Logic and Reality

It has become fashionable to assert that "Logic doesn't govern the real world" or "Humans behave illogically at times" or "Logic is not the be-all and end-all of everything."

Even treatises on logical fallacies make this claim. E.g., an article on Logic and Fallacies begins as follows:

It's worth mentioning a couple of things which logic is not.

First, logical reasoning is not an absolute law which governs the universe. Many times in the past, people have concluded that because something is logically impossible (given the science of the day), it must be impossible, period. It was also believed at one time that Euclidean geometry was a universal law; it is, after all, logically consistent. Again, we now know that the rules of Euclidean geometry are not universal.

Second, logic is not a set of rules which govern human behavior. Humans may have logically conflicting goals. For example:

* John wishes to speak to whomever is in charge.
* The person in charge is Steve.
* Therefore John wishes to speak to Steve.

Unfortunately, John may have a conflicting goal of avoiding Steve, meaning that the reasoned answer may be inapplicable to real life.

This document only explains how to use logic; you must decide whether logic is the right tool for the job. There are other ways to communicate, discuss and debate.

If the above sounds reasonable, then read on.

The error the author of the article commits in limiting the domain of logic is so simple and egregious that it escapes most people.

Logic is not a theory which is applicable in some cases and is inapplicable in others. It is the very structure of thought and language. Wittgenstein's first book, Tractatus Logico-Philosophicus was seminal in clarifying the role of logic. Tractatus has many flaws, but its elucidation of the difference between logical propositions (which are self-evident or self-contradictory) and truth-value propositions (which are true or false depending upon the state of affairs in the world) was a milestone in the history of western thought.

In his words:

3.03 We cannot think anything unlogical, for otherwise we should have to think unlogically.

3.031 It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an "unlogical" world how it would look.

3.032 To present in language anything which "contradicts logic" is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist.

With this understanding, it is easy to see where the author of the original article is going wrong.

His first example is wrong because he confuses the invalidity of a scientific theory with a fault of logic. There is just no such thing as a "logically impossible" state of affairs. There are only logical contradictions, which are false by their very structure, without recourse to state of affairs in the world.

Euclidean Geometry is a set of axioms which, when talked about (i.e. when logically played around with), lead to certain propositions (usually called theorems). Whether those propositions are true or not is not the responsibility of their logical form, that is the domain of experience. A triangle in two dimensional space whose three inner angles do not add up to 180 degrees is a logical impossibility, and this can be proven just by symbolic manipulation of the basic axioms of Euclid.

Whether Euclid's axioms are a "universal law" or not is not the domain of logic, that is the domain of physical sciences. Hence, it is inaccurate to say that "logical reasoning is not an absolute law that governs the universe." What can be said is that "at any time, propositions which follow from the axioms of a theory in geometry or in the physical sciences may not correspond to state of affairs in the world, and therefore may be false."

Simply stated, the proposition "the universe is Euclidian" or "the universe is Einsteinian" is not the same, not by a long shot, as saying "the universe is logical".

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The second example is even simpler to address. It is a simple fallacy of introducing an additional factoid or premise, and then discrediting a conclusion based solely on the set of premises which exclude it.

The full set of premises in the second example is as follows:

* John wishes to speak to whomever is in charge.
* The person in charge is Steve.
* John wishes to not speak to Steve.

Conclusion: John has two wishes which cannot be fulfilled at the same time.

The conclusion is entirely logical (what else can it be?). The author introduces the fact of John's dislike of Steve later and then somehow comes to the astonishing conclusion that "the reasoned answer may be inapplicable to real life." That a human being has a conflict of interests is not somehow a limitation of logic. It is similar to saying that a car does not "behave logically" because its wheel is stuck in mud while its engine is trying to thrust it forward.

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In modern logic, a proposition can be false in three ways:

• The proposition is atomic (e.g. "India's PM is xyz") and does not correspond to the state of affairs.
• The proposition is complex (e.g. "India's PM is xyz AND He is unmarried") and its truth value (as computed from logical signs and the truth values of its atomic propositions) is false.
• The proposition is contradictory (e.g. "x AND NOT x")

You may think that you can formulate an argument in which you can prove a false proposition from true premises. Try it! I guarantee that you will fail.