A Treatise on Probability, Chapter 1

In chapter one, Keynes lays out his terms.  He begins by distinguishing direct knowledge and knowledge attained by argument.  With respect to the latter, what does it mean to say that a proposition is probable?

"The terms certain and probable describe the various degrees of rational belief about a proposition which different amounts of knowledge authorize us to entertain."

So we have two sets of related propositions: for now, let's label them as evidence and conclusion(s).

"Between two sets of propositions, therefore, there exists a relation, in virtue of which, if we know the first, we can attach to the latter some degree of rational belief."

I'm interested to see how Keynes will show that such a relationship exists.  Furthermore, it seems we must know about this relation between evidence and conclusion before we can rationally affirm anything about the probability of the conclusion. 

Questions that come to mind
1. How do we quantify the degree to which evidence confers support on a conclusion? 
2. How do we know this relationship, and how does that knowledge give rise to a degree of rational belief? 
3. Is one's degree of rational belief commensurate with the degree to which evidence confers supports on the conclusion?

Keynes says there is a "purely logical" relationship between the evidence and the conclusion.  So while we may not have certainty about the truth of the conclusion, we may have certainty about the appropriate degree of  belief that one should rationally hold with respect to that conclusion...how provocative!  'Hmm so I'm not sure about x, but I'm perfectly certain about the degree to which I'm not sure about x.'  I couldn't put the book down at this point.

The first chapter drives home the point that the stated probability of a conclusion is relative to the evidence or "corpus of knowledge."  Add or subtract relevant evidence and the probability of the conclusion may change.  But doesn't this imply that rational belief is subjective, since not everyone considers the same evidence when assessing the probability of conclusions?  Not quite.

Subjective Sets of Propositions
Propositions can be given differing probabilities with respect to differing bodies of evidence.  Person A has evidence 'a', and person B has evidence 'b'.  When assessing some proposition p, A and B needn't have the same rational degree of belief in p, since these may be different:
1. The probability of p given a, or P(p/a)
2. The probability of p given b, or P(p/b)

As a second example: ask me tomorrow, and my degree of belief might have changed due to new evidence.  So it's all mushy relativistic psychology stuff right?  Wrong. 

Objective Relations Among Propositions
The evidential content may vary, but the degree to which evidence confers support on the conclusion is "purely logical."  This again raises the issue in question #3.  He has more or less used 'degree of rational belief' and 'degree to which y confers evidence on x' synonomously in the first chapter.  He does mention this towards the end:

"I do not believe that any of [the initial terms and definitions] accurately represent that particular logical relation which we have in our minds when we speak of the probability of an argument."

So perhaps my head scratching is warranted, and things will become clearer as we move along.  For now the overall idea seems clear.  Let x be a conclusion and y be some set of propositions given as premises in a probabalistic argument.  When Keynes says 'x is probable' he means 'x is probable given y', which is longhand for P(x/y).  Thus, when one has knowledge of P(x/y), they can have a rational degree of belief in x.  What I'm not sure of, is if P(x/y) is .75 then is my degree of rational belief in x also .75?  All this talk about having knowledge of P(x/y) raises some epistemic questions, which Keynes will address in chapter 2.

A thought experiment, so to speak

Well now I've gone and done it: unintentionally spouted off a wild suggestion made in a poem...a suggestion that hasn't quit nagging me. Is it possible that writing on the computer is reducing my ability to think and express thoughts clearly? There's only one way to find out!

The rules:
1. Any posts labeled as "Notebook" will be originally recorded in a notebook, and then typed here
2. Only minor edits can be made on the computer (spelling, grammar).
3. Only written sources can be referenced while writing. No Google.

How I got here
I recall (sometime during middle school) learning to write a research paper the old fashioned way. Making an outline, numbering note cards, and then (and only then) penning a paper. Around the time the Windows 3.1 operating system became popular, I started my plunge into the world of technology, eventually getting a bachelor's degree in computer information systems. Something which has only occurred to me recently, is that during my entire college career I never indexed a note card. I spent a lot of time playing around with MS Word: manipulating visual aids (bullets, pictures, alignment, spacing, margins, page breaks, etc.), but the writing itself consisted of rapid spurts of thinking (brain diarrhea if you'll forgive the analogy), with some Googling in between to see if things were coming out okay. After enough thoughts had been dumped onto my computer, and enough information gathered from the internet, it was simply a matter of raking over the paper a few times to make sure verb conjugations matched and grammar was reasonable. Of course, being a computer info systems major didn't require much writing, so these experiences were largely drawn from papers written in general education classes such as history, philosophy, English, and interpersonal skills. My present worries about literary (or even cognitive) atrophy aren't restricted to the computer: also there are simply too many things eating away at my attention. So, I'm going to write the old fashioned way: in a notebook. I'm also trimming my Google Reader to a few blogs of interest. I will focus more on my current book reading list: A Treatise on Probability by John Maynard Keynes, Orthodoxy by G.K. Chesterton, and At Home by Bill Bryson.  So perhaps the overall goal is to reduce the flow of useless chatter that seems to have become a natural part of my daily life.  Hopefully some modest gains in thinking and writing can be made, or at least the relationship between the two can be improved.