I am supposed to be brushing up on my statistics, but I keep getting distracted by the foundations of statistics. I feel that I need to get it straight in my own head so that I don't come away with a confused jumble. I was reading an article "Logic and Probablity" by C. Howson in the British Journal for the Philosophy of Science (1997) today. I found the following statement:
Definitions, of course, being stiputations about terminology are not true or false, but they can be arbitrary or non-arbitrary, useful or not.
I reflected that the author probably has no idea that this is in fact a controverted point that bears directly on his subject. I found a post about this on Just Thomism, which I just added to the blogroll.
The element of most modern logics is the proposition. From their point of view, Aristotle’s logic is “term logic” for it begins with a term- the element of a proposition. Aristotle, however, understands his elements not as terms but as universals- and the various relationships of universality generate both propositions and arguments. The Categories, for example, is ordered toward manifesting those things which are most universal and therefore the measure of logical universality.
I was really struck by this feature of Aristotelian logic when I first studied it. I have taken several formal logic courses in various disciplines at the undergraduate level (math, computer science, philosophy), and in all cases what stood out to me was how useless the subject seemed as presented. Being illogical is a term of opprobrium, but in practice that usually means someone saying something that one doesn't agree with. Not precisely illogical. Part of the reason for that is likely that the formal logic taught in school has no instrinic relationship to any real thing or things. It is all A and B and modus ponens.
Aristotelian logic begins the other way round. For Aristotle, the first thing to do is to figure out what something is, which he called the first act of the mind. Once you know what something is, then you can begin to reason about it. Modern formal logic never addresses this topic at all, except in the dismissive, implicitly nominalist fashion of of Howson. Formal logic always talks about propositions and syllogisms first, which is where Aristotle's deductive logic ends.
This affects probability and statistics because if definitions are not mere words, but are in fact how we know the nature of things, then probability has a logical foundation in reality, rather than being merely a subjective degree of belief in a given proposition. And with that, I need to get back to my stats. I'm currently working my way through Statistics for Experimenters, by Box, Hunter, and Hunter.