radarmark
Quaker-in-the-Making
Okay. This is a crash course on radar’s belief system, to include what he means by truth, evidence, reason, empiricism, reality. It focuses on how to think like a scientist or philosopher, or like de Bono or Polanyi (this is a process I focus on every day, and one of the reasons I come to this site, to learn how to do this).
The Kosmos is everything there is, was, will be. If there is a G-d, he or she is included. The universe is the sum total (again, across time) of every entity consciousness experiences as matter-energy. The knowable universe is that part of the universe our (humanity’s) consciousness can experience. The knowable universe is a subset of the universe (the boundary of the two is where events are receding from us at over the speed of light and where singularities exist, because humanity can get no information from a singularity). The universe is a subset of the Kosmos (the Kosmos includes those kind of entities and experience usually referred to as mental or subjective vis a vis physical). Reality is then the Kosmos, and I believe in it.
The knowable universe is modeled by physics, the universe by cosmology (remember the universe includes the knowable universe), and the Kosmos by metaphysics (remember that the Kosmos includes both the knowable and unknowable universes).
One aspect of metaphysics is the platonic world of Penrose, mathematics-logic. Neither logic nor mathematics are formal systems, in general. They cannot (except in limited circumstances) provide “hard truth”. “Hard truth” is a provable relationship between a thought or proposition and reality (the Kosmos) whereby the thought “corresponds to reality” always, everywhere (“All men are mortal, Socrates was a man, therefore Socrates was mortal” or “1+1=2”). “Hard truth” is only obtainable via deductive logic (tautologies with no reference, in specificity, to the universe) or arithmetic (proven by Gödel) or ostensive definitions (but the truth value is not about the object being defined, but the concept being applied). Outside of these three cases, anything we know we know as a probability or possibility.
Induction works in the world; mathematics beyond arithmetic works in the world; linguistic reasoning beyond ostensive definitions work in the world. Work so well we human beings see the requirement for stating that inductive, mathematical and linguistic knowledge are not “hard truths” but soft truths… only very, very likely.
Early in the XXth century two of the greatest mathematical and logical minds of the time were working to prove the notion of another member of that group’s “Second Problem”. The second problem was that of Hilbert (see his 1900 presentation to the International Congress of Mathematicians or “Hilbert’s Problems” or “Hilbert’s axioms”), the two working on it were Whitehead and Russell (see their Principia Mathematica or look it up on the web). It all has to do with what is called Peano arithmetic and Zermelo-Frankel set theory s and formal systems. What Hilbert proposed it that someone could use arithmetic and set theory to deductively with mathematics the truth or falsity (in the “hard truth” sense). Whitehead and Russell were busy trying to provide that proof.
A mathematical nobody named Kurt Gödel (later acknowledged as one of the two or three greatest mathematical and logical minds of the XXth century) showed that (in his two incompleteness theorems, look them up, wiki has a pretty good rap of them as does mathematica) the problem was ill-formed. That is, if one creates any formal system (set theory, geometry, vector-matrix-tensor analysis, calculus and so on up the line) that includes Peano arithmetic (a way to express all of arithmetic based on a few axioms), especially the notions of induction and the “successor function”, can never be complete and consistent at the same time (what was required in Hilbert’s problem and what was rigorously applied in the Principia Mathematica. In one swoop the work of three of the giants in mathematics was refuted.
The bottom line is that any mathematics beyond arithmetic is, in terms of “hard truth”, false. That does not mean the mathematics does not work, is not logically structured, or is merely an article of faith. What it means is that mathematics is ultimately provable in terms of induction (a kind of probability requiring evidence) and not deduction (where “hard truth” is possible).
The problem in most argumentation is that the people involved do not understand the limitations of mathematics due toGödel, the actual “probability only” notions induction gives us and the limited applicability of deductive logic. A good example comes from General Semantics: the use of “no” or “all” should be avoided. Why? If I propose “all Us are Vs”, it only takes one counter example (W is a U, but it is not a V) to invalidate the argument. Likewise if I propose “no Xs are Ys”, it again only takes one counter example (Z is a Y and an X) to invalidate the argument.
So I always try to avoid sweeping generalizations like “truth”, “all”, and “no”. And I believe I have sufficient cause to believe the above to me (to a very high degree of confidence) to be “probably true”. Notice I do not claim “hard truth”.
