Friday, 22 November 2013

Why you should make improbable claims.

There is a sense in which the title of this entry may seem misleading. If 'improbable' is read in a certain way, the assumption will be that my intention is to encourage theories that are bizarre relative to what would be a more practical conclusion given our best (by which I mean most successfully tested) theories. A concrete example of a 'bizarre' or improbable theory of this sort would be something like this:

Light speed is relative to human imagination. Much like pixie dust in Neverland, the human subject has to believe and then it will behave how they want it to. 
This theory is clearly 'bizarre' or improbable. It makes claims about light, and the power of the human mind to directly interfere with the laws of nature, which are contrary to our best knowledge in science. More precisely there's an arbitrariness or variability to it. Why does the ritual require 'believing' as a control mechanism and not say a song, or a dance. Or why indeed this theory at all and not another theory of light, say that: human can't control light speed because it's the work of the gods. Not working within the confines of epistemology opens the door for theories as fiction or nonsense.

So I'd clearly have my work cut out for me if this was at all the reading I intended. Which it was, but only so I could turn it all around and show that there is another reading, which makes a lot of sense.

'Probable' has two meanings in ordinary language, at least two proper meanings (it may also be misused in certain ways).

(i) The first is the one we have seen above, a soft meaning. We may find this kind of 'probable' in sentences like 'I'm probably going to the party Saturday' or 'probable she forgot'. What it means in this usage is that we are not sure either way, but theory A (going to the party, or 'she' forgetting) has tested better than theory B (not going to the party, 'she' not forgetting). So going back to the world of science, we might describe Einstein's theory as much more probable than Newton's.

(ii) The second meaning is stricter. Here 'probable' refers to the probability calculus.

A common mistake is when (ii) will be assumed to show (i). That is, if the probability calculus is high, then it's our best/most tested theory, and vice versa.

Consider the prevalence of this view. We see it in our every day lives when we flick (or more accurately scroll) through a popular magazine and read about topics claiming things like 'studies have found blonds really do have more fun', where surveys and statistics are used to establish generalisations.

We also see it in the supposed solution to the problem of induction. Induction attempts to show a proposition true for having a pattern of occurrence. The problem is, the future doesn't always resemble the past. By making the mistake, however, that (ii) implies (i), philosophers have argued that we should believe propositions reached through inductive logic not because they're guaranteed, but because they're probable. So for example, if the proposition P was that the sun will rise tomorrow, and our induction was that it has always risen previously, it is thought that we can accept P because it scores highly with probability calculus.

So what's the problem with equating (i) and (ii)?

The problem is the rule 'obtain high probabilities!' (ii) puts a premium on ad hoc hypotheses. Put simply, (ii) is mostly likely to wield high results the less information it actually has to work with, which far from leading to (i) is actually at odds with it, as (i) has it that our best theory is the one that has been successfully tested the *most*.

You can make 'the sun will rise tomorrow' less and less probable according to (ii), just by adding more information: That the sun will burn out, that weather conditions can hid sun rises, or the plenitude of distastes that can occur such as supernovas and meteoroids. In doing this the (ii) would go down, even though we could speak more expertly on (i).


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