Issue involving Descriptive ICE and several of its subclasses

[gregfowlerphd]

According to the definition for Descriptive ICE, such an ICE ‘consists of a set of propositions’. However, according to the definition for Point Estimate Measurement ICE (which is one of the subclasses of Descriptive ICE), such an ICE ‘consists of a single value’. Thus, a Point Estimate Measurement ICE must both consist of a set of propositions and consist of a single value. For this to be possible, though, either a value must be a set of propositions (which seems false) or it must be possible for something to consist of a set of propositions while also, separately, consisting of a single value (which seems impossible). Hence, given the definitions and the asserted subclass relation, Point Estimate Measurement ICE seems to be an unsatisfiable class.

Analogous remarks apply with respect to several other subclasses of Descriptive ICE. (I can post a list if desired.) Furthermore, a related issue arises in the case of Proportional Ratio Measurement ICE. Its definition indicates that a Proportional Ratio Measurement ICE has a numerator and a denominator. However, it would seem that no set of propositions can have a numerator or a denominator.

The simplest fix for these issues might be to simply remove the reference to a set of propositions from the definition for Descriptive ICE:

An Information Content Entity that describes some Entity.

[gregfowlerphd]

Since I haven't received any response on this one, I thought I'd reframe the issue and see if doing so prompts any thoughts.

I think the current definition of 'Descriptive Information Content Entity'

An Information Content Entity that consists of a set of propositions that describe some Entity.

should be changed to something like

An Information Content Entity that describes some Entity.

Here's why. The current definition seems to be in tension with the definitions for some of the subclasses of Descriptive ICE. To take just one example, consider the definition of 'Point Estimate Measurement Information Content Entity':

An Estimate Information Content Entity that consists of a single value for the measured entity.

Given this definition, the following claim is true:

(A) Any Point Estimate Measurement ICE consists of a single value.

However, given the subclass relation between Point Estimate Measurement ICE and Descriptive ICE and the current definition for the latter presented above, the following claim is true:

(B) Any Point Estimate Measurement ICE consists of a set of propositions.

But (A) and (B) can both be true only if (i) a value is a set (perhaps unary) of propositions or (ii) something can both consist of a value and, separately, consist of a set of propositions.* Neither (i) nor (ii) seem true, though.** So, assuming we keep the relevant subclass relation, at least one of the definitions must be revised. And I think the least drastic revision is the one proposed at the beginning of this comment.

*Strictly speaking, there's a third possibility, which is that the Point Estimate Measurement ICE class is unsatisfiable. But I'll ignore that.

**Note: Neither this claim nor the argument as a whole is intended to rely on a set-theoretic understanding of the term 'set' as it appears in the definition for Descriptive ICE, in case anyone was worried about that.

[neilotte]

@gregfowlerphd Perhaps @APCox has more context for the intent behind the decision and I prefer your revision. That said, it seems to me that a set of propositions can contain only a single proposition which may appear, in data parlance, as a value. I'm also not sure why a set of propositions could not contain both a numerator and a denominator.

Is there a particular view on propositions you're appealing to here?

[alanruttenberg]

It's fundamentally a problem to use propostion in a definition without defining what a proposition is.

[gregfowlerphd]

@neilotte: It's certainly true that a set of propositions can contain only a single proposition (which is why I said 'perhaps unary' in my reply), and no, I'm not appealing to any particular view on propositions.

Your "data parlance" suggestion is interesting. A couple of thoughts:

• It's certainly true that a data value could express a proposition. However, it's pretty fundamental to the notion of a proposition--on pretty much every view on propositions--that one and the same proposition can be expressed by multiple entities (e.g., by one sentence in one language and by a different sentence in a different language). So even though a data value could express a proposition, that same proposition could be expressed by, say, a sentence in a natural language, in which case neither the data value nor that sentence would be the proposition. But my argument shows that the definitions for Descriptive ICE and Point Estimate Measurement ICE jointly entail that, in the case where the set of propositions is unary, the value (in the sense relevant to the Point Estimate Measurement ICE definition) must be the proposition. (Or that a Point Estimate Measurement ICE must both consist of a value and, separately, consist of the proposition, but that doesn't seem to be the horn of the dilemma you're concerned with.)

• Based on the definitions for Point Estimate Measurement ICE and its parent class as well a bit of research concerning point estimates, I think 'value' in the former definition means numerical value rather than data value.

As far as numerators and denominators go, I suppose a set of propositions can, in some sense, contain both a numerator and a denominator. But, at least on least on my reading of the Proportional Ratio Measurement ICE, a Proportional Ratio Measurement ICE doesn't just contain a numerator and a denominator, it has them--something only a number can do. And numbers aren't propositions, since they don't have the features propositions do on pretty much every view of propositions (i.e., being true/false, being the objects of attitudes like belief, etc.), nor do they seem to be (non-unary) sets of propositions.

@alanruttenberg: Yeah, I think I agree with that. I might even be inclined to think that if a fraught term like 'proposition' is used, there should be a Proposition class with an accompanying definition (which might involve taking a stand w.r.t. the issues dividing different views on propositions).

PS--Sorry I took a bit to get back to you guys, Neil and Alan. I was quite busy and then my internet was out for a few days. :(