Philosophers' Carnival LXXVI

Welcome, readers, to the 76th fortnightly Philosophers’ Carnival!

Enigman asks what philosophical reasons mathematicians have for assuming the axiom of infinity in his post Philosophy of Mathematics. It’s not clear what sorts of reasons he’s looking for; fundamental questions about mathematical truth and the role of axioms seem to be lurking just below the surface here. The comments thread hasn’t grown prohibitively long yet, so hop on over and pitch in your $.02.

Alexander Pruss criticizes several ways of construing the supernaturalness of magic in Magic, science, and the supernatural. I’m not convinced by a lot of what he says, but the discussion is very clear and open-minded. Peruse the other entries while you’re there, if you haven’t visited before – it’s a nice blog.

Avery Archer works on a theory of rational agency in Why Questions and Rational Agents (more about the latter than the former). I like this post, even though I don’t like a lot (of the little) I have read elsewhere on rationality. It’s not clear to me that the appearances of the good (allegedly) involved in desire are reflections of a perspective held by some subsystem of an agent which is involved in producing the agent’s desires, just because I’m not sure that subsystems of agents are the sorts of things that can have perspectives. This might be a quibble. When a person’s reasoned course of action conflicts with her desires, there obviously does seem to be some sub-agential system bearing some interesting relationship to the course of action desired but not taken, or a mental representation of that course of action. It might be useful to spell out what is not quite “perspectival” about that relationship, though. I have more to say about this, but you don’t need to read it.

Over at Possibly Philosophy, Andrew Bacon weighs in on Counterexamples to Modus Ponens. I’m not sure I understand why he thinks that a syntactic characterization of modus ponens won’t work, and I don’t understand accessibility (between possible worlds) well enough to follow the rest of the argument. The McGee counterexample is super-interesting, though, and deserves attention from those of you out there with more logical competence than your humble host.

Thom Brooks of The Brooks Blog lets us in on his Five Secrets to Publishing Success, published on InsideHigherEd.com. Helpful to those looking for, well, publishing success.

Richard Chappell offers a brief but convincing discussion of Fair Shares and Others’ Responsibilities. He argues that, in the interest of fairness, we should pick up the slack for others’ moral failings. I think I agree, although I do not live up to the conclusion in my own life. Also, it’s not clear to me how well this sits with Richard’s views on the “demandingness objection” and the permissibility of living a basically decent life expressed here.

Bryan Norwood presents some objections to epistemological internalism, with an alternative, in Internalist Justification vs. Virtuoso Expertise. There is a lot I don’t understand here – the distinction between subjective and objective blame, the relationships between foundationalism and this distinction, and the relation between internalism and K = JTB. Still, I think there are some good ideas about epistemic blameworthiness brewing here.

Chris Hallq discusses Gettier and the purpose of analyzing “knowledge” in The case against Gettier. Some of the literature on what knowledge is for – the relation between knowledge and assertion, or knowledge and the attribution of other factive mental states – could help here. Still, the basic point, that philosophers interested in a concept need to keep the distinctive intended uses of the concept, is worth reiterating.

Lastly, Gualtiero Piccinini disambiguates “connectionism” for us, and spells out some of the morals of the disambiguation in The Ambiguity of "Connectionism". I was taught that connectionism is the view that the brain does most everything using Parallel Distributed Processing, but these other senses of “connectionism” are useful to distinguish as well.

That wraps up this edition of the Philosophers’ Carnival. If you’re still jonesing for more philosophy after all that, I invite you to check out some of the posts here on Think It Over. And, as always, keep your eye out for the next edition upcoming at Kenny Pearce’s blog.

Is Anything Wrong With My Ontology of Languages?

The notion of language I've been using here makes unusually fine-grained distinctions. By what criteria do I individuate languages? This is still not very clear to me, and contains some theoretical presuppositions which I’d like to make more explicit. Maybe the presuppositions are inconsistent or involve factual error. A little help figuring out whether this is the case would be appreciated. Anyway - the presuppositions.

