Saturday, February 23, 2013

Probability and Certainty

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Probability

Ellery Eells explains probability is a numerical value that can be attached to items of various events, and kinds of events and measures the degree to which this may or should be expected. Eells (1996: 649). Eells reasons there are multiple interpretations of probability and there are abstract formal calculi and interpretations of the calculi. Eells (1996: 649).

Blackburn writes that 'probability is a non-negative, additive set function whose maximum value is unity'. Blackburn (1996: 304). Applying probability in the real world is more difficult and the first application is statistical. Blackburn (1996: 304). Statistical as in the tossing of the coin, heads versus tails and the frequency of a particular outcome and then calculating the probability of the outcome. Blackburn (1996: 304). One account of probability is therefore known as 'frequency theory', as in the probability of an event with frequency of occurrence. Blackburn (1996: 304). A second account of probability is described as 'an hypothesis as probable when the evidence bears a favoured relationship to it'. Blackburn (1996: 304). These are not empirical measures of frequencies. Basically they would be based on philosophical deductions based in reason. A third approach is sometimes referred to as subjectivism or personalism. Basically not an objective or real evaluation of the world, but rather a subjective evaluation of personal reality. Blackburn (1996: 304). However, Blackburn does write that one should not be governed by empirical frequencies and not by 'licentious thinking' (without restraint). Blackburn (1996: 304).

Certainty

As noted previously on this blog, Edward Gettier has argued in ‘Is Justified True Belief Knowledge?’ that believing something is true does not make it knowledge because the person lacks sufficient conditions for knowing a proposition. Gettier (1997)(1963: 3). In other words, many true propositions would have been deduced as true, not by knowledge but by felicitous (fortunate) coincidence. Klein (2005)(1998: 2-3). I can agree that finite human beings can deduce that something is true without really knowing it. As well, with the human lack of 100% knowledge of anything (only the infinite God has 100% knowledge), it does mean that it is also possible that there could be conditions in existence not known and that a proposition that is held as true is really false. However, I do not think that Gettier’s argument should trouble those who view the Christian faith as certain because Klein points out concerning Gettier’s view that to many thinkers felicitous coincidence can be avoided if the reasons which justify belief are such that they cannot be defeated by further truths. Klein (2005)(1998: 2-3). Klein’s certainty concept in regard to felicitous coincidence is similar to the one described below from The Cambridge Dictionary of Philosophy. In other words, if views are reasoned by deduction and evidence, they can be considered knowledge provided they are not countered by superior arguments. This does not require 100% certainty of anything, but rather an accurate understanding of conditions that would lead to the formation of propositions and arguments.

As mentioned previously on this blog, from my PhD, a definition of certainty which I would consider helpful would be along the lines of what I found in The Cambridge Dictionary of Philosophy. Peter D. Klein describes the Cartesian account of certainty as being that a proposition is true if there are no legitimate grounds whatsoever for doubting it. Klein (1996: 113). I like the similar idea that a proposition is certain if there are no counter propositions that are superior. Therefore in regard to the religiously historical, Christian faith, and its belief in Scripture inspired by God, the atoning work of Christ, the resurrection, and everlasting life, these things could be viewed as certain provided there are no legitimate counter arguments that are superior. I believe that evidence shows Christianity is philosophically certain in this sense.  I would consider posts/articles from my this blog and my other blog, Satire And Theology, offering cumulative evidences of certainty.

A classic view on certainty discussed in my PhD and in a previous blog article, I shall briefly review is that of Ludwig Wittgenstein:

He does admit that there is in a sense objective truth, but something would be objectively true only within a system of reason and knowledge through the understanding of reasonable persons. Wittgenstein (1951)(1979: 108). His view allows for the logical possibility that something considered objective truth in one system, is not objective truth in another. Wittgenstein (1951)(1979: 108). Philosophy should, therefore, not be understood as primarily making discoveries, as much a reminding persons of the issues that need to be dealt with when one turns to unfamiliar and uncertain issues. Wittgenstein does act with certainty, but it is his own. This does not in his mind justify his view as objective truth to others, it is simply belief. Wittgenstein (1951)(1979: 175). He reasons that ‘knowledge and certainty belong in different categories.’ Obtaining knowledge is very important, and more vital than having certitude. Wittgenstein (1951)(1979: 308) Knowledge and certainty are two different mental states. Wittgenstein (1951)(1979: 308).

A classic view, but not one I hold to from what I noted.

In regard to probability, I suppose that truth claims could also be made in terms of probability as well as certainty. For example, one could hypothetically state Christianity is 9?% probable using Blackburn's second account as in 'an hypothesis as probable when the evidence bears a favoured relationship to it.'  However, providing a number as percentage does seem somewhat subjective in comparison to using certainty, although not without intellectual value.

Eells states three axioms for probability:

1. Pr (Probability)(X)>0 for all
2. Pr (Probability)(X)=1 if X is necessary
3. Pr (Probability)(X  (or) Y) = Pr (Probability) (X) + Pr (Probability) (Y) where   means logical disjunction or set theoretical union, if X and Y are mutually exclusive. X and Y may be contradictions that both cannot both logically occur as events. Eells reasons these are provable axioms. Eells (1996: 649).

BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.

EELLS, ELLERY (1996) 'Probability', in Robert Audi (ed.), The Cambridge Dictionary of Philosophy, Cambridge, pp. 649-650. Cambridge University Press.

GETTIER, EDMUND L. (1997)(1963) ‘Is Justified True Belief Knowledge?’, in Analysis 23, 1963, 121-123, Nottingham, England. Analysis 23. http://www.ditext.com/gettier/gettier.html

KLEIN, PETER D. (1996) ‘Certainty’, in Robert Audi, (ed), The Cambridge Dictionary of Philosophy, Cambridge, Cambridge University Press.

KLEIN, PETER D. (1998, 2005). ‘Epistemology’, in E. Craig (ed.), Routledge Encyclopedia of Philosophy, London, Routledge.

WITTGENSTEIN, LUDWIG (1951)(1979) On Certainty, Basil Blackwell, Oxford.

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