimes partly A and partly not A, but the truth-value would be dependent on HOW much of A is really A. So, "The coffee in my mug is black and is not black" -- that statement by itself DOES NOT preclude the idea that the coffee may also be dark brown, for example. Since all it asserts is with regard to the color black, we cannot say with full logical certainty (presumably according to logical principles) that the coffee could also be or not be brown or any other color of which we don't know. Thus, in such cases, the logical truth of a statement is not deduced from the analysis of pure logic (like how classical Aritotelian logic does) but through an actual and demonstrable proof or theorem. Unless, my negative statement (the coffee is not black) is PROVED to be true or untrue and not just analyzed to be true or untrue, we cannot have any certainties of its truth statements. Now, the implications of such a logical approach is that *concepts* in essence lose all its meaning. And this is the current nature of philosophical dialogue in contemporary culture. Contemporary and modern philosophers argue that concepts no longer hold the universality of truth as we believed it did. According to them, concepts like "black" and "exists" are merely our feeble attempts at having our biased languages interpret ideas into universality. Some go so far as even arguing that Math is also inadequate as a universal language and that because numbers hold different positions in different bases (base 10 or base 2 for example), one cannot accept their universality either. For instance, note my Paul Tillich quote. According to Tillich, using concepts like "existence" to make inquiries upon the concept "God" is futile because he believes that it essentially works to deny His "existence". Thus, claiming A exists means claiming A does not exist. Thus, A is an existent being and is not an existent being. Thus, in the above example there is not meaning to word "exist" but apparently there is some vague, ungraspable meaning to the word "God" and we should just SHUT OUR MINDS DOWN and accept that that"God" just is - without making any attempts to understand what "just is" means! In such a scenario, anyone could make an equally arbitrary statement and demand that you divorce your concepts from any coherent integration and just accept the arbitrary statement as "just is". Like I could argue that Superman "just is", and give you no method to prove me wrong because I just denied you all recourse to any sensible use of universal concepts. Anything you say, I will respond with "that is just what you say!" And therefore, coming back to my coffee in the mug is black and is not black -- when I begin to understand that concepts are not actually arbitrary, and that concepts infact do hold mathematical absolutism, I will be able to understand that the statement I made is infact a contradictory. I understand that at any one given time, "black" will only be "black", that if it is not "fully black", then it is probably grey or some other color and therefore NOT black, and this I DO NOT need a proof for, all I need is an objective analysis of concepts involved. Now, some may argue that, well if the entire world was split equally into color-blinded and normal vision people, then you would have half the people arguing that the color is black and half arguing that the color is grey, and how could you know what the truth of the coffee is!? Here your concept of what "black" is might actaully fail. The response to this situation is still the same consistent position of objectivity. Concepts hold universal absolutism. When I say "black", I have created a concept out of the essence of what it means to be be the color "black". The color "black" is NOT what is percieved by the observer but is what is essentially the wavelengths that such pigmentation reflects of light so as to give us the color "black" based on our current visual equipment. In other words, if I wear blue sunglasses and everything begins to look blue or in hues of blue, I should NOT conclude that suddenly everything has changed their pigmentation to reflect blue, but my own VISUAL equipment has changed that filters the light to appear as blue. Thus, if you are color-blind, your visual equipment might be different, but you are still percieving the SAME wavelengths of color black, just not seeing it manifest as the same COLOR as others do. Anyway, the point of all this is to argue that logical principles can get pretty crazy and absurd if they are divorced from all referents to reality, and if concepts are degraded to an arbitrary status. In such a paradigm of the world, everything becomes anything and nothing at the same time. The mind, the world, reality and existence are all invalidated by those ideas. Infact, those ideas are self-defeating because they argue for their own negation! Thus, so called "philosophers" like Tillich, who get paid thousands of dollars by academic institutions like the University of Chicago to churn out crap never cease to baffle and amuse me. Yet, I'm also aware of how pernicious their influence on society can be.


Blogger Semperviva said...

my post shall be an apologia of why i failed it because its done WRONG HAHAHHAHA lol at least by the majority of ppl...there.. you'll see soon

9/23/2005 12:13:00 PM  
Blogger Tyrel said...

ok, so i was confused about your comments about assertion and affirmation. So, I looked up the definitions and became even more confused.

affirmation - a positive assertion

assert - to state or declare something positively and often forcefully or aggressively

to demonstrate the existance of

So what is the differnce?

9/27/2005 02:53:00 PM  
Blogger Ergo Sum said...

An "assertion" merely makes a statement, a statement that exists because it is being asserted. It does not mean that the statement being asserted is necessarily TRUE (or affirmed).

An "affirmation" is kinda like a conformation. It is like saying that the asserted statement is infact true or valid or correct or has evidence supporting it, etc.
Hence, an affirmation is making a judgment about a statement.
Just like a negation is making a judgment about a statement by saying that it is false, invalid, or incorrect, or unsubstantiated.

Does that help?

9/27/2005 11:08:00 PM  

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