Sunday, November 20, 2011

Contextual triviality. What Has to be Done When Someone Uses the Word "Logic".

When someone uses the word "logic"he/she should immediately point out what is initially assumed to be true/false and what truth results are derived, i.e. what can be proved from those initial assumptions.Word logic is nice to use, it can be fancy, it can show you want to be precise in your communication or explanation. However, the axiomatic system should be known and understandable for all the parties that are part of the "logic" communication. Saying that something is logical doesn't mean it is obvious, and it doesn't mean it does not require a proof. If something appear to be "trivial", the logical context of axioms and premises should be clear to all participants who want to accept that "trivial" remark. Contextually "trivial" is OK.

The other day, while browsing mathematics section at Indigo bookstore, I have noticed a book "Logic for Mathematicians" by A. G. Hamilton, (Google books I was pleased to see that the book reflects my view that logic is an independent discipline from mathematics and that mathematics is only one of the area of the application of logic. While Frege may have integrated both directions of thinking, I am glad that A. G. Hamilton "presented the subject matter without bias towards particular aspects, applications or developments, but an attempt has been made to place it in the context of mathematics and to emphasise the relevance of logic to the mathematician.".

To me, this is important because of my view (most of the posts in this blog) to differentiate clearly the worlds that define what is to be counted, measured etc, from the mathematical world that accepts pure numbers as starting points. Logic is used in both worlds.

[ logic, mathematical logic, math, math concepts, axioms, mathematics, teaching math, teaching mathematics, understanding mathematics, Frege, Hamilton, ]

Monday, November 7, 2011

Real World Example of Natural Numbers

In real world application of math we have to keep track what we have counting, while pure math cares only about pure numbers.

This is an example of counting rounds in an UFC match (UFC - I do not approve nor like).

[ math, mathematics, math application, axioms, examples of natural numbers, natural numbers, axioms, sets, number theory, ]

Saturday, November 5, 2011

Free Will

In the very moment, when you breath, when oxygen molecules split the molecules of your brain biochemical energy storage, the very state of neural firing, dynamics, neurotransmitters rush and retreat that exist at that moment, is the consequence of your free will, the will riding on neural paths configurations and their energy that you release by thinking in exactly that that moment..