Quine is disputing the idea of definitons just as much as analyticity. Perhaps this is a good way to think about his argument: How would you find out whether a given belief is a definition or not? You could of course ask, but what if you don't originally share a language? He then argues that there is no way to distinguish a word for "definition" from any other word designating a set of logically independent beliefs they hold, without making assumptions about how people use "definitions" we usually consider to be results of empirical psychology.
Now the infinity of a series consists in the fact that it can never be completed through successive synthesis.
I'm surprised how many philosophical arguments are based on the lack of imagination.
Rather than chasing after the one true meaning of a term, you can stipulate. Winding that up to the max, you get the claim that analycity is only strictly definable in the context of a formal system (such as maths, logic, or computation). In addition to the more common claim that formal truths are always analytical truths.
Interesting thought. I wouldn't go so far as to say it's only definable within a formal system. But without formal definitions, it's going to be kind of fuzzy/dependent on exact interpretation.
Is this a good argument?
I'd say it is a bad argument, since it doesn't notice that the negative integers and zero are an infinite series.
While reading Quine's Two Dogmas of Empiricism I was struck by the importance of analyticity. In philosophy, there are many arguments that are deeply challenging to evaluate. Take for example this argument from Kant for finitism:
If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in that world an infinite series of successive states of things. Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away, and that a beginning of the world is therefore a necessary condition of the world's existence.
Is this a good argument? Like many abstract philosophical arguments, it's actually very difficult to tell. But if we had a method for determining which statements are analytic and which are synthetic, we'd have a better idea of whether to consider it seriously or to dismiss it out of hand.
I won't be providing a method of distinguishing analytic from synthetic today. I don't know how to do that. However, I believe I have one puzzle piece.
Quine states that is it unclear whether statements like, "Anything green is extended" are analytic even though he know perfectly well what "green" and "extended" mean.
I would actually dispute this - the definitions of either of these words aren't clear at all. Take for example green - are we talking about what color we perceive or a wavelength that is emitted? What if we discovered tomorrow that vision didn't actually utilise light, but tiny particles? Would green be defined in terms of then? What about a green hallucination? Does that count as a "thing" that is green?
And what counts as extended? If we discovered we were characters in the matrix, would we count the virtual space we move around as extended? Would the real space count as extended? Arguably, we could say that space refers to an underlying structure that plays a particular role in our experiences and that since we are experiencing the virtual and not the "real" world when we talk about "extension" we mean extension in this virtual world.
Another way to think about this is in terms of import statements. Like in order to define green we may have to import the concept of light which then requires us to import the concepts of time and space.
Of course, these definitions are arbitrary so it is up to humans to choose how we use these words. Perhaps we want to follow Quine and say that if the world was different we'd probably define some of these words differently (ie. if we define water by chemical symbol and it were actually HO instead of H2O, then we'd change the definition). Or perhaps we want to say that words like object come attached with background assumptions such as "green" being limited in application to "objects" which are defined to be things with a spatial component. In any case, it seems to all be dependent on the definitions we utilise. And even though I can't tell you what analyticity mean conceptually, once we've provided sufficient clarification on what is being asked, we should be able to determine this practically.