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, E1 = “All Martians wear hats and George is a Martian.” Now given E1 G is true. Another way to say it: Conditional on E1, G is true. Another: The probability G is true given E1 is 1, or 100%. Another: Accepting for the sake of argument E1, 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 E2 = “Most Martians wear hats and George is a Martian.” Given E2, 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 E3 = “No Martian wears a hat and George is a Martian.” The argument then (ideally, anyway) moves away from G and to which of E1, E2, or E3 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 aren’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.
Is this the “new” new layout? It looks suspiciously like the old.
Thinking about the assumptions of geometry and the parallel line postulate, it seems obvious we need to minimize what we “just know” to be certain or true. We don’t want to let our certainty about math interfere with our changing understanding of reality.
So what is the bare minimum? I think we can get by in math with just the proposition of consistency–Aristotle’s Law of Non-Contradiction. The experimental equivalent of this is Bayes’ Theorem.
Lies I tell you! Lies! You are a bishop of nasty teachings mr Briggs! May the almighty goddess of relativism strike you with relative hardship … sometime. Maybe!
It is a conservative blog.
We all know what you mean, but too much informality can lead astray too much. Just say ‘a priori’ and tell them what you mean, and be done with it.
I much prefer ‘a priori’ to ‘faith’, ‘belief’ ‘heart of hearts’, etc. I sometimes explain ‘a priori’ in terms of the Grandfather paradox for time machines. A real a priori sets the terms within which reasoning can begin and proceed; as such, a real a priori cannot be questioned from within the terms of the reasoning — like going back in time to kill your own grandfather — because then you yourself go poof.
A priori is to be preferred particularly to ‘belief’, principally because Wikipedia and everybody else says that Bayesianism is automatically what you would term ‘subjective Bayesianism’ and thus “describes degrees of belief” (= feeling, whim, what have you). And secondarily, because ‘belief’ and ‘faith’ can describe belief and faith in a person, which is an entirely different order of thing.
‘Intuition’ is philosophically loaded and no better informally than ‘feeling’ (whim, etc.)
Re relativism: Philosopher Alasdair MacIntyre outlines 18th and 19th century philosophy’s “quest for foundations” and lays bare its vulnerability to the postmodernist critique; in essence, postmodernism simply asks (over and over) if it’s turtles all the way down.
But MacIntyre also opines that pre-modern Western philosophy, particularly in Aquinas’s hands, is/was not vulnerable to the same critique.
MacIntyre himself does not go there, but it might be fair to say that for a long time, philosophy in the West really was (at least partially) based on ‘belief’ — in a Person — but that this eventually and methodologically, formally (= saying-it-out-loud) stopped being true of philosphy, which generated the ‘quest for foundations’, which …. Of course, nobody nowadays can even imagine founding serious philosophy on belief in a Person.
Webster’s 1918 gives this, complete with a quote from Coleridge:
a priori:
1. (Logic) Characterizing that kind of reasoning which deduces consequences from definitions formed, or principles assumed, or which infers effects from causes previously known; deductive or deductively. The reverse of a posteriori.
3. (Philos.) Applied to knowledge and conceptions assumed, or presupposed, as prior to experience, in order to make experience rational or possible.
“A priori, that is, form these necessities of the mind or forms of thinking, which, though first revealed to us by experience, must yet have preexisted in order to make experience possible”. Coleridge.
Re…”But I cannot write:
Pr( Y ) = something”
I get it, but why can’t I interpret Pr( Y ) as the probabliltiy that Y is true, given all possible prior conditions. That is
Pr( Y ) = Pr( Y | everything that may have a bearing on the occurrence of Y )
After all, isn’t this the sense of Pr( Y ) as contained in Bayes Theorem?