Fundamentals of Liberal Thought, Ctd.

Hypothesis: Every deduction is a concealed induction. (See below)

The previous post, Fundamentals of Liberal Thought, offered a beginning discussion of foundations—of the grounds of reason.

This post attempts elementary notes on the nature of fact and truth, from the Enlightenment liberal perspective. As before, the chief contestant for prevailing concept of truth is the archaic assumption implied by Plato's philosophic idealism. This is that entities have essences, that truth is a knowledge of essences, and thus that truth is absolute. A corollary is that what is true is necessarily so.

Liberalism's concept of truth is closely related to the perspective of empirical science: Truth is probabilistic. If a fact arrived at by induction is falsifiable—Karl Popper's famous proposition—it cannot be absolute.

Let's try a couple of definitions derived from the premise that truth is empirical and probabilistic:

1. Truth is a function of the current state of our knowledge; and
2. A truth is that conclusion, from the best available evidence that, when acted on, tends to produce the expected results.

(1) fits the Newton/Einstein case. At one time Isaac Newton's Philosophiae Naturalis Principia Mathematica was considered the ultimate revelation of the laws of nature. 'Nature and Nature's laws lay hid in night: God said, Let Newton be! and all was light,' exclaimed Alexander Pope. But a glitch was discovered:

A long-standing problem in the study of the Solar System was that the orbit of Mercury did not behave as required by Newton's equations.

The work of Albert Einstein revealed what had happened. Newton's conclusions were based on  observations of non-relativistic phenomena, and worked satisfactorily under those conditions. The Principia was a brilliant analysis of the knowledge of its time. Newton's formulae are still widely used in a wide number of practical cases, where velocity is not even close to the speed of light, and the sort of powerful close-to-a-star gravity well experienced by Mercury is not a factor. In such non-relativistic conditions, Newton's math is far simpler.

Newton's treatment of the regularities of nature is a subset of Einstein's treatment of the regularities of nature. Einstein's propositions and equations apply under a much wider set of conditions. (There was a debate in the USENET discussion group rec.arts.books, where humanities professors could not understand scientists' argument, that to say that Newton was "wrong" and Einstein was "right" is simplistic. Degrees of confidence does not fit an outlook derived essentially from Plato.)

It could be said that Plato's philosophical idealism was an attempt to solve the problem of induction* by deriving all knowledge from deduction, thereby achieving metaphysical certitude. (His model may have been theoretical mathematics, which some mathematicians see as a great structure of a priori truths existing before and outside of the "reality" we think we experience. The idea or Form is a similar a priori construction which is immaterial, eternal, perfect, unchanging, and imperceptible to the senses.)

The scientific/liberal response is that there are no absolutes, and metaphysical certitude is a will-o-the-wisp. The Forms, after all, are off in some invisible Platonic heaven (which only the Philosopher can see). By contrast, "The moderns [liberals] built on low but solid ground" (Leo Strauss quoted by Allan Bloom). Induction can give results which are certain for all practical purposes. Did you ever run across a street dodging cars? In doing so, you wagered your life on where moving cars would be (an ephemeral truth if there ever was one) when you went.

Hypothesis: Plato's effort was doomed from the start for the reason that it is impossible to start from deduction because every deduction is a concealed induction. A familiar universal principle, i.e. deduction, from theoretical mathematics such as "2 plus 2 equals 4" becomes, in applied mathematics,** an induction, such as "2 oranges plus 2 oranges equals 4 oranges." This induction is falsifiable. All it would require is a case where a grocery clerk put 2 oranges in a sack, then another 2 oranges, and the sack, upon inspection, contained any other quantity than 4 oranges.***

"2 plus 2 equals 4" is not necessarily true; if it were, it would be a prophecy about the future which we mortals are not permitted to make. (Nevertheless, most of us do not anticipate a disjuncture between integer mathematics and household purchases.)

For a more wide-ranging discussion of liberal modernity's objection to Plato, see Footnotes to Plato: Is Your Child's Humanities Professor Scornful of Your Values?



(*) The problem of induction is that it consists of conclusions derived from observation of physical reality (which Plato calls the realm of "appearances") and, according to Plato, produces "opinion" rather than "knowledge." A future observation could contradict those on which the induction is based—that is the problem.

(**) One can say that Plato engaged in equivocation, acting as if applied mathematics possessed the immutability of theoretical mathematics. (Equivocation: When a key term is used in two different senses in the same passage without acknowledgement. An example of legitimate equivocation (because the reader is aware of it) is Pascal's The heart has reasons of which reason knows nothing.)

(***) Perhaps this would be an example of definition (2) above: A truth is that conclusion, from the best available evidence that, when acted on, tends to produce the expected results.