All it can be verified by looking up and reading (or reading about) the topics.
The Kosmos is everything there is, was, will be. If there is a G-d, he or she is included. The universe is the sum total (again, across time) of every entity consciousness experiences as matter-energy. The knowable universe is that part of the universe our (humanity’s) consciousness can experience. The knowable universe is a subset of the universe (the boundary of the two is where events are receding from us at over the speed of light and where singularities exist, because humanity can get no information from a singularity). The universe is a subset of the Kosmos (the Kosmos includes those kind of entities and experience usually referred to as mental or subjective vis a vis physical). Reality is then the Kosmos, and I believe in it.
The knowable universe is modeled by physics, the universe by cosmology (remember the universe includes the knowable universe), and the Kosmos by metaphysics (remember that the Kosmos includes both the knowable and unknowable universes).
One aspect of metaphysics is the platonic world of Penrose, mathematics-logic. Neither logic nor mathematics are formal systems, in general. They cannot (except in limited circumstances) provide “hard truth”. “Hard truth” is a provable relationship between a thought or proposition and reality (the Kosmos) whereby the thought “corresponds to reality” always, everywhere (“All men are mortal, Socrates was a man, therefore Socrates was mortal” or “1+1=2”). “Hard truth” is only obtainable via deductive logic (tautologies with no reference, in specificity, to the universe) or arithmetic (proven by Gödel) or ostensive definitions (but the truth value is not about the object being defined, but the concept being applied). Outside of these three cases, anything we know we know as a probability or possibility.
Induction works in the world; mathematics beyond arithmetic works in the world; linguistic reasoning beyond ostensive definitions work in the world. Work so well we human beings see the requirement for stating that inductive, mathematical and linguistic knowledge are not “hard truths” but soft truths… only very, very likely.
Early in the XXth century two of the greatest mathematical and logical minds of the time were working to prove the notion of another member of that group’s “Second Problem”. The second problem was that of Hilbert (see his 1900 presentation to the International Congress of Mathematicians or “Hilbert’s Problems” or “Hilbert’s axioms”), the two working on it were Whitehead and Russell (see their Principia Mathematica or look it up on the web). It all has to do with what is called Peano arithmetic and Zermelo-Frankel set theory s and formal systems. What Hilbert proposed it that someone could use arithmetic and set theory to deductively with mathematics the truth or falsity (in the “hard truth” sense). Whitehead and Russell were busy trying to provide that proof.
A mathematical nobody named Kurt Gödel (later acknowledged as one of the two or three greatest mathematical and logical minds of the XXth century) showed that (in his two incompleteness theorems, look them up, wiki has a pretty good rap of them as does mathematica) the problem was ill-formed. That is, if one creates any formal system (set theory, geometry, vector-matrix-tensor analysis, calculus and so on up the line) that includes Peano arithmetic (a way to express all of arithmetic based on a few axioms), especially the notions of induction and the “successor function”, can never be complete and consistent at the same time (what was required in Hilbert’s problem and what was rigorously applied in the Principia Mathematica. In one swoop the work of three of the giants in mathematics was refuted.
The bottom line is that any mathematics beyond arithmetic is, in terms of “hard truth”, false. That does not mean the mathematics does not work, is not logically structured, or is merely an article of faith. What it means is that mathematics is ultimately provable in terms of induction (a kind of probability requiring evidence) and not deduction (where “hard truth” is possible).
The problem in most argumentation is that the people involved do not understand the limitations of mathematics due toGödel, the actual “probability only” notions induction gives us and the limited applicability of deductive logic. A good example comes from General Semantics: the use of “no” or “all” should be avoided. Why? If I propose “all Us are Vs”, it only takes one counter example (W is a U, but it is not a V) to invalidate the argument. Likewise if I propose “no Xs are Ys”, it again only takes one counter example (Z is a Y and an X) to invalidate the argument.
So I always try to avoid sweeping generalizations like “truth”, “all”, and “no”. And I believe I have sufficient cause to believe the above to me (to a very high degree of confidence) to be “probably true”. Notice I do not claim “hard truth”.
All it can be verified by looking up and reading (or reading about) the topics.
