There are four kinds of truth: physical, logical-mathematical, psychological-emotional, and judgmental. The first two are closely related, as are the last two. After considering each of the two closely related pairs, I will link all four kinds of truth.

PHYSICAL AND LOGICAL-MATHEMATICAL TRUTH

Physical truth is, seemingly, the most straightforward of the lot. Physical truth seems to consist of that which humans are able to apprehend with their senses, aided sometimes by instruments. And yet, widely accepted notions of physical truth have changed drastically over the eons, not only because of improvements in the instruments of observation but also because of changes in the interpretation of data obtained with the aid of those instruments.

The latter point brings me to logical-mathematical truth. It is logic and mathematics that translates specific physical truths — or what are taken to be truths — into constructs (theories) such as quantum mechanics, general relativity, the Big Bang, and evolution. Of the relationship between specific physical truth and logical-mathematical truth, G.K. Chesterton said:

Logic and truth, as a matter of fact, have very little to do with each other. Logic is concerned merely with the fidelity and accuracy with which a certain process is performed, a process which can be performed with any materials, with any assumption. You can be as logical about griffins and basilisks as about sheep and pigs. On the assumption that a man has two ears, it is good logic that three men have six ears, but on the assumption that a man has four ears, it is equally good logic that three men have twelve. And the power of seeing how many ears the average man, as a fact, possesses, the power of counting a gentleman’s ears accurately and without mathematical confusion, is not a logical thing but a primary and direct experience, like a physical sense, like a religious vision. The power of counting ears may be limited by a blow on the head; it may be disturbed and even augmented by two bottles of champagne; but it cannot be affected by argument. Logic has again and again been expended, and expended most brilliantly and effectively, on things that do not exist at all. There is far more logic, more sustained consistency of the mind, in the science of heraldry than in the science of biology. There is more logic in Alice in Wonderland than in the Statute Book or the Blue Books. The relations of logic to truth depend, then, not upon its perfection as logic, but upon certain pre-logical faculties and certain pre-logical discoveries, upon the possession of those faculties, upon the power of making those discoveries. If a man starts with certain assumptions, he may be a good logician and a good citizen, a wise man, a successful figure. If he starts with certain other assumptions, he may be an equally good logician and a bankrupt, a criminal, a raving lunatic. Logic, then, is not necessarily an instrument for finding truth; on the contrary, truth is necessarily an instrument for using logic—for using it, that is, for the discovery of further truth and for the profit of humanity. Briefly, you can only find truth with logic if you have already found truth without it. [Thanks to The Fourth Checkraise for making me aware of Chesterton’s aperçu.]

To put it another way, logical-mathematical truth is only as valid as the axioms (principles) from which it is derived. Given an axiom, or a set of them, one can deduce “true” statements (assuming that one’s logical-mathematical processes are sound). But axioms are not pre-existing truths with independent existence (like Platonic ideals). They are products, in one way or another, of observation and reckoning. The truth of statements derived from axioms depends, first and foremost, on the truth of the axioms, which is the thrust of Chesterton’s aperçu.

It is usual to divide reasoning into two types of logical process:

• Induction is “The process of deriving general principles from particular facts or instances.” That is how scientific theories are developed, in principle. A scientist begins with observations and devises a theory from them. Or a scientist may begin with an existing theory, note that new observations do not comport with the theory, and devise a new theory to fit all the observations, old and new.

• Deduction is “The process of reasoning in which a conclusion follows necessarily from the stated premises; inference by reasoning from the general to the specific.” That is how scientific theories are tested, in principle. A theory (a “stated premise”) should lead to certain conclusions (“observations”). If it does not, the theory is falsified. If it does, the theory lives for another day.

But the stated premises (axioms) of a scientific theory (or exercise in logic or mathematical operation) do not arise out of nothing. In one way or another, directly or indirectly, they are the result of observation and reckoning (induction). Get the observation and reckoning wrong, and what follows is wrong; get them right and what follows is right. Chesterton, again.

PSYCHOLOGICAL-EMOTIONAL AND JUDGMENTAL TRUTH

A psychological-emotional truth is one that depends on more than physical observations. A judgmental truth is one that arises from a psychological-emotional truth and results in a consequential judgment about its subject.

A common psychological-emotional truth, one that finds its way into judgmental truth, is an individual’s conception of beauty.  The emotional aspect of beauty is evident in the tendency, especially among young persons, to consider their lovers and spouses beautiful, even as persons outside the intimate relationship would find their judgments risible.

