Truth exists. Therefore, so does falsity. That truth exists is one of the many things we know to be true based on no external evidence. Naturally there are a very large number of things we know to be true given external evidence: most of what we believe to be true is this way.

Incidentally, though I can’t lay my hand on the book, and therefore must paraphrase, a statement by Roger Scruton in his *Modern Philosophy: An Introduction and Survey* is useful to us. Scruton cogently argues that relativists, in saying that it is certainly true that there are no truths, invite us to disbelieve them. Consequently, I shall not here argue against this (ever) seductive but obviously false philosophy.

If evidence for truth isn’t external, it must be internal. For example, we know via introspection, in our heart of hearts, or, even better, by accepting it on faith, that the following proposition is true: A = “For all numbers x,y = 1, 2, 3, …, if x = y then y = x.” Another way to put it: *Given* our faith, A is true. Or *given* our belief, A is true.

We know A is true relative to our faith, our belief. In this way the truth of proposition A is relative, but it’s a special kind of relativity, as we shall see. Contrast A with the proposition G = “George wears a hat” (yes, an old example, well known to regular readers, but still a good one). We have no sense that G is true or false, while A appears true after even momentary reflection. Why? Well, it turns out we are equipped—somehow, never mind here how (but it cannot be an empirical process which gives us this knowledge)—with the knowledge that A is so. But none of us comes pre-made with knowledge of G.

Suppose I give you this evidence, E_{1} = “All Martians wear hats and George is a Martian.” Now given E_{1} G is true. Another way to say it: Conditional on E_{1}, G is true. Another: The probability G is true given E_{1} is 1, or 100%. Another: Accepting for the sake of argument E_{1}, then G.

The truth of G is, just as A was, relative. But *we* had to supply external evidence which made G true, while we all of us come equipped-from-the-factory with the evidence that makes A true. This is made even clearer by supposing we supply evidence E_{2} = “Most Martians wear hats and George is a Martian.” Given E_{2}, G is not true, but neither is it false. It is somewhere in between. That somewhere in between falsity and truth is where probability lies.

G then can be true, false, or merely probable depending on the evidence with which it is assessed. It is important to understand that for most everyday propositions it is we who supply the evidence. For example, your enemy may insist that G is false because he holds that E_{3} = “No Martian wears a hat and George is a Martian.” The argument then (ideally, anyway) moves away from G and to which of E_{1}, E_{2}, or E_{3} is true.

But how do we know that any of these are true? Well, they aren’t any of them obviously true, as A was, so we need to supply further evidence with which to gauge each E. What if we take F = “There are no Martians”? What happens to G for each E? What if F = “Observations suggest there are no Martians”? How about F = “I have no idea if there are any Martians”? And F = “There are either Martians or there aren’t”?

That’s it for the post; much more in the book, which you must read to keep up (Chapters 1 and 2 today). But there’s also material in this post which isn’t in the book. Which means I have to finish re-writing the book. Time…

**Homework**

Read then do the questions in Chapter 1, paying especial attention to the challenge to name other propositions which you “just know” are true. Are they really true, or are there hidden or tacit assumptions which you are using? You have to be careful because it is easy to fool yourself. However, this is not necessarily a bad thing.

For example, a person may hold that B is true “just because”, or by faith, or relative to introspection, or whichever synonymous phraseology you prefer. But it might turn out we can prove that B is true only because W, X, Y, … and so on are true; and they true only because some fundamental axiom C is true. But none of this makes B false. Indeed, suppose B = “Four divided by two equals two.” Well, it’s just true! It isn’t, but if you were to believe it, you would not be making an error, at least about the truth of B.

Here is an exercise to prove that probability is not subjective. The United Nations Conference on Sustainable Development, or Rio+20 Earth Summit begins this week (guess where: no, really, guess: why is your guess right or wrong?). Canada’s Environment Minister Peter Kent said “We just arenâ€™t seeing people arriving in the frame of mind to make significant progress towards significant commitments. And we clearly need that.”

What is the probability that H = “The Rio+20 Leaders make significant progress towards significant commitments”? Supply the *exact* evidence and chain of argument you use to specify this probability. Try not to be facetious and you will learn something. This is a real assignment, incidentally.

The moral of today’s lesson is: know what you’re arguing about.