"The insights of the philosophers I studied seemed murky and inconsequential compared to the dazzling successes of physics and mathematics. From time to time since then I have tried to read current work on the philosophy of science. Some of it I found to be written in a jargon so impenetrable that I can only think that it aimed at impressing those who confound obscurity with profundity." Steven Weinberg

"What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another. A propositional sign is a fact." Wittgenstein

What is a fact?

Most people seem to know, but at the beginning of the 20^th century, a troubled young man called Wittgenstein had a strange notion. People still debate what he meant, but he inferred that any statement containing a formal structure would be a fact, and the totality of facts would be the totality of statements that could be evaluated logically.

Perhaps Wittgenstein meant that "facts" are statement that could only be contradicted by statements of a similar type. A statement; "the moon is made of green cheese" would be a fact, because it could be contradicted by the statement that; "the moon is made of metals and silicates". Wittgenstein in this case would not be interested in what the moon was made of. He was only ensuring that statements were made in a manner that we could logically evaluate.

Why insist on such a weird concept?

Wittgenstein wrote when philosophers were searching for a logical basis for reasoning, but were running into paradoxes. Earlier definitions of facts used terms like 'sense impression', but if this sounded recondite, it was misleading. If people spot a strange object in the sky one person might have an impression 'weather balloon', and another 'alien spaceship'. But a monkey would see a 'strange object' because weather balloon and spaceship are not sense impressions, but concepts expressed by language. So, whereas sense impressions are available to all creatures, facts are only available to humans, and because of language. Moreover, to derive utility from facts we must place them in a language context. In Western language useful statements form a subject-predicate relationship in a sentence, co-joined by a verb. If we see a strange object in the sky say, we should assert, explicitly; "That is a weather balloon" or "That is an alien spaceship". Then we can have a productive discourse about what the strange object in the sky really is.

Moreover, there exist true statements that cannot be contradicted by facts. The maxim of former Vice President Dan Quayle that "if we don't succeed, we run the risk of failure" is a statement that is true but cannot be contradicted by facts. Such statements are tautologies (always true). But while Dan Quayle's tautology was not profound, some tautologies are so useful that we might mistake them for facts, not just facts of the Wittgenstein type, but common sense facts as well.

Despite these concerns this book will use a formal definition of facts. Kant called statements that can be contradicted synthetical. So facts are synthetical statements that cannot be contradicted further by other valid knowledge. Thus; "a carbon atom has 12 protons" can be contradicted, but not by valid knowledge. It is a fact. This allows facts to be the thing which people expect of them; an assertion which is true. But making facts depend on statements does have advantages. For one, we could have assuaged the deeply troubled Wittgenstein (he is now dead) that if any person claimed to know a fact, we would require that person to assert in unambiguous terms exactly the proposition that was intended.

Now, let us consider the next problem.

If science had discovered 1,000,000 facts, and mathematicians had proven 1,000,000 equations true beyond contradiction, how many useful pieces of information would humanity know?

1. Less than 1,000,000
2. 1,000,000
3. 1,000,001 (one million and one)
4. 2,000,000
5. 2,000,001 (two million and one)
6. More than two million and one
7. All the above except 1. (Less than 1,000,000 is incorrect.)

Radical philosophy would teach that any answer except 2 (1,000,000 pieces of information) would be a form of insanity. Yet ironically, if any answer other than 2 were incorrect, 3 would be the correct answer! (We would know 1,000,000 facts plus some extra information about what constituted an act of insanity.)

But why does the 1,000,000 equations not add any new knowledge? All any equation does is state that all objects to the left of the equals sign are equivalent to those on the right. So Einstein's equation

These only present the same logical equality in a different form. So, equations are another form of tautology, and 1,000,000 equations do not tell us any more than one does. It sounds strange, but consider a simple example. If I had budgeted $1,000 for a project and I spent already $257, I might write an equation;

The number "$643" might appear to tell us something, but it does not. If I changed the budget to $2,000 then the number on the right simply adjusts to "$1,643" and so on. So, the only "fact" is that I have spent $257. The budget does not change what I have spent. The equality;

It is true all the time and cannot be contradicted by new information.

Einstein's equation (E = mc²) is also a tautology, until we assert the meanings of E, m, and c, as facts, such as E is energy, m is mass, etc. (This becomes controversial when one uses unfamiliar equations, as this author does in Chapter 2.4.) Statements that cannot by contradicted by facts are analytical. And while analytical statements include them, we restrict tautology to statements with a logical structure "A or not A" ("it is raining or it is not raining"). Such statements are impossible to be false. So Quayle's maxim is a tautology, though in everyday speech we say it is 'irrefutable', then let people figure out why.

Plus the class of analytical propositions including equations, would only be tautologies if humans were infinitely wise. If one were infinitely good at arithmetic, the equality 357 x 459 = 163,863 is a tautology. But if one were poor at arithmetic and required to calculate 357 x 459, the answer would be useful information because it would free the mind for tasks which were not tautologies. That is why computers are so useful. They show us how tautologies can be resolved instantaneously, leaving the mind free for other tasks.

The acquisition of knowledge then, should be a three-step process. (Or a cyclic three-step process, as acquiring knowledge is iterative.) First, try to uncover as many facts as possible. Second, use reasoning and logic to prove the non-contradiction of things that are already known, against concepts that we are attempting to discover. Third, having exhausted the resources of the first two steps, make a choice over which actions to take, or which things to believe.

1. Establish the facts.
2. Prove the non-contradiction of facts against situations we that we hypothesize about.
3. Make a choice.

Apart from the third step, all this has been said before. Facts are statements of a type that can only be contradicted by other facts, but no contradiction can be found. "The Earth is five billion years old" is a fact, unless it can be contradicted by another fact. Proof of non-contradiction is analysis. Formal analysis includes logic and mathematics. If humans were infinitely wise proof of non-contradiction would be tautology. If we wish to transpose facts that apply in one circumstance to a situation about which we hypothesize, we need to transpose the facts by methods free from contradiction. It is not rocket science, but suppose we did wish to send a rocket to Mars, and all the facts we knew concerned how rockets flew on Earth. We would use mathematics to prove non-contradiction of everything we knew about how rockets flew on Earth to how we presume they would fly on Mars. Before sending one there, we still will not know all the facts about how rockets will behave on Mars. But we hope the equations we are using that transpose Earth facts into Mars facts are themselves free from contradiction. In other words, we hope that the equations are themselves tautologies.

Knowledge is to increase options. We evaluate the usefulness of any statement by seeing if it presents viable choices. This gives primacy to factual knowledge, which always confronts us with the most discernible choices. If there is a drought, praying for rain might be a choice, but it is not a productive one if we can verify that the climate will not allow rain at that time. So, any knowledge system requires choices, such as how to deal with drought. But when seeking options we do not dismiss moral knowledge, if it provides meaningful choices. Churchill's statement; "We will fight them on the beaches... We will never surrender..." presented people with real choices over what to do next. Even the usefulness of tautologies can be evaluated this way. Statements that; "we can only prove that humans seek to maximize options by acting out our choices wisely" and; "if we don't succeed, we run the risk of failure" are both tautologies, saying almost the same thing. ("If it is A it cannot be not A.") But in practice tautologies have different values depending on the options they present over what to do next.

Facts or analyses, even from science, come in the confrontational "these are the facts, now what are our options". So though it arises from analytical philosophy, far from being dismissive of them, the Theory of Options teaches that choices made beyond the limits of facts and analyses are the crux of human action. We seek facts or analyses not for inherent qualities, but so these might delimit for us in the most unambiguous way, what our real human choices are.

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