There Is No Such Thing As Intrinsic Probability

This is less fun than looking at the so-called principle of indifference, which you must read first, and I realize we’re wading into the depths and on a Friday, but I wanted to finish Draper’s paper for two reasons: a few people are interested, and if I don’t do it now, I never will.

Draper defines intrinsic probability for a hypothesis (proposition) as the “probability independent of the evidence we possess for or against it.” Since probability is epistemological and not ontological, and since all probability is conditional of stated premises, I cannot see how this definition makes any sense. There is no such thing as unconditional probability, therefore there can’t be “intrinsic” probability. The closet we could come is if probability was ontological, which it isn’t. Nevertheless, let’s examine his justification and see what comes of it.

Intrinsic probability “consists of three postulates: that intrinsic probability depends on modesty, that it depends on coherence, and that it does not depend on anything else.”

Modesty

“The degree of modesty of a hypothesis depends inversely on how much it asserts (that we do not know by rational intuition to be true). Other things being equal, hypotheses that are narrower in scope or less specific assert less and so are more modest than hypotheses that are broader in scope or more specific.”

One example of “modesty” he gives is “the hypothesis that either Hilary Clinton or Nancy Pelosi will be the 45th President of the United States is less specific and thus intrinsically more probable than the hypothesis that Joe Biden will be the 45th President.”

This is meaningless as it stands, unless it is accompanied by conditions/evidence/premises. It is the same as asking, “What is the probability that ‘A Schmenge will come out‘”? There is no tying that proposition to anything; it has no probability, not unconditionally. No proposition does. You are left groundless if you are wholly ignorant of the meaning or context of the proposition. It is like asking what is the intrinsic probability of ‘雪是黑的’ (which I hope I have right)? Unless you read traditional Chinese, unless, that is, you accept premises such as the meaning of the symbols, you can’t answer. There is no intrinsic probability.

Now if I offer E = ‘There are 12 people in the room two of which are Schmenges and one person must come out” the probability of ‘A Schmenge comes out’ given E is 1/6. But if E = ‘There are two people in the room both of which are Schmenges and one person must come out’ the probability of ‘A Schmenge comes out’ given this E is 1. Change the premises, change the probability.

I think Draper might have in mind evidence something like E = ‘There will be n candidates for the 45th President of the US, and these include Clinton, Pelosi and Biden, and only one candidate will win’. Given that, and given only that E, the probability of ‘Clinton or Pelosi wins’ is 2/n, which is higher than ‘Biden wins’, which has probability 1/n.

With the ‘A Schmenge comes out’, unless you knew, as all good people should know, Cabbage Rolls and Coffee, you had nothing to bring to the mental table. No evidence or premises sprang to your mind, thus the probability seemed incalculable. There was no intrinsic evidence for it, thus no intrinsic probability.

Premises surely do swim into view—it is impossible for most of us to keep from this—when assessing whether Joe “Are My Hair Plugs Too Tight?” Biden versus Hilary “What’s A Benghazi?” Clinton will win the Democrat nomination, let alone the presidency. For myself, I judge Mrs Clinton to have a higher chance than Mr Biden, who in my opinion missed the turn off to Sanity quite a few miles back. But maybe you have a different idea. If so, you will have a different probability for Draper’s propositions, but only because you have different evidence. No piece of evidence is more intrinsic than any other. But if we agree on the evidence, such as that I supposed Draper might have had in mind, then we have to agree on the probability.

Coherence

“To the extent that the various claims entailed by a hypothesis support each other (relative only to what we know by rational intuition), the hypothesis is more coherent.” His example, which will take a couple of readings:

Consider, for example, the hypothesis that all crows are black. This hypothesis is identical to the hypothesis that all non-Asian crows are black and all Asian crows are black. Now compare this hypothesis to a second hypothesis, namely, that all non-Asian crows are black and all Asian crows are white. The two hypotheses are equally modest, but not equally coherent. The first half of both hypotheses states that all non-Asian crows are black. This supports the second half of the first hypothesis, which states that Asian crows are also black, while it counts against the second half of the second hypothesis, which states that Asian crows are white. Thus, the hypothesis that non-Asian and Asian crows are all black is more coherent and thus intrinsically more probable than the equally modest hypothesis that all non-Asian crows are black and all Asian crows are white.

Proposition 1: P1 = ‘All non-Asian crows are black and all Asian crows are black’. Proposition 2: P2 = ‘All non-Asian crows are black and all Asian crows are white.’ Draper claims the probability of P1 is “intrinsically more probable” than P2.

Again, since both propositions are anchor-free there just is no probability. Suppose I invent E = ‘All the crows I have seen are black’, then P1 is more probable than P2 given this E, only because P2 allows crows of a color I haven’t yet seen. Or suppose E = ‘Animal species coloring is independent of continent’ then again P1 is more probable than P2 given this E. But then I might have E = ‘Animals are lighter colored in Asia than in other continents’, then P1 is less probable than P2 given this E.

If Draper thinks P2 less probable than P1 he must have some sort of “uniformity of animal color” evidence in mind. Maybe that evidence is even right, or close to right. But it’s still evidence even if it’s unstated, meaning there is no “intrinsic” probability of either proposition only probabilities conditional on tacit premises. And indeed Draper closes this section with the words (meant as self-proving), “More generally, hypotheses that attribute objective uniformity to the world are, other things being equal, intrinsically more probable than hypotheses that postulate synchronic or diachronic variety.”

Nothing else needed

“[I]ntrinsic probability does not depend on anything else besides modesty and coherence.” His proof is “ask yourself: what else could the intrinsic probability of a hypothesis depend on besides how little the hypothesis says (its modesty) and how well what it says fits together (its coherence)?” Meh.

Extensions & Homework

There’s more to Draper’s paper, but that’s enough for us. I believe Draper recognized the weaknesses given above, which is why the paper was never published, so there’s no point going on and on. He does bring up the venerable grue (which I just realized we never did), and Richard Swinburne’s ideas of intrinsic probability (which I say are also wrong), and induction. But enough’s enough for today.

Now homework. Dissect these examples in the manner I did above, to show they do not have intrinsic probability, but that all have tacit unacknowledged premises. Hint about the arsenic example: how hard is it to exclude all you already know about arsenic before answering this?

1. Under modesty. “First, the hypothesis that all cats are curious is narrower in scope and so intrinsically more probable than the hypothesis that all animals are curious.”

2. Under coherence. “[T]he hypothesis that all arsenic is poisonous to human beings is intrinsically more likely to be true than the hypothesis that, while all observed arsenic is poisonous, all unobserved arsenic is nutritious.”