The Logic of Logic

Logic means inference, consistency, and inevitability. By inference, one proposition implies another. For example, if California is within the United States, then being located in California implies being located in the United States. By consistency, if A = B and B = C, then A = C. By inevitable determinism, the constants of the universe must be what they are, and cannot be otherwise.

The word “logic” derives from the Greek “logos,” meaning “reason.” In dictionaries “logic” is often defined as “reason,” but then “reason” is defined as “logic,” which makes that definition circular and meaningless. Dictionaries also say that logic is about validity, but that too is circular. The meaning of logic cannot logically come from the implications of logic.In the application of logic, there are “truth tables” for various logical functions such as “and” and “inclusive or.” For the “and” function, if propositions x and y are each true, then “x and y” are true. All other combinations are false, e.g. if x is true and y is false, then “x and y” is false because for the combination to be true, both have to be true. That is inference.

Another example of inference is the “contrapositive.” For example, if California is within the USA, then by the contrapositive, if one is not in the USA, one is not in California.

Reason is the application of logic to observation. The ultimate basis of evidence is observation filtered through logic. Facts are always tempered by interpretation, and logic should be applied to interpretation in order for the observation to be objective. Bias and stereotypes can make observations subjective, since the bias may apply to some but not all occurrences.

Reasoning can be deductive or inductive. Deduction starts with premises, to which logic is applied, and conclusions inferred. Induction begins with observations, and then a generalization is inferred with some probability. The premises for deduction are based on evidence, ultimately from observations to which inductive logic is applied. If one starts with a conclusion and infers a cause, that is “abduction” as a combination of deduction and induction. “Lateral reasoning” seeks to find out if the premises for deduction are complete or adequate.

There are constant numbers in the universe that have a logical foundation. For example, pi equals the circumference of a circle divided by the diameter. This natural number is a logical necessity, inevitable and determinist. One could also say that pi determines the ratio of the circumference divided by the diameter. Another logical number is e, which determines the rates of growth and decay. If a population is continuously growing at a rate of 100 percent, then one year later, it will have increased by e, or 2.71+. The number e is a logical necessity.

Physical constants such as the speed of light, gravitational attraction, and the energy and mass of subatomic particles are what they are by logical inevitability. Scientists do not yet understand the ultimate reality of these particles. In some cases, such as string theory, their existence is inferred by the logic of mathematics, using the principle of consistency, but the problem there is that there are multiple hypotheses, and physicists do not yet have the ultimate logic which would find the “true” string or other ultimate reality.

Ultimately, the physical constants are determined by logic. Although logic is immaterial, it determines the nature of the material world. Physics determines the nature and evolution of the universe, and logic determines the laws of physics.

Logic too determines the laws of biology and the genetic programming of DNA. Animal brains were developed to apply logic to life. Animal hunters understand, by genetic programming, the logic of economizing, of not wasting energy chasing creatures that cannot be caught. So too the human brain is programmed to understand and apply logic.

There is a branch of economics that applies psychology to human action. Behavioral economics finds that much of human action is driven by emotion and the irrationality of being over-confident, being anchored to some previous or recent experience, herd behavior, and seeking short-term pleasure over long-term well-being. Human action is based on reason, yet people are often foolish.

But human action is inherently rational. People rank their ends or goals into those most important to those less important, and at the moment of choice, they economize in reaching the most important ends. Economic rationality is based on consistency and economizing. If preferences are inconsistent and people do not economize, then economics cannot explain that behavior, and we send those people to the department of psychology, perhaps abnormal psychology.

Thus there are people who, sometimes under the influence of drugs, other times due to mis-programmed brains, are not in touch with reality, refuse to accept facts, or mis-apply reason. Perhaps some international negotiations fail due to one or both parties being “crazy.” But the logic of inference implies that there is a reason for everything. Every effect has a cause. Therefore there is a logical explanation for craziness or seemingly irrational behavior.

We see the paradox in economics of people wanting to live well, yet being subjected to poverty, unemployment, crime, war, pollution, and waste. There are laws of economics that explain how to optimize, how to maximize well being, but these law are ignored by governments. The logic of human action has two motivations, self-interest and sympathy for others. Social and political evolution has brought us to a mass democracy that inherently exploits ignorance and apathy to reward greed. But people optimize by being too lazy to think for themselves and seek truth.

What is seemingly illogical has logical explanations. But the logic of how to reform the world and move it towards peace and justice is illusive, and perhaps the social logic is that people are genetically anchored to their beliefs and will only be shaken by experience rather than by reason.

[Editor’s note: this essay first appeared on Dr. Foldvary’s blog, the Foldvarium, on April 15 2012]

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