in lieu of a real post

In this week's Science:

"The first scientific conference held in Azeroth, the online universe of the role-playing game World of Warcraft, went off virtually without a hitch. Although the participants all died during the final day's social event — a massive raid on an enemy fort — they agree that this event is a glimpse at the future of scientific exchange."

I may have a real post up soon: I just got back from Vancouver, where I attended the 8th History of Philosophy of Science conference, and I may file a brief report from the field.

Experimental Philosophy of mathematical intuition

So this is straight psychological research, not done by 'experimental philosophers,' but it does seem highly relevant to any philosophers who appeal to the notion of mathematical intuition:

Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures, Stanislas Dehaene et al. in Science May 30 2008.

We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education.

Scientific Realism via the internets

I recently found out that Philosophy of Science has conditionally accepted an article I wrote on the no-miracles argument. This is a stroke of good luck, and it's also a testament to the philosophical blogosphere: basic ideas in this paper were hashed out on this blog (see especially here), and honed by readers' astute criticism. Perhaps the paper wouldn't have been good enough for acceptance otherwise.

I would greatly appreciate further help on the paper before I send away the final version; the current draft (in rich text format) is here. Here's an abbreviated abstract:

1. Scientists (usually) do not accept explanations that explain only one type of already accepted fact.
2. Scientific realism (as it appears in the no-miracles argument, or NMA) explains only one type of already accepted fact.
3. Psillos, Boyd, and other proponents of the NMA explicitly adopt a naturalism that forbids philosophy of science from using any methods not employed by science itself.
Therefore, such naturalistic philosophers of science should not accept the version of scientific realism that appears in the NMA.

And as long as I am singing the praises of the blogosphere and begging for readers, P.D. Magnus (of the excellent Footnotes on Epicycles blog) and I have a draft of a paper on another aspect of the scientific realism debate (in pdf format) here. We ask, and give a partial answer to, the question: When should two empirically equivalent theories be regarded as variants of one and the same theory? Comments large and small are appreciated!

Against negative free logic

'Free logic' is an abbreviation for 'logic whose terms are free of existential assumptions, both singular and general.' Free logics attempt to deal with languages containing singular terms that do not denote anything, such as 'Pegasus'.

Free logics come in 3 basic flavors, which differ over what truth-values should be assigned to (atomic) sentences containing non-denoting names.
- Negative free logics declare all such sentences false;
- Neutral free logics declare all such sentences neither true nor false; and
- Positive free logics declare at least some such sentences true (in particular, 'Pegasus=Pegasus').

Tyler Burge argued for negative free logic over its rivals in "Truth and Singular Terms," Nous (1975). I came up with a little argument against negative free logic; but I do not know the argumentative landscape for these 3 options particularly well, so this may be extant already. (Note: if any readers have references for arguments pro and con negative free logic, I'd be very interested. I've found a couple of nice articles by James Tomberlin, and a short response by Richard Grandy to Burge's piece, but not much else.)

According to the negative free logician, all atomic sentences containing non-denoting names are false. Some people reject this because calling 'Pegasus=Pegasus' false seems wrong; here's another problematic type of case. Consider the following three sentences (and assume for the sake of argument that 'Atlantis' is a non-denoting name):
(1) Atlantis is West of London.
(2) Atlantis is East of London.
(3) Atlantis and London have the same longitude.
In negative free logic, all three of these must be false. But for the three predicates 'is west of,' 'is east of,' and 'has the same longitude as,' any one of the three can be defined in terms of the other two using only negation and conjunction. E.g.:
'x is west of y' means 'x is not east of y, and x does not have the same longitude as y.'
But now we've got a problem: If 'Atlantis is west of London' is false (as the free logician says), then at least one of 'Atlantis is east of London' or 'Atlantis and London the same longitude' has to be true -- but that contradicts the earlier assumption (of the negative free logician) that all of (1)-(3) are false.

And this same problem will crop up in general when we have a set of predicates that are definable in terms of one another and negation; in the simplest case, P = ~Q. And this is not that rare: {'before', 'after', 'simultaneous'} is another example. The negative free logician could save her position by maintaining that two of the predicates are somehow really basic, and the other really derivative. But at least in these two cases, it doesn't look legitimate to hold that 'west' is somehow fundamental and 'east' merely derivative.

