Longbow

A common reaction to the existence of philosophical vagueness is to reject philosophy as a legitimate pursuit of truth. By "pursuit of truth", I do not mean "Truth" with a capital "T", I just mean that it is an attempt to establish the truth or falsity of propositions. Or more generally, it is a pursuit of knowledge. It has been proposed that common philosophical "facts" (such as Ockham's Razor) aren't really "true" but are more like recommendations for "good" reasoning.

Without elaborating much more on any of that, I want to make what philosophical vagueness is more clear. Philosophical vagueness is usually introduced with the Sorties Paradox. The paradox goes like this:

Then we can actually mathematically prove that any collection of grains is a non-heap.

In particular, for n=10,000, such a collection is not a heap, contradicting 2 above. We can also show (with the Well-Ordering Principle which is equivalent to Mathematical Induction) that no collection of grains of wheat is a heap.

So, no matter what we do, we seem to end up in a contradiction.

This paradox is the result of philosophical vagueness. A more interesting example might be found in abortion. The idea of when exactly a fertilized egg develops into a person has the same problem. A fertilized egg is not a person. A new born baby is. No particular instant in the development of the egg into a baby seems to make the difference between it being a person and not being one. What this does to the issue of abortion as a moral dilemma is make the concept of a "person" sort of fuzzy. It is this fuzziness that causes many to reject the whole discussion as subjective. Perhaps one might claim that almost surely a fertilized egg is not a person, but strictly speaking the definition of what a "person" is is arbitrary. Some might argue that embryos in various stages of development are neither persons nor non-persons. There are a variety of responses to this problem.

My position is that there actually is a precise boundary. What is imprecise or "philosophically vague" is our understanding of the concepts. I believe that it is not just a linguistic laziness in defining our terms (because the relevant definition of terms in any topic is not arbitrary or up for grabs). I do not think that borderline cases are unclassifiable. I think that through a process of informal philosophical examination we "precisify" our understanding of philosophically vague concepts, one borderline case at a time, ad infinitum, probably never completely precisifying any concept.

(So, then the propositions of philosophy are indeed propositions and not recommendations. They are true or false, and "philosophical knowledge" is not an oxymoron.)

[ October 12, 2002: Message edited by: Longbow ]</p>

Clutch

Longbow, that's nice layout of the problem of vagueness.

Your adoption of the Epistemic View (EV) is not without precedent, Williamson and Sorenson being two of the more prominent defenders. But I don't think that the views you say you reject amount to anything like an accurate (or better, exhaustive) characterization of the alternatives to EV. I am sceptical of EV, but I do not think that vagueness is a matter of linguistic "laziness", nor that borderline cases are unclassifiable. (Patently they are classifiable; indeed, they are multiply classifiable.)

Finally, maybe you wouldn't mind saying a bit more about how any of this reflects on "the propositions of philosophy". Vagueness is ubiquitous in natural language, and has no obvious special relevance to philosophical discourse. So your closing comments seem somewhat opaque.

Longbow

Well, I had to cut my post short in the interests of getting any replies. As you can see, I've pushed it to the limit already in length. So, I didn't give very much air time to the alternatives and more importantly didn't spend a lot of time connecting it to the broader issue I am trying to.

Basically, a lot of positivists reject philosophy (moral philosophy, in particular) because it lacks rigor. What they reject is the idea of an informal pursuit of knowledge. The degree of formality is intimately tied to the lack of vagueness that comes into the subject. (Note that it could be a subject about philosophically vague concepts, but where the vagueness doesn't come into play, perhaps because the discussion centers around the clear cut cases. Such a discussion would not be as unappealing to positivists and could even conceivably be formal.)

In any case, my contention, then, is that this aspect of philosophical topics -- their philosophical vagueness -- does not actually render the subject matter subjective (or otherwise lacking in propositional content). It also explains why these topics, though rich with propositional content, remain informal, a priori pursuits without ever becoming a subarea of science or math. (And of course, this is meant to apply to all of philosophy not just moral philosophy.)

It has particular relevance to a discussion I was having in the Moral Philosophy discussion board.

Clutch

Thanks for amplifying.

I don't think the positivists were inclined towards emotivism because they thought that moral discourse lacked rigour. That, rather, would have struck them as a side effect of its lacking verification conditions -- hence, for them, truth-conditions. Vagueness did not much enter into it, for them, unless I am misremembering my positivists. The basic approach was more or less Hume's "show me the viciousness" argument.

And whatever the positivists thought, I don't see that formal v. informal captures a distinction in the problem of vagueness. Wang's Paradox, for example, is a Sorites paradox run on numbers themselves -- so it's not just the soft and squooshy moral stuff. One can certainly formalize the natural language predicates that evince vagueness. It's just a question of how to square the formalism with (i) the observed facts and (ii) antecedent conception of what logic laws ought to govern natural language reasoning. Classical logic in particular seems ill-suited to express the operations of vague predicates.

Anyhow, I agree with your main point: nothing about vagueness undermines philosophy in general. There is a question as to who held otherwise, but if this is addressed to points made on another thread, that might explain it.