A more serious psychological-emotional truth — or one that has public-policy implications — has to do with race. There are persons who simply have negative views about races other than their own, for reasons that are irrelevant here. What is relevant is the close link between the psychological-emotional views about persons of other races — that they are untrustworthy, stupid, lazy, violent, etc. — and judgments that adversely affect those persons. Those judgments range from refusal to hire a person of a different race (still quite common, if well disguised to avoid legal problems) to the unjust convictions and executions because of prejudices held by victims, witnesses, police officers, prosecutors, judges, and jurors. (My examples point to anti-black prejudices on the part of whites, but there are plenty of others to go around: anti-white, anti-Latino, anti-Asian, etc. Nor do I mean to impugn prudential judgments that implicate race, as in the avoidance by whites of certain parts of a city.)

A close parallel is found in the linkage between the psychological-emotional truth that underlies a jury’s verdict and the legal truth of a judge’s sentence. There is an even tighter linkage between psychological-emotional truth and legal truth in the deliberations and rulings of higher courts, which operated without juries.

PUTTING TRUTH AND TRUTH TOGETHER

Psychological-emotional proclivities, and the judgmental truths that arise from them, impinge on physical and mathematical-logical truth. Because humans are limited (by time, ability, and inclination), they often accept as axiomatic statements about the world that are tenuous, if not downright false. Scientists, mathematicians, and logicians are not exempt from the tendency to credit dubious statements. And that tendency can arise not just from expediency and ignorance but also from psychological-emotional proclivities.

Albert Einstein, for example, refused to believe that very small particles of matter-energy (quanta) behave probabilistically, as described by the branch of physics known as quantum mechanics. Put simply, sub-atomic particles do not seem to behave according to the same physical laws that describe the actions of the visible universe; their behavior is discontinuous (“jumpy”) and described probabilistically, not by the kinds of continuous (“smooth”) mathematical formulae that apply to the macroscopic world.

Einstein refused to believe that different parts of the same universe could operate according to different physical laws. Thus he saw quantum mechanics as incomplete and in need of reconciliation with the rest of physics. At one point in his long-running debate with the defenders of quantum mechanics, Einstein wrote: “I, at any rate, am convinced that He [God] does not throw dice.” And yet, quantum mechanics — albeit refined and elaborated from the version Einstein knew — survives and continues to describe the sub-atomic world with accuracy.

Ironically, Einstein’s two greatest contributions to physics — special and general relativity — were met with initial skepticism by other physicists. Special relativity rejects absolute space-time; general relativity depicts a universe whose “shape” depends on the masses and motions of the bodies within it. These are not intuitive concepts, given man’s instinctive preference for certainty.

The point of the vignettes about Einstein is that science is not a sterile occupation; it can be (and often is) fraught with psychological-emotional visions of truth. What scientists believe to be true depends, to some degree, on what they want to believe is true. Scientists are simply human beings who happen to be more capable than the average person when it comes to the manipulation of abstract concepts. And yet, scientists are like most of their fellow beings in their need for acceptance and approval. They are fully capable of subscribing to a “truth” if to do otherwise would subject them to the scorn of their peers. Einstein was willing and able to question quantum mechanics because he had long since established himself as a premier physicist, and because he was among that rare breed of humans who are (visibly) unaffected by the opinions of their peers.

Such are the scientists who, today, question their peers’ psychological-emotional attachment to the hypothesis of anthropogenic global warming (AGW). The questioners are not “deniers” or “skeptics”; they are scientists who are willing to look deeper than the facile hypothesis that, more than two decades ago, gave rise to the AGW craze.

It was then that a scientist noted the coincidence of an apparent rise in global temperatures since the late 1800s (or is it since 1975?) and an apparent increase in the atmospheric concentration of CO2. And thus a hypothesis was formed. It was embraced and elaborated by scientists (and others) eager to be au courant, to obtain government grants (conveniently aimed at research “proving” AGW), to be “right” by being in the majority, and — let it be said — to curtail or stamp out human activities which they find unaesthetic. Evidence to the contrary be damned.

Where else have we seen this kind of behavior, albeit in a more murderous guise? At the risk of invoking Hitler, I must answer with this link: Nazi Eugenics. Again, science is not a sterile occupation, exempt from human flaws and foibles.

CONCLUSION

What is truth? Is it an absolute reality that lies beyond human perception? Is it those “answers” that flow logically or mathematically from unproven assumptions? Is it the “answers” that, in some way, please us? Or is it the ways in which we reshape the world to conform it with those “answers”?

Truth, as we are able to know it, is like the human condition: fragile and prone to error.