Idag hålls ett alldeles speciellt event på Thothica Public Plaza och det är helt i sin ordning att imma MarkMonet med frågor i förväg!
Thothica hosts a SPECIAL EVENT this week: MarkMonet Thor on Philosophy of Math--on Sunday, Aug 29 at 12:30 pm SLT
As a mathematician in the social and behavioral sciences, I have found it useful to understand three things about mathematics that I believe should be general knowledge.
One is that it is a distinct system of thought that is set apart from the empirical natural and social sciences, and their ideas and theories. It is a deductive system, with axioms, theorems, definitions, and operations. Think
of Euclidean Geometry as an example.
Two, the symbols contained within the mathematical system, such as x, y , z, a b, and c are empty concepts, really place holders for something that may be defined empirically. In geometry there is angle, line, circle, to which the scientist may give special meaning. In my empirical work, a point stands for a nation, and a vector or angle for a relationship between whatever about a nation, such as conflict, and an attribute like economic development.
This can be profound. I have taken the same matrix analysis (the characteristic equation) used in quantum physics to identify the unknown movement and position of a particle, to measure the hidden expectations and situational vectors of a nation at war.
And three, theorems in mathematics follow logically from its axioms, such that if the axioms are true, so its theorems. This is profound. If the axioms of a mathematical system, like geometry are empirically true, then empirical deductions must be true, and we thus have a way of establishing empirical truth.
This possibility so impressed philosophers, like Descartes especially, that their philosophy was a search for axioms that were so self-evidently true that they could base an empirical philosophy on theorems deduced from them. And this philosophy would have to be true. Necessarily. I should note that Descrates' method of search for these true axioms led him to invent the incredibly valuable coordinate system we are so familiar with from analytic geometry and algebra.
So, mathematics is a deductive system of which the theorems are have to be true logically, true in an formal analytic sense. Not necessarily true empirically. Truth in mathematics is a grand tautology--truth by definition.
Think about this. Philosophy concerns itself fundamentally with what is true. Some meetings begin here with the question, "what is truth". Most at such meetings believe that there is no absolute truth. But now, what we have with mathematics is, as I have argued, absolute truth. Truth of the kind that if a = bc, then b = a/c, absolutely.
Thus, we have among the truths to deal with as philosophers the absolute truth of mathematics (and logic, but that is another talk).
By: MarkMonet Thor