Financial Mathematics Text

Monday, September 3, 2012

That's an Empirical Question: Part II

See here for Part I.

Thus far I've conjectured that an empirical question in some way or form entails the use of empirical tools as distinct from other kinds of tools. One type of alternative tool is mathematical while another is philosophical. This interpretation rests on the idea that (some) philosophers believe there to be a distinct set of questions which can be addressed only with a particular set of tools. I would like to further explore this issue.

One way to characterize this difference is between a set of similar distinctions found in the philosophical tradition. Hume called these relations of ideas and matters of fact. For Kant, they were a priori and a posteriori. For some of the logical positivists, they were analytic and synthetic. All of these distinctions (or are they dichotomies?) attempt to differentiate two kinds of questions which are answerable by different means.

There are many different overlaps and differences between these distinctions. One consideration is the difference between whether a statement is contingent or necessary. Another issue is whether a proposition can or cannot be proven by contradiction. Kant complicates matters by suggesting some propositions (e.g. those from mathematics and metaphysics) can be both necessary but not follow from contradiction.

There are many problems with using these distinctions (especially if taken as dichotomies). For example, it's not always clear how to apply these distinctions. For example, how do you determine if something is necessary as opposed to contingent? I do think it's critical that, whatever distinction is employed, it be spelled out what methods are employed for concluding that certain judgements are of this kind or another. In this I believe myself to be following Frege's interpretation of Kant:

Now these distinctions between a priori and a posteriori, synthetic and analytic, concern as I see it, not the content of the judgement but the justification for making that judgement.
-Gottlob Frege, The Foundations of Arithmetic.
As a result I largely believe introducing distinctions of this sort are only useful provided we specify what tools are used in order to arrive at the judgements. This still leaves us with the question of what are "empirical tools" as opposed to "philosophical" or "mathematical".

To explore this issue further, I will take a closer look at a tool generally regarded as "empirical" (and often confused as the only or most important empirical tool): Induction.

In addition, see Part III in this series if you're interested.

No comments:

Post a Comment

Some common OpenID URLs (no change to URL required):