Longbow

Well, I am not saying that the Logical Positivists went on a crusade against informality. What I am saying is that it is just such a matter that drives positivism in general. That is, even though the Logical Positivists, for instance, had a general program based on the idea of verification that systematically attacked philosophy, the real key to the approach was attaching the vagueness in philosophy. This sort of thing is borrowed very directly from Russell. And in any case, you cannot help but notice that all that is left over for positivists are things that are, at least in principle, formally analyzable (i.e. science and math).

Also, I do not think that you must abandon classical logic when dealign with philosophical vagueness. This is largely the point. It is just such a view (that you do have to abandon classical logic) that is usually the contortions one must go into to maintain their positivist world view. In fact, the very same thing goes on in math to avoid Godel's incompleteness theorem that essentially blocks the formalization of mathematics. It is all just an effort to push for formality or precision. The idea is that if you cannot be precise, then you aren't really making sense (i.e you're just BSing).

ohwilleke

I see the initial example as simply a set of inconsistent assumptions. The problem is in the assumption and not the logic (as is so often the case). No amount of reason can save you from poor assumptions. The problem with philosophy, in many cases, is that too little time is taken to analyze how good underlying assumptions are, and too much time is spend looking at the implications of ill considered assumptions.

Naked Ape

I agree with ohwilleke.

My illogical philistine view of this particular example
1 This number of objects is not a heap.
2 Another number of objects is a heap.
3 The label ‘heap’ is not indicative of the number of items in a collection.

The third premise seems to me to contradict the first two premises.

Cheers,

Naked Ape
…who later went on to prove black is white, but tragically was killed at a zebra crossing.

Longbow

Well the question is which premise do you not agree with. If you are saying that one grain of wheat would (in principle) make the difference, then you are epistemicists (like me). This view suggests a certain metaphilosophical position. Rather than dismissing the borderline cases, it simply posits our ignorance about them. That's where philosophy (informal pursuits of knowledge, in general) come in. In order to acquire knowledge about and reduce the vague boundary, one must philosophical (and informally) scrutinize the limits of these fuzzy concepts.

On the other hand, one could take a different approach to this sort of an issue. Here are some of the alternatives given in the <a href="http://setis.library.usyd.edu.au/stanford/entries/sorites-paradox/" target="_blank">Stanford Enclyclopedia of Philosophy</a>:

All of these approaches (elaborated on in the <a href="http://setis.library.usyd.edu.au/stanford/entries/sorites-paradox/" target="_blank">Stanford Enclyclopedia of Philosophy</a>) have one thing in common. They all tend to view philosophical vagueness as an inherent, static aspect of philosophy that they seek to identify, explain and be done with. That is, they all try to explain what is currently vague and either devise a way of handling it or dismissing it. I suggest that what is currently vague may not be vague many years from now. Soemthings that were vague in Plato's day are not vague now. But, some amount of vagueness will probably always exist.

To draw a mathematical analogy, suppose we were beings that lived in the space consisting of the union of the open intervals (0,1) and (1,2). It often comes up as to whether things are in the neighborhood of 1/2 or in the neighborhood of 3/2. (The issue used to come up with the point 1/4 and 3/4, but with the discovery of 1/2 by Alfred North Halfski close to a century ago, we now know exactly how that works.) Currently, there is fairly wide agreement that 3/4 is more in the neighborhood of 1/2 than 3/2 and conversely with 4/3 being in the neighborhood of 3/2. There is still lively dispute over the points between 3/4 and 4/3.

If we lived in this space, we would not be able to even "see" 1. It just wouldn't exist except implicitly. And we would keep making observations or arguments (as the case may be) to narrow that interval of disputable cases down. We could settle any given borderline case after sufficient examination since such a case would exist in our world. But we could never actually observe the point 1 and that it was the precise boundary that was half way inbetween. And similarly, there are subjects that are just poorly formulated but that through a process of informal philosophical scrutiny can be completely explicated and understood. On the other hand, there are subjects that no amount of philosophical and certainly no other kind of scrutiny will ever completely understand. These latter fundamentally philosophically vague subjects will always be susceptible to philosophical scrutiny, but never completely submit to it.

[ October 17, 2002: Message edited by: Longbow ]</p>

Naked Ape

quote:
Premises:
1) A single grain of wheat is not a heap
2) 10,000 grains of wheat clearly is a heap
3) The addition or subtraction of a single grain of wheat from a collection of grains of wheat cannot make the difference between the collection being either a heap or a non-heap.

The way I see this, the first two premises define heap or non-heap states in terms of two different numbers. The third premise says that if you move incrementally from the lower bound (defined as not a heap) to the upper bound (defined as a heap) or vice versa the ‘heap state’ of the collection does not change. I lack the knowledge of formal philosophical lingo to explain with any real precision why I feel this way but the third premise seems to be invalid. It seems self-evident to me that somewhere between grain one and grain 10,000 the collection must make a state transition from non-heap to heap. If it does not, then 10,000 grains is NOT clearly a heap and premise two is invalid. Is there a special word I should now use to label my word view in light of how I see this puzzle?

Cheers,

Naked Ape

galiel

The fallacy is in using a non-specific, relative term like "heap" as if it were a specific, absolute constant. The argument falls apart if you use a term like "metric ton".