Saturday, December 13, 2008

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".

...

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.

...

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.

6 comments:

Anonymous said...

The lack of the spiritual, because of its value to life, or the requirement of a practical life philosophy and life psychology of the current time, is manifoldly responsible for the crisis in the life of people, and in their concerns.

pankaj said...

nice exposition.

it could be said however, that the solutions to the problems of living, don't emerge from logic. it could be said though, that the laws of logic, or more widely, the method of reason, are the best device to try and solve these problems.

science however, is completely indifferent to the problem of living, nor does it claim to be interested.

Harmanjit Singh said...

Hi Pankaj:

Your first paragraph ("it could be said ...") is on the spot. Actually, nothing true about the world can be deduced from merely logical deduction. One can formulate axioms ad infinitum and prove infinite theorems, but ultimately, the validity of the theorems depends on the correspondence of the axioms with the state of affairs, which is not the domain of logic.

The second paragraph ("science however ...") is more interesting.

What is this "problem of living" that you speak of? And what is "science", according to you?

If you mean that no scientific discipline is interested in human happiness and well-being, that is obviously not true. Medicine, economics, psychiatry, ecology, etc. are all aimed towards providing humans with greater well-being. They may be inadequate (no science has reached its final frontiers), but they are surely interested in human happiness.

pankaj said...

science's indifference to the "problem of living" is adequately summed up in camus' quote "whether the earth or the sun revolves around the other is a matter of profound indifference."

that is to say, answers to questions relating to value, what is "good" or "bad", love, to questions of "purpose" (how should one ideally live ones life? is there a better or a worse way to lead ones life? or are all ways equally futile [bertrand russell very eloquently expresses this in his introduction to "history of western philosophy"]), science has nothing to contribute to them.

science merely seeks to unravel the workings of the physical world. some sciences that you have mentioned, though they're not exactly sciences (economics is a psuedo science, psychology is even more obscure - a mixture of social science, science, philosophy), assume betterment of humanity, but add nothing to these questions.

these questions of value, however, are confronted in existing at every moment, choice between right and wrong, determination of purpose, the problems of relationships. these questions are more immediate, & more focal to an existence than a question of science.

Harmanjit Singh said...

Hi Pankaj:

I understand what you are trying to say, but bear with me. Science, esp. if done collectively, is not about one man's happiness. It is about increasing our knowledge as a whole. And knowledge does lead to an increase in overall human happiness. Our lives of comfort, health and instant communication are due to scientific progress.

Now a highly evolved person may say that happiness does not lie in /these things/ but in an inner state of calm and peace and contentment which no outside agency can help with. Well, consider neurology and Psychology/Psychiatry then. These sciences which deal with the brain and mind tell us interesting things
about our inner states, wouldn't you say?

"science's indifference to the "problem of living" is adequately summed up in camus' quote "whether the earth or the sun revolves around the other is a matter of profound indifference.""

# To him, obviously! But not to a great many people, since people were violently persecuted for their research in astronomy. Notwithstanding that astronomy has valid applications in our understanding of the universe, pure science (e.g. proving that a certain sequence sums to e, or theorizing about computation) is akin to the higher reaches of one's intellect, just like art. It may not have an immediate (or even long term) use, but it is a celebration of our mental faculties.

"that is to say, answers to questions relating to value, what is "good" or "bad", love, to questions of "purpose" (how should one ideally live ones life? is there a better or a worse way to lead ones life? or are all ways equally futile [bertrand russell very eloquently expresses this in his introduction to "history of western philosophy"]), science has nothing to contribute to them."

# Questions of "should" and "meaning" seem to be outside the domain of science, but that is because they are questions of subjective feelings. However, even there, recent advances in science has told us a lot about the evolutionary basis of our morals (the shoulds) and behavior (the goals and means of society and individuals).

More to the point, if science has nothing to contribute to them, what has? For example, theists claim that God's presence or Will is not something that is the domain of science, but then the question is asked: whose domain it is then? Of superstition? Of shifting feelings? Of cultural beliefs and standards?

"science merely seeks to unravel the workings of the physical world."

#And what other world there is?

"some sciences that you have mentioned, though they're not exactly sciences (economics is a psuedo science, psychology is even more obscure - a mixture of social science, science, philosophy)"

Many of these are budding sciences, i.e. have lots of untested hypotheses. And they are difficult sciences, since they deal with subjective experiences. But there is certainly a progress in their methods, their adherence to scientific norms, and in their explanatory ability of human behavior.

"assume betterment of humanity, but add nothing to these questions."

Questions of what values are good or bad is a question which assumes that there is something inherently "good" or "bad". The question may be unanswerable by its very ambiguity and assumption.

Insofar as there is clarity about what /is/ good (e.g. contentment, low stress, health, longevity, saving of life) or bad (injustice, high stress, corruption), science does help, actually. Religious sentiments have been touched upon by recent neuro-scientists (e.g. V S Ramachandran's God and the Limbic System), feelings have been touched upon by evolutionary biologists, social issues such as corruption and inequality has been occupying economists, and great strides have been made in reducing corruption by institutional reform in many countries.

"these questions of value, however, are confronted in existing at every moment, choice between right and wrong, determination of purpose, the problems of relationships. these questions are more immediate, & more focal to an existence than a question of science."

That is the human condition, but science tells us why these questions become important at a certain age, in a certain prosperous milieu, in a certain brain. E.g. Maslow's hierarchy of needs was one theorization of human needs. An infant, or a starving man in Africa, has little use for Camus' meaning of life, he has more use for an intravenous drip and an effective government.

As for those to whom these questions /are/ important, they disregard the advances in scientific understanding about the
human brain and mind to their own detriment. Do inquire on your own, and share in others' findings, and share your own.

Publishing of a Buddhist sutta is sharing of the Buddha's findings. Unless someone felt that these were applicable to a large number of human beings' quest for happiness, why would they do it?

They shared their research!

This similarity in the natures of human beings leads me to say that solutions which further human happiness may be widely applicable.

Ujwal Batra said...

Brilliant!
Many people disregard logic as the basis of their faith.They claim that logic cant solve the human problems, and therefore, is not a suitable means to approach reality.
But in doing so, they complicated what could have been easily be solved with logic.
Though, as Pankaj said, solutions to human problems dont always emerge from logic..
Which leaves us with the question, if not religion, nor logic, what can be the basis of action?