Does anyone see a good response to this objection on behalf of the proponent of negative free logic?

HOPOS 2008 program posted

The International Society for the history of philosophy of science (a.k.a. HOPOS) has just posted the program for its 2008 conference in Vancouver, taking place June 18-21. (According to the program, I'm speaking about someone named 'Quien.')

Hope to see you there! If you are going, and want to meet up, send me an email.

Are there empty natural kind terms? (The 2nd in a series)

There are empty names, like 'Santa' and '(Planet) Vulcan'; there is a fairly large literature dealing with them in both the philosophy of language and in logic (called 'free logic'). But there has not been any discussion of empty natural kind terms -- which prompts the question: are there any such terms? I ask because it seems to me that 'phlogiston,' 'caloric,' and other central terms of now-discarded scientific theories may qualify as empty natural kind terms.

This question is complicated by the fact that there is not widespread agreement on what natural kind terms are. The two candidates are (I) predicates and (II) names. (Predicates are the leading contender, so you can skip the final paragraphs if your patience for this kind of thing is limited.)

(I - Predicates) This takes us back to the subject of the previous post: are there any empty natural kind predicates? As noted in the last post on this subject, if 'empty' just means 'has the null set as its extension, and the whole domain of discourse as its anti-extension,' then the answer is obviously yes. But then it's uninteresting -- empty names are interesting because (both for direct reference theorists and Frege) sentences containing them will lack truth-value, unless the direct reference theorist proposes an ad hoc fix (cf. David Braun). If empty predicates behave classically/ nicely, they won't generate truth-value gaps.

So here's an argument that natural kind predicates like 'phlogiston' are empty in the same way that 'Vulcan' is, i.e. they can fail to express semantic content sufficient to determine truth-value. How? On a Kripkean account, natural kind terms express properties that objects have essentially. To determine what property is expressed by a natural kind term, we take samples of the stuff that that term refers to in the actual world, and determine what is essential to them, i.e. what property (or combination of properties) those samples must have in order to be that kind of stuff. So the natural kind term ‘water’ expresses the property of being H2O, because in the actual world, having that inner constitution suffices for something to be water. But what is the essential, inner constitution of all the stuff we call ‘phlogiston’ in the actual world? Nothing —- since there is no such thing as phlogiston, there is no essential property or inner constitution to discover. (Note: James Woodbridge helped me a lot with this argument; if you like it, you should attribute it to him, not me.)

So if phlogiston has no inner constitution, then 'phlogiston' lacks semantic content. And thus (atomic) sentences containing the term will be semantically defective, and thus (presumably) will lack a truth-value. But is this argument any good?

(II. - names) One might think natural kind terms are names, because they appear in subject position:
'Water is wet'
But if they are names, what are they names of? Scott Soames (Beyond Rigidity) gives two 'obvious candidates':
(i) the merelogical sum of all the water everywhere, or
(ii) an "abstract type" that is instantiated by the stuff that comes out of our faucets etc.

If it's (i), then there are clearly empty natural kind terms, and 'phlogiston' and 'caloric' are examples. However, Soames gives two arguments against (i): first, if (i) were correct, then 'Water weighs more than 1 million pounds' should be true and felicitous, but it seems clearly not so. Second, if (i) were right, then 'water' would not be (anywhere close to) a rigid designator, and there is a widespread intuition (or Kripkean dogma?) that it is.

If it's (ii), it's not clear to me that there are empty natural kind terms; I don't know how one shows a type does not exist (or, for that matter, how one shows a type does exist). As James Woodbridge and Seyed (in the comments on the first installment of this series) pointed out to me, it seems reasonable to say that an abstract type that is somehow contradictory does not exist, but we'll have nothing like the set-theoretic or semantic paradoxes when it comes to natural kind terms. But I am not all that worried about (ii), because it's not clear (again following Soames in Beyond Rigidity) that natural kind terms are names at all -- they seem to be predicates first and foremost. As Soames points out, 'Whales are mammals' is naturally understood as 'Anything that is a whale is a mammal.' So natural kind terms are not names.

