Saturday, 19 September 2015

Two Opposite Types of Granularity Difference

This is another post in my series on semantic granularity. The others so far, in chronological order, are:

John and Mary both use the word 'happiness', and understand each other perfectly in most conversations. They use it in propositions in such a way that we would say that they both attach the same meaning to the propositions used, are on the same page, etc. But in certain relatively peripheral regions of application, they differ systematically.

We want to be able to tie John's peripheral uses of 'happiness' together with his non-peripheral uses - we want to say he's using the word in the same sense in both cases, but we also want to bundle his non-peripheral uses with Mary's. However, we also want to be able to make a semantic distinction between Mary's peripheral use and John's.

The solution is two operate at two granularities. A relatively coarse-grained bundling can tie all John and Mary's uses together - roughly, by ignoring peripheral use features. But we can use a more fine-grained bundling to describe the linguistic difference between Mary and John - at this granularity, we say they mean slightly different things by 'happiness'.

But there is another sort of descriptive problem which we solve with granularity shifts. For example, consider the normal uses made of the word 'hard' in the phrases 'hard man' (meaning something like 'tough guy'), 'hard wood' and 'hard test' (meaning a difficult test). We can distinguish three different senses here - very roughly, (i) toughness, (ii) solidity and resistance, and (iii) difficulty. Or two, a literal sense ('hard wood') and a "metaphorical" sense ('hard man', 'hard test'). Or we can bundle all these together.

Visually, we can think of the first kind of fine-graining as a kind of broadening of considerations which go into bundling, and the second kind of fine-graining as a kind of narrowing.

This is perhaps one of the things which have made granularity considerations, although quite natural, seem difficult - or not even arise as a serious possibility - from the point of view of analytic philosophy. That two different, in a sense opposing, things can be going on in shifts toward finer granularity, can make the matter confusing. But once we see what is happening and master it, it just reveals the richness and power of the approach.

From these examples, it may look like the first, 'broadening' type of fine graining is concerned with intersystematic distinctions – distinctions between different sign systems (in the example above, John's and Mary's idiolects) – and that the 'narrowing' type is concerned with intrasystematic distinctions – between elements and uses of some given sign system.

But this doesn't generally hold. In the broadening case, for example, we may have spoken about two very similar but subtly distinguishable meanings of quite different words in, say, John's idiolect. 'Envy' and 'jealousy', perhaps. Or 'rage' and 'fury'. Likewise, in the narrowing case, where we, at finer grain, distinguish the meaning of 'hard wood' from 'hard test', we could instead make that distinction between these words as used by two different people, or two different words used by two different people.

One thing we can say, perhaps, is that the 'broadening' type of fine graining is about considering how more ground is covered, factoring in more stuff about 'the lay of the land', where the 'narrowing' type is more about marking off different regions. The first involves making more distincions among expression-uses based on how the expressions cover the ground they cover, the second involves making more distinctions among expression-uses based on what ground they are covering in that use.

Tuesday, 8 September 2015

Forthcoming in Logos & Episteme

(UPDATE 8 July 2016: See this post for some information and links regarding a debate brought about by this paper.)

My paper 'Two New Counterexamples to the Truth-Tracking Theory of Knowledge' is forthcoming in Logos & Episteme. It derives from this blog post. The final draft is available at PhilPapers.

An interesting point about its origin: I was originally playing with what I thought might be a type of counterexample to the truth-tracking account involving weird self-referential propositions. After investigating for a stretch I concluded that the approach was no good, at which point the counterexamples in the present paper (which have nothing to do with self-reference) came into my head. Something about the disappointment at the weird self-referential approach failing, together with the fact that I had during the investigation started to get used to the idea that I was able to refute the truth-tracking theory, caused me to think of the actual counterexamples.

For another recent counterexample to the truth-tracking theory (which also works against some other theories) see Neil Sinhababu and John Williams's paper 'The Backward Clock, Truth-Tracking and Safety' and Sinhababu's blog post about it.