For many years
(without benefit of intense supervised study, mind you), i have always ...figured that formal logic contains internal contradictions/inconsistencies that render it nominally but ultimately incapable of determining the truth; that it is, at its core a nonlinear dynamic system, filled with innumerable variables that interact with each other despite the use of strict axioms, premises and formulae. Hardcore materialists (who depend heavily on logic to support their philosophy) insist that all that matters is matter, that no emergent properties (metaphysical phenomena, perhaps) exist, that whole internal and external body/mind/spirit/Nature unity and interdependence is not a consideration. Then, there's complexity theory....called chaotics....the merging and balance of chaos and order (in a very real sense, we are all merely decimal points away from catastrophe or annihilation or bliss). In a delicate, life on the edge of chaos, spiral spacetime - nothing that happens ever repeats itself in cyclical time -- events are probabilistic, predictable (some more than others), resemble each other with certain self-similarities, and there is always the possibility of spontaneous fluctuation in any pattern (even in the system of formal logic).
Example:
-- pre-Big Bang: there exists matter collapsing into a singular point in spacetime in a universe that is made up of an almost infinite number of particles coalescing into a system governed by mutual gravitational forces.
-- enter Big Bang: there exists a situation of chaos which, according to the classical 2d law of thermodynamics, must increase in entropy.
-- enter complexity theory....systems have proven themselves to spontaneously self-organize into a state of complex order, structure and pattern (look at galaxies, evolution, or perhaps an anthill).
So, from this I digress completely and gather that the artist, in never being able to truly define the creative process because of the inadequacies of spoken language, nonetheless can create order from chaos....assemble cogency that incorporates fundamentals like composition, color, form, balance, etc., into a complex system of communication that has the ability to help bind humans to each other (pretty/not pretty, art/not art). So chaos settles back into a decreased entropic state....idea takes physical shape; therefore, perhaps idea, thought, and "being-ness" might just exist outside the scope of matter alone. But what of those who say the life of ideas, thoughts and being-ness are all manifestations of the cerebral/neurological/chemical variety which stem from the animated, complicated and sometimes quite inefficient computer known as the human brain? I ask, what force or energy is it that can transform increasing entropy into increasing order, in human and non-human complex systems alike?
So what does all this have to do with formal logic, you ask? Well, in mathematical logic, there exist those variables that cannot be reconciled with the laws of logic that are supposedly inherent in the algorithmic workings of the universe....irrational numbers, f'rinstance. The square root of two is in mathematical logic a reductio ad absurdum. Examine the theories of Boole, Russell, Godel and Tarski, take a leap and reflect on the fact that some real numbers are as precisely indefinable as the symbols of language we use to try to not contradict ourselves, and what you have is the logic of language and mathematical logic living on the edge of chaos.
Example:
-- draw a line and put some points on it, let's call it a number line.
-- now describe those points between the whole numbers. as the numbers become fractions of fractions, decimals of decimals, there is an infinite number of points existing on that line. Randomness begins to occur as some numbers become irrational, chaos emerges from the order of the whole number line. no single irrational number or whole number contains all the knowledge necessary to define the line: interdependency of two or more points must be present to define the line. contradictions or incompleteness or both within this seemingly closed system are present, even though nothing has been done to alter the initial state of the line and points.
--it is precisely this interdependency of irrational numbers that forms the complex definition of the line. the line is mathematically true, but it can't quite explain its own inconsistencies; once one scrutinizes the definition of the number line, chaos breaks down its pattern, its structure.
All this, in my opinion, ties in with the Heisenberg Uncertainty Principle, which asserts that no speck of matter in spacetime can be wholly defined. While light may be measured as a particle or a wave (as matter or as energy) it cannot be measured as both at the same time...by knowing its velocity, it is not standing still enough to determine its position. Pin-point its position and lose the capability of measuring its velocity.
No argument, regardless of how sound the logic, can be proven to be true. Either the consistency of the argument is skewed, or the validity of the conclusion is in question. The gap between proof and truth can be infinitesimally narrowed, but never closed. Logic breaks down. Even the illustrious Turing and his infamous thought experiment (basically mathematical recursion theory), leaks flaws: for one, the behaviour of variables is undecidable -- a certain function in question cannot be calculated mechanically, no matter how complex the machine. Think about the processing and storage capability of any huge computer, then ponder infinity.