Indeterminism in developmental biology

There's a review article in this week's Science (v.320, April 4 2008, 65-68) that is potentially of philosophical interest, "Stochasticity and Cell Fate". The bumper sticker version: although a cell's transformation into a specialized subtype is deterministic in most cases, "[i]n some cases, however, and in organisms ranging from bacteria to humans, cells choose one or another pathway of differentiation stochastically, without apparent regard to environment or history."

Discussions of indeterminism in biology have usually been restricted to the 'random' mutations that drive evolutionary change. This, if it holds up, looks to be a quite different kind. And interestingly, the authors point out reasons why a certain degree of indeterminism may confer selective advantage upon organisms whose development contains stochastic elements.

Are there empty predicates?

Empty names are names that fail to refer, like 'Santa,' 'Pegasus,' and 'Planet Vulcan.' 'Santa Claus' fails to refer because (on most semantics for empty names) there is no entity that is assigned to 'Santa' as its referent. This is clearly distinct from another view (e.g. Frege's) that 'Santa' should be assigned e.g. the empty set as its referent. That is, there is a difference from having no referent and referring to the empty set -- for my cat has no referent, but '∅' refers to the empty set.

So are there empty predicates? That is, are there predicates that do not signify properties (or extensions, kinds, intensions (= functions from possible worlds to extensions), or whatever your preferred semantic value for predicates is). There are of course predicates whose extension is the empty set (e.g. 'is not identical with itself') -- these predicates signify uninstantiated properties (assuming you think predicates signify properties). But they still signify a property.

There is a fairly massive literature on empty names. (I can recommend Ben Caplan's 2002 dissertation as a nice survey of the empty names landscape.) But there is no talk of empty predicates -- is this because somehow every predicate, unlike names, automatically refers?

Related issue: Philosophers of science often say things like 'phlogiston' and 'caloric' fail to refer. Often, in explaining their claim "The word 'phlogiston' does not refer", these philosophers will say things like "The extension of the predicate 'is phlogiston' (or 'contains phlogiston') is empty." But having the empty set for your extension is different from failing to refer. So when we say that 'contains phlogiston' fails to refer, it seems like we should be saying that it has no (determinate?) extension, not that its extension is empty.

So are there any empty predicates? Are such things even possible? And can the usage of the philosophers of science be defended?

stuff seen in Science

There's been a few items in Science the last two weeks that are potentially philosophically interesting:

[This week]
1. Rats can learn rules and then generalize them to new, different situations to a degree that people previously thought was confined to humans or at least primates.

2. Two smells that are initially indiscriminable to a human can, with painful conditioning, be made discriminable. (The initial indiscriminability was not just in terms of verbal reports of conscious states; the scientists did fMRIs on the patients too.)

[Last week]
3. After your basic needs are met, having more money does not make you much happier (that's been known for a while); however, giving that money away instead of spending it on yourself does have a significant effect on your (self-reported) happiness.

4. One of my favorite biologists, Günter Wagner, argues that pleiotropy (one gene having several effects) is actually not as significant as once thought (philosophers of biology have used pleiotropy to argue for various points).

Of course, this is just the bumper-sticker version of each of these claims; the actual positions will be more sophisticated, and require various caveats. Nonetheless, it seems like each of these studies could merit philosophical attention.

Logical Pluralism, take 2

This post supersedes the previous one on logical pluralism; it's the post I would've written, had I bothered to do a bit of research before posting. I apologize in advance for how long it is...

Beall and Restall say we should be pluralists about logical consequence, because there are multiple acceptable ways of spelling out the notion of case in the standard criterion of validity:
(V) C is a logical consequence of P1 ... Pn iff in every case where all of P1...Pn are true, C is true also.
Different specifications of case, say B&R, yield different consequence relations.

My impulse is to address this issue 'from above'; that is, in general, when is any sort of pluralism an acceptable stance? Well, one case (though probably not the only one) in which it can be acceptable is when ambiguity is present. E.g., there are multiple, equally acceptable ways of spelling out 'Aaron is at the bank'. And Beall and Restall, on the 3rd page of "Defending Logical Pluralism," state that they think logical consequence is ambiguous; presumably the ambiguity is traced back to the word 'case' in (V) (what else in (V) could it be?). So if 'case' really is ambiguous, and (V) captures the core notion of consequence correctly, then we should be logical pluralists.

