On Counting (Exploring Operational Definitions Part III)

For the first two parts in this series see:

Exploring Operational Definitions: Part I
Exploring Operational Definitions: Part II - Distance

Perhaps the "simplest" procedure that most folks have learned is the technique(s) of counting. What I would like to explore is that there are a variety of techniques that we call counting. In some cases they build on one another. In other cases, they are techniques which give "approximate" solutions.

Of course not all societies count things (see here). Nonetheless, I suspect that many of our "intuitions" about mathematics ultimately stem from our earlier experience with counting. Our attachment to such intuitions will somewhat determine how willing we are able to accept alternative definitions and techniques for counting. Today I'll explore a few of these definitions.

Gold, Hedges and Correlations

Today I'm going to touch on a sort of theme I have here and that's regarding on how to assess correlated data. How much can we actually read into it? How do we determine that there's a fundamental relationship that, not only holds well in the past but will continue to do so in the future?

To do that I'll be taking a quick look at gold and why I consider the "inflation hedge myth". In short, gold is not an inflation hedge. At least not on any reasonable time scale.

Exploring Operational Definitions: Part II - Distance

So in Part I, I began discussing operational definitions. In particular, I've been focusing on the concept of distance.

I proposed that we might consider our intuitions regarding answering the question - what is distance? - by means of early experience of operational definitions of distance. The idea being that what we consider distance is going to be closely related to ways we were taught to measure distance.

Correlation as a Substitute for Critical Thinking in Finance?

I frequently come across graphs like these on various blogs and articles. I'm going to single out one, not because there is anything particularly wrong about it (they're all wrong), but only to use it for illustrative purposes. I could really pick out any of these and offer the same criticisms.

This one I found in the article The Declining Inflation Expectations Chart That Should Have Stock Investors Very Concerned. The original chart apparently come from Dan Greenhaus via twitter.

Exploring Operational Definitions: Part I

An operational definition is a way to define a concept by the set of operations or procedures which are used to make a judgement with that concept. This idea, along with a philosophical thesis on meaning known as operationalism, was popularized by Percey Bridgman (see his The Logic of Modern Physics).

One example he liked to use is the concept of distance.

The Structure of Arguments: Deduction, Induction and Abduction

So this is a brief overview of three types of logical arguments.

P/E to VIX Ratio - Are you complacent or skeptical?

So Bloomberg had a chart of the day from David Bianco relating the Price to Earnings ratio for the S&P 500 and the VIX (which measures implied volatility of S&P 500 options). Bianco used this as an indicator of sentiment, whether investors are complacent or skeptical.

I took a look at this using data from Robert Shiller and yahoo finance:

Gettier Intuition

One common criterion used to determine whether or not something is knowledge is the "justified true belief" criterion (JTB). It has many forms but the basic idea is this:

S knows that P means:

1. S believes that P.
2. S has justification for believing P.
3. S is true.

In 1963 Edmund Gettier proposed counterexamples to the above relationship. The idea is pretty simple. Construct a scenario in which (1), (2) and (3) are satisfied, but it fails to be knowledge. We'll look at an example from his original paper: Is Justified True Belief Knowledge? In particular, we'll look at Case I.

That's an Empirical Question: Part IV

This is the 4th part in a series called "That's an Empirical Question". For the other parts of this series see here:

Part I
Part II
Part III

I think this one deserves an appropriate subtitle.

Is Induction Always Empirical?

In Part II, I suggested that induction is an important "empirical tool". Assuming that's true, that still raises the question whether all uses of the "induction tool" necessarily amounts to an "empirical investigation".

To explore this, as per usual, I will use an example: The Goldbach Conjecture.

That's an Empirical Question: Part III

This is a follow-up in a series exploring what the difference between "empirical" versus "mathematical" versus "philosophical" questions. For the other posts in the series see:

That's an Empirical Question: Part I
That's an Empirical Question: Part II

I'd like to consider a thought experiment though I think you can probably find some similar at manufacturing firms in the real world.

Methodists Vs. Particularists

In Intuition in Philosophy, I suggested that one difference between, say, mathematicians and philosophers is that philosophers will willingly privilege an intuition over a derived result whereas the mathematician will reject the intuition in favor of the derived result. To some extent I think this characterization may not have been entirely accurate. At the very least some clarification needs to be made.

I here will argue that many philosophers are particularists whereas mathematicians tend to be methodists. "Intuition" plays a role in what particulars the philosopher claims to have knowledge. This allows for there to be something along the line of "mathematical intuition" of which I think is believed to be present by many mathematicians. I will briefly sketch out the issue here.

Intuition in Philosophy

Intuition has an interesting role in philosophy, particularly analytic philosophy. One of its functions is epistemic. It's used to test various assumptions and conclusions in philosophy for validity or truth. If something fails to stand up to intuition the propositions in question get dismissed.

There's also a good deal of literature in a field known as "experimental philosophy". The research often takes the form of surveys to different groups of individuals (intro to philosophy students, professional philosophers, etc). The purpose of the surveys is to assess what "intuitions" people have. What the research tends to indicate is that intuitions vary greatly between groups depending upon a variety of circumstances (culture, philosophical exposure, etc.)

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.