Deduction, Induction, and Knowledge

Syllogism:

All Greek males are bald.

Herodotus is a Greek male.

Therefore, Herodotus is bald.

The conclusion is false because Herodotus isn’t bald, at least not as he is portrayed.

Moreover, the conclusion depends on a premise — all Greeks are bald — which can’t be known with certainty. The disproof of the premise by a single observation exemplifies the HumeanPopperian view of the scientific method. A scientific proposition is one that can be falsified  — contradicted by observed facts. If a proposition isn’t amenable to falsification, it is non-scientific.

In the Humean-Popperian view, a general statement such as “all Greek males are bald” can never be proven. (The next Greek male to come into view may have a full head of hair.) In this view, knowledge consists only of the accretion of discrete facts. General statements are merely provisional inferences based on what has been observed, and cannot be taken as definitive statements about what has not been observed.

Is there a way to prove a general statement about a class of things by showing that there is something about such things which necessitates the truth of a general statement about them? That approach begs the question. The “something about such things” can be discovered only by observation of a finite number of such things. The unobserved things are still lurking out of view, and any of them might not possess the “something” that is characteristic of the observed things.

All general statements about things, their characteristics, and their relationshships are therefore provisional. This inescapable truth has been dressed up in the guise of inductive probability, which is a fancy way of saying the same thing.

Not all is lost, however. If it weren’t for provisional knowledge about such things as heat and gravity, many more human beings would succumb to the allure of flames and cliffs, and man would never have stood on the Moon. If it weren’t for provisional knowledge about the relationship between matter and energy, nuclear power and nuclear weapons wouldn’t exist. And on and on.

The Humean-Popperian view is properly cautionary, but it doesn’t — and shouldn’t — stand in the way of acting as if we possess general knowledge. We must act as if we possess general knowledge. To do otherwise would result in stasis, or analysis-paralysis.

Quick Hits

There’s work underway to

find any of the genetic variants associated with intelligence, however weak and inconsistent they may be, and then look up the published literature to see how frequent those variants are in any racial group.

I’m fairly certain how it will turn out, if the work isn’t sabotaged by those who fear the truth.

Academe’s war on conservatism continues. What else is new?

There’s also a (not new) internet-based war on conservatism (e.g., here and here). Cass Sunstein, a leading light of the anti-free speech forces, was Obama’s regulatory czar. Connect the dots.

Robert Higgs hates the use of “we,” “us,” and “our” in policy discourse. So do I.

Steven Horwitz offers a concise and elegant gloss of Hayek’s “The Use of Knowledge in Society.” I’ve addressed Hayek’s essay here, and a related one (“The Pretence of Knowledge“) here.

Rationalism, Empiricism, and Scientific Knowledge

Take a very large number, say, 1 quintillion. Written out, it looks like this: 1,000,000,000,000,000,000. It can also be expressed as 1018 or 10.E+18.

I doubt that any human being has ever discerned 1 quintillion discrete objects in a single moment. Including the constituents of all of the stars and planets, there may be more than 1 quintillion particles of matter in the visible portion of the sky on a clear night. But no person may reasonably claim to have seen all of those particles of matter as individual objects.

I doubt, further, that any human being has ever discerned 1 million  objects in a lifetime, even a very long lifetime. And if I’m wrong about that, it’s certainly possible to conjure a number high enough to be well beyond the experiential capacity of any human being; 101000, for instance.

Despite the impossibility of experiencing 101000 things, it is possible to write the number and to perform mathematical operations which involve the number. So, in some sense, very large numbers “exist.” But they exist only because human beings are capable of thinking of them. They are not “real” in the same way that a sky full of stars and planets is real.

Numbers and mathematics are rational constructs of the minds of human beings. Stars and planets are observed; that is, there is empirical evidence of their existence.

Thus there are two1 types of scientific knowledge: rational2 and empirical. They are related in the following ways:

1. Rational knowledge builds on empirical knowledge. Astronomical observations enabled Copernicus to devise a mathematical heliocentric model of the universe, which was an improvement on the geocentric model.

2. Empirical knowledge builds on rational knowledge. Observations aimed at verifying the heliocentric model led eventually to the discovery that the Sun is not at the center of the universe.

3. Empirical knowledge may affirm or contradict rational knowledge. Einstein’s general theory of relativity, which is given in a paper written in 1915, says that light is deflected (bent) by gravity. Astronomical observations made in 1919 affirmed the effect of gravity on light. Had the observations contradicted the postulated effect, the general theory (if any) might be markedly different than the one set forth in 1915. (A scientific theory is more than a hypothesis; it has been substantiated, though it always remains open to refutation.)

4. Rational knowledge may lead to empirical knowledge. One of the postulates that underlies Einstein’s special theory of relativity is the constancy of the speed of light; that is, the speed of light is independent of the motion of the source or the observer. This is unlike (for example) the speed of a ball that is thrown inside a moving train car, in the direction of the train car’s motion. An observer who is stationary relative to the train car will see the speed of the ball as the sum of (a) its speed relative to the thrower and (b) the speed of the train car relative to the observer. Einstein’s postulate, which drew on James Clerk Maxwell’s empirically based theory of electromagnetism, was subsequently verified experimentally.

These reflections lead me to four conclusions:

  • Knowledge is provisional. Human beings often don’t know what to make of the things that they perceive, and what they make of those things is often found to be wrong.
  • When it comes to science, rational and empirical knowledge are intertwined, and their effects are cumulative.
  • Rational knowledge that can’t be or hasn’t been put to an empirical test is merely a hypothesis. The hypothesis may be correct, but it doesn’t represent knowledge.
  • Empirical knowledge necessarily precedes rational knowledge because hypotheses draw on empirical knowledge and must be substantiated by empirical knowledge.3

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Related reading:
Thomas M. Lennon and Shannon Dea, “Continental Rationalism,” Stanford Encyclopedia of Philosophy, April 14, 2012 (substantive revision)
Peter Markie, “Rationalism vs. Empiricism,” Stanford Encyclopedia of Philosophy, March 21, 2013 (substantive revision)

Related posts:
Hemibel Thinking
What Is Truth?
Demystifying Science
Are the Natural Numbers Supernatural?
Pinker Commits Scientism
The Limits of Science (II)
The Pretence of Knowledge
“The Science Is Settled”
The Limits of Science, Illustrated by Scientists

__________
1. This post focuses on scientific knowledge and ignores other phenomena that are sometimes classified as branches of knowledge, such as emotional knowledge.

2. In this context, rational means by virtue of reason, not lucid or sane. The discussion of rational knowledge is restricted to knowledge that derives from and is a logical extension of observed phenomena, as in the example with which the post begins. I will not, in this post, deal with intuition, innate knowledge, or innate concepts, which are also treated under the heading of rational knowledge.

3. Unless it is true that human beings are born with certain kinds of knowledge, or with certain concepts that can be filled in by knowledge. The article by Markie treats these possibilities at some length.

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