But I'm not sure 'case' is ambiguous -- prima facie, it doesn't feel like 'bank,' or 'duck'. It might just be 'general in sense' or 'lack specificity': for example, 'sibling' is general in sense between 'brother' and 'sister', the same goes for 'parent' and 'mother' and 'father.' And nobody wants to be a 'sibling-pluralist' or 'parent-pluralist.' (Note: 'thing', which seems to me closer to 'case', does not seem ambiguous either.)

Linguists, fortunately, have devised a test to distinguish ambiguous expressions from ones that are general in sense: the 'conjunction reduction' test. Suppose my friend Pat is making a monetary deposit, and my friend Tracy is sitting next to a river. Then the two sentences
'Pat is at the bank' and
'Tracy is at the bank'
are both true. However, these truths cannot be expressed in a 'conjunction reduced' sentence
'Pat and Tracy are at the bank,'
for this can only mean that both of Pat and Tracy are next to a body of water, or both are at a financial institution. No 'crossed reading' is possible. The impossibility of crossed readings in the reduced sentence suffices for the ambiguity of 'bank' (Jay D. Atlas, Philosophy without Ambiguity, OUP 1989, p.40). From the little I've seen, almost all linguists and linguistically-inclined philosophers accept this as an ambiguity test. And most also accept: If crossed readings are possible, then there is no ambiguity. E.g., 'Pat and Tracy are parents' can be read as saying that Pat and Tracy are both fathers, both mothers, or one of each -- and the possibility of that 'one of each' reading is what makes 'parent' non-ambiguous, but rather just general in sense.

With a test for ambiguity in hand, we can see if 'case' and 'consequence' are ambiguous (so pluralism is the right stance) or merely general in sense (in which case pluralism is not obviously the right stance). Let C0 be a construction (of the sort used in semantics for intuitionistic logic), and let S0 be a situation (of the sort used in semantics for relevance logic). (Cf. previous pluralism post if that doesn't make sense.) Then, I think, Beall & Restall would say
'C0 is a case'
is true, and so is
'S0 is a case'.
(If they don't, then 'case' is not ambiguous, but something else.)
Now the question is: Are 'crossed readings' possible for
'C0 and S0 are cases'?
That is: can that last sentence express that C0 is a construction and S0 a situation, or can it only be read as saying that C0 and S0 are both constructions or both situations? I lean towards the possibility of crossed readings, but I'm just not sure.

We might try the conjunction-reduction test with logical consequence as well:
not-not-A (relevantly) implies A [but not intuitionistically]
not-not-A (intuitionistically) implies 'If B, then B' [but not relevantly]
The conjunction reduced sentence is:
not-not-A implies A and 'If B, then B'
Here, a crossed reading DOES seem impossible, to me at least. So that makes it look like 'implies' is ambiguous. (Note: I'm not certain I've formed the correct conjunction reduction sentence.)

Now I'm stuck: it looks like 'implies' is ambiguous, while 'case' is not. If this is right, then we could deny (V) -- but what could we put in its place?

Final speculative thought: 'implies' is like 'before' in relativistic physics. If two events are spacelike related (= no signal can be passed between them), then 'e1 is before e2' is neither true nor false until a frame of reference is specified. In one frame of reference e1 will be before e2, and in another frame, e2 will be before e1. But once the frame (and a simultaneity convention) is chosen, then it becomes fully determinate which precedes the other. BUT no one frame is the 'right' one; each frame 'has equal rights'.

The analogy: picking a particular frame of reference is like picking situations over constructions or models etc. As there is no one right frame, so too there is no one right truth-maker. So 'A implies B' is then NOT like 'Aaron is at the bank', for I can use that second sentence meaningfully (= truth-valued-ly) without supplying some further information -- unlike 'e1 is before e2' for spacelike-related events. But once one picks a frame, all instances of 'e1 is before e2' become truth-valued; analogously, once one picks a specification of 'case', every instance of 'Does C follow from {P1, ... Pn}?' has a determinate answer.

In sum: ambiguity may not be the best way of thinking about the different consequence relations; rather, perhaps we should see how well we can make out this analogy with relativistic physics.