Perceived in my own little way....reality and nonreality are apparent and undeniably present. Both matter and illusion exist, a bit of the time independent of each other... prove something exists and the truth of the matter is highly suspect; declare something as true and I dare you to unequivocally prove it .....the trick? To balance the two and come to the conclusion that you're getting better at approaching the truth....and getting there is where all the fun is. Life is infinite fun, if you know how to work the knobs and dials.
Example:
-- pre-Big Bang: there exists matter collapsing into a singular point in spacetime in a universe that is made up of an almost infinite number of particles coalescing into a system governed by mutual gravitational forces.
-- enter Big Bang: there exists a situation of chaos which, according to the classical 2d law of thermodynamics, must increase in entropy.
-- enter complexity theory....systems have proven themselves to spontaneously self-organize into a state of complex order, structure and pattern (look at galaxies, evolution, or perhaps an anthill).
So, from this I digress completely and gather that the artist, in never being able to truly define the creative process because of the inadequacies of spoken language, nonetheless can create order from chaos....assemble cogency that incorporates fundamentals like composition, color, form, balance, etc., into a complex system of communication that has the ability to help bind humans to each other (pretty/not pretty, art/not art). So chaos settles back into a decreased entropic state....idea takes physical shape; therefore, perhaps idea, thought, and "being-ness" might just exist outside the scope of matter alone. But what of those who say the life of ideas, thoughts and being-ness are all manifestations of the cerebral/neurological/chemical variety which stem from the animated, complicated and sometimes quite inefficient computer known as the human brain? I ask, what force or energy is it that can transform increasing entropy into increasing order, in human and non-human complex systems alike?
So what does all this have to do with formal logic, you ask? Well, in mathematical logic, there exist those variables that cannot be reconciled with the laws of logic that are supposedly inherent in the algorithmic workings of the universe....irrational numbers, f'rinstance. The square root of two is in mathematical logic a reductio ad absurdum. Examine the theories of Boole, Russell, Godel and Tarski, take a leap and reflect on the fact that some real numbers are as precisely indefinable as the symbols of language we use to try to not contradict ourselves, and what you have is the logic of language and mathematical logic living on the edge of chaos.
Example:
-- draw a line and put some points on it, let's call it a number line.
-- now describe those points between the whole numbers. as the numbers become fractions of fractions, decimals of decimals, there is an infinite number of points existing on that line. Randomness begins to occur as some numbers become irrational, chaos emerges from the order of the whole number line. no single irrational number or whole number contains all the knowledge necessary to define the line: interdependency of two or more points must be present to define the line. contradictions or incompleteness or both within this seemingly closed system are present, even though nothing has been done to alter the initial state of the line and points.
--it is precisely this interdependency of irrational numbers that forms the complex definition of the line. the line is mathematically true, but it can't quite explain its own inconsistencies; once one scrutinizes the definition of the number line, chaos breaks down its pattern, its structure.
All this, in my opinion, ties in with the Heisenberg Uncertainty Principle, which asserts that no speck of matter in spacetime can be wholly defined. While light may be measured as a particle or a wave (as matter or as energy) it cannot be measured as both at the same time...by knowing its velocity, it is not standing still enough to determine its position. Pin-point its position and lose the capability of measuring its velocity.
No argument, regardless of how sound the logic, can be proven to be true. Either the consistency of the argument is skewed, or the validity of the conclusion is in question. The gap between proof and truth can be infinitesimally narrowed, but never closed. Logic breaks down. Even the illustrious Turing and his infamous thought experiment (basically mathematical recursion theory), leaks flaws: for one, the behaviour of variables is undecidable -- a certain function in question cannot be calculated mechanically, no matter how complex the machine. Think about the processing and storage capability of any huge computer, then ponder infinity.
Perceived in my own little way....reality and nonreality are apparent and undeniably present. Both matter and illusion exist, a bit of the time independent of each other... prove something exists and the truth of the matter is highly suspect; declare something as true and I dare you to unequivocally prove it .....the trick? To balance the two and come to the conclusion that you're getting better at approaching the truth....and getting there is where all the fun is. Life is infinite fun, if you know how to work the knobs and dials.