An empirical fact, as I call it, is a claim about motion in his/her locality which may/can be observed and tested experimentally by any individual who chooses to look and think for him/her self. It may also be that individuals who do the necessary work can honestly agree that a new empirical fact is a logical consequence of known empirical facts.
What makes an empirical fact locally true is that communicating individuals who honestly think about that claim agree about it. This is the subtle way in which Reality/Nature discovers/reveals its local truths to any individual who seeks to understand what happens in his/her locality.
Euclidean Geometry is the ancient science of drawings that can be made, with ruler and compass, upon a flat surface called the Euclidean plane. Euclid’s logic was/is a useful way of inferring surprising empirical facts from simpler empirical facts.
In the logic of Euclid, the Theorem of Pythagoras, an astonishing empirical fact, about the ruler and compass drawings which can be made on the Euclidean plane, is inferred from the simple/obvious empirical fact that the area of a triangle does not change when the triangle is moved in the plane. [That idea persists in modern Physics under the name gauge invariance.] There are many proofs of the Pythagoras Theorem using this empirical fact — including the proof of Euclid which impressed me, millennia later, as a mid-20C Tasmanian schoolboy.
The logic of mathematics is a way of inferring surprising empirical facts like the Pythagoras Theorem from simpler empirical facts like invariance of the area of a triangle under movements of the triangle.
The logic of mathematics must be distinguished from the incorrect thinking called “Logic”, of Aristotle and others in ancient Athens, when they made the very consequential error of thinking that the precise logic used so successfully to prove theorems of Euclidean geometry would work for the imprecise/vague talk that individuals use in their every-day communications with others. That was the hubris of a younger man repudiating the teaching of his teacher, Plato. [Plato’s thinking about Reality, though different, was/is also incorrect.]
“Logic”, as conceived by Aristotle, is a way of inferring “objective facts” from “objective facts. But plainly a chain of such inferences must begin with a fact that is objective in the very strong sense that it is not inferred from other truths. Euclidean Geometry offers brilliant examples of this.
Until the Twentieth Century, Aristotle’s plain error, with the imprecise/meaningless talk it is about, was blindly accepted by those who call themselves “Philosophers”. And hence by many individuals who would like to understand the Reality in which they find themselves.
It is as instructive now as ever to think about what is wrong with Aristotle’s misconceived “Logic”. As you will see, the key for this is to recognise the clear separation of Reality itself from the many ways for talking about Reality that are allowed/supplied (in/by Reality!) to individual human beings like you and me.
The classical inference rule Modus ponens, as in
all men are mortal, Socrates is a man
Socrates is mortal
relies upon the incorrect belief that the “Logic” which embraces it is about Reality and displays, to whoever looks closely, the correct belief that logic is about Language, not about Reality.
That specific inference fails because its language, unlike Euclid’s, is imprecise. In the simple philosophy I call Science, this specific inference embraces two distinct errors. A more precise paraphrase would be:
all men die, ‘Socrates’ is the name of a man”
Here we may see that the inference must fail because a fact about a unique individual cannot be inferred from a fact about his/her name.
A second reason that the inference must fail is that the claim that “all men die” cannot be tested; hence that claim must be excluded (as meaningless) from whatever science is here considered.
Unfortunately, it is all too easy to imagine that the weasel word “mortal” has a non-empirical (“metaphysical”? or “transcendental”?) meaning.
Of course, I do not deny that an individual who subscribes to the inference rule in its original form, and who believes that he knows the objective meanings of the claims “all men are mortal” and “Socrates is a man” and believes that both are true is thereby compelled (by his “reason”!) to believe that “Socrates is mortal” must also be true!
I think that just this refutation of Modus Ponens demolishes Aristotelian “Logic”. Be that as it may, one may apply similar arguments to other instances of Aristotelian “Logic” like the one which follows.
Graham Priest (in his book Logic - A Very Short Introduction) considers the following to be a “very straightforward” inference:
If the burglar had broken in through the kitchen window, there would be footprints outside; but there are no footprints; so the burglar did not break in through the kitchen window.
The confusion of empirical reality with talk about empirical reality is here plainly on display. The chosen inference does not deal with Reality itself, only with English-language talk about Reality. Clearly the truth or otherwise of such talk depends upon what the individual talker means by the words he uses. And individual listeners may have their own ideas of those meanings. Plainly there is room here for fruitful discussion by individuals open to changing their minds if necessary.
It is enlightening to replace Professor Priest’s objectivist formulation of his straightforward inference by a subjectivist paraphrase, as follows:
Priest, truthfully believes that any one who truthfully says “if the burglar had broken in through the kitchen window, there would be footprints outside” and who also truthfully says that “there are no footprints” is obliged thereby to truthfully conclude that “the burglar did not break in through the kitchen window.”
I agree with that, not because I accept Aristotelian “Logic” but because I think that evolution has generated human brain/minds which are able to think, in accord with strict empiricism, telling the truth and trusting others who tell the truth. While an individual is able to lie, he knows that it is wrong to do so.
One of the many incorrect/wrong consequences of “Philosophy”, the Aristotelian way of thinking, is the modern story/theory called Artificial “Intelligence”. To cut a long story short, that is the silly idea that a computer might be able to think like you or me. Briefly, a computer cannot tell the truth and know it, as you can and I can; but a computer easily lies if that is what its program requires.
What a computer is able to do is retain far more information than you or I can memorise and to slavishly process that information by following the sometimes useful, sometimes harmful instructions, called programs, that are specified by human programmers. The 1996 defeat of Gary Kasparov by Big Blue was an example of this. Big Blue is/was a brain without a mind.
[Apologies for the conceptual difficulties of this page; as you may have realised, I am trying to unravel the incorrect/bad objectivist way of thinking that has cumulatively armed itself against the correct/good subjectivist alternative for around 2,300 years.]