Since I am still (and ever-more) involved in planning and writing several papers, I thought instead of writing a substantial post today, I would offer some interesting quotes for pondering (n.b. I do not necessarily agree with any of the views in the following).

The Quotes

When living in their original independence, [men] do not have sufficiently stable relationships among themselves to constitute either the state of peace or the state of war. (Rousseau, On the Social Contract Bk. 1, Ch. 4)

Suppose, for example, you are in the middle of a conversation with a friend who suddenly glances behind you. Furthermore, suppose that you quickly follow his gaze, but then immediately return to the conversation with hardly a break at all. Now, what if you are later asked why you turned and looked away. Most likely you would confidently claim that you did so because you wanted to know what your friend was looking at. We contend that this self-report is often not derived from propositional memories of what you had earlier known through introspection, nor from a current vivid recollection of the behavior and the mental states that purportedly attended it. Rather, we suggest that, at the time when it occurred, the behavior was generated by low-level psychological mechanisms unrelated to second-order mental states. (Povinelli and Giambrone, Folk Physics for Apes, 70)

When abstract, nonintuitive formulas, as, e.g., Maxwell’s equations of electromagnetism, were proposed as new axioms, physicists endeavored to make them “intuitive” by constructing a “model”, i.e., a way or representing electromagnetic micro-processes by an analogy to known macro-processes, e.g., movements of visible things. Many attempts have been made in this direction but without satisfactory results. It is important to realize that the discovery of a model has no more than an aesthetic or didactic or at best a heuristic value, but it is not at all essential for a successful application of the physical theory. (Carnap Foundations of Logic and Mathematics, section 25)

[Kant] explained… that the most general laws of nature are the principles of our knowledge or nature (as principles of the possibility of experience). In other words… he identified the self-evident general statements of natural science with the principles that constitute the objects of experience. (Schlick, letter to Reichenbach, qtd. in Coffa, The semantic tradition from Kant to Carnap, 201)

I have started reading a book on Measurement theory, so I’m going to try to write a little bit about the little bit I understand of it.

What is Measurement Theory

In general, measurement theory deals with relating physical things and mathematical things meaningfully. That is, it is a theory of taking a physical relational structure and, via “measurement”, attaching a corresponding mathematical relational structure.

The book I am reading focuses on isomorphisms of structures exclusively. This in general bothers me, because a lot of the examples are isomorphisms of physical things with real continua without justification of why the physical stuff is actually continuous and not just dense. However, I am assured that similar results can be obtained with homomorphisms in place of isomorphisms, allowing for the math to come out substantially more messy.

Why should we care about it?

My personal take on this goes back to my view on conventionality in general. A theory such as this can be useful in explaining the details of something like¹ the correspondence rules of Reichenbach or the conventionality of Schlick with respect to the connections between mathematics and physics.

Somewhat separately, measurement theory can illuminate why we can² bring to bear totally unrelated mathematical tools to a physical problem — perhaps from quite disparate domains of mathematics — while still getting a reasonable result at the end of the calculation or transformation.

There are surely other reasons, but I am only at the beginning of the text that is introducing me to the subject. I will write more as I get further along.

¹ Read: perhaps a caricature of the ideas of

² Or, perhaps more interestingly, why we can’t in some situations.