A language has a set of wffs (or perhaps a function that assigns degrees of well-formedness to strings), so that if s is well-formed (to degree n) in L1, and not in L2, then L1 is not the same language as L2.

A language can also have a logic. We might conceive of a logic as a class of "transformation rules" in Carnap's sense. If a sequence of strings proves s in L1, but not in L2, then L1 is not the same language as L2.

A language has a semantics. In some sense, perhaps involving no platonistic ontological commitments, a language assigns meanings to sentences, words, and phrases. If x has some semantic property relative to L1, but not relative to L2, then L1 is not the same language as L2.

The meaning of a word, whatever it is (or however it is to be eliminated in favor of some less committal idiom), is sometimes derived in part from the word’s role in some larger theory. “Electron” derives its meaning, in part, from its occurrence in a central chunk of physical theory. “Phlogiston” derives its meaning, in part, from its occurrence in a central chunk of phlogiston theory. Now, “electron” occurs both in

(E) Every electron has a charge of -1

and in

(E`) Every electron has a charge of -10.

“Phlogiston” occurs both in

(P) When a flammable substance is burned, phlogiston escapes it

and in

(P`) It is not the case that when a flammable substance is burned, phlogiston escapes it.

We might suppose that “electron” derives its meaning, in part, from its occurrence in (E) but not in (E`), and that “phlogiston” derives its meaning, in part, from its occurrence in (P) but not in (P`). So there must be some special property of (any combination of) “electron”, (E), and the languages containing them in virtue of which this is the case; likewise for (P) and “phlogiston”. It can’t just be that (E) is true and (E`) is not, because the same distinction can’t be made between (P) and (P`). I don’t think it can just be that (E) is actually in physical theory, and (P) in phlogiston theory. This is because I think theories are best thought of as classes of sentences. “Electron” occurs in both physical theory and physical` theory, which is the set of sentences gotten by replacing (E) with (E`) in physical theory; likewise for “phlogiston”. If physical theory is well-formed or expressible in a language, then physical` theory is almost certainly well-formed or expressible in that language; likewise for phlogiston theory and phlogiston` theory. There is certainly something special about physical theory and phlogiston theory, and it has to do with the meanings of “electron” and “phlogiston”, but it isn’t yet clear what this special something is.

My guess about how to make it clear is basically to individuate languages more finely. Assume that languages have unique assignments of truth-values to certain of their sentences. These include the sentences from which words derive their meanings. Words can derive their meanings only from sentences which are assigned a truth-value by a language. If L1 assigns a different truth-value to s than L2, and t derives its meaning in part from s, then t has a different meaning in L1 than in L2. The hypothesis is that “electron” actually has the meaning it does in the language of physical theory in part because that language assigns the value “true” to (E) but not to (E`), and “electron” is actually used in the language of physical theory, not the language of physical` theory.* We avoid the problems related to “phlogiston” in the following way. (P`) is not incoherent or analytically false in our language. Rather it is elliptical for a complicated statement about the sub-optimality of the language of phlogiston theory. This is the language which gave and continues to give “phlogiston” its meaning. Fully unpacked, (P`) might be glossed “The language of phlogiston theory is sub-optimal because there is no worthwhile concept to which (P) lends meaning.” “Phlogiston” means what it does, and is to be unpacked this way, because it was introduced in the language of phlogiston theory, and not, for instance, the language of phlogiston` theory.

I guess the idea overall is that theories in which theoretical terms derive their meaning, in part, from their occurrence in other sentences of the theory are, as Ayer might have said, disguised linguistic proposals. Or maybe the idea is that languages are disguised theoretical proposals.

I understand that the apparatus here involves a number of assumptions, but I’m ready to take them on unless they’re controverted by fact or internal inconsistency. Well - are they?

* - I say “language”, but I allow that physical theory – the class of strings assigned certain meanings – could be conducted simultaneously in many different languages. The actual meaning and use of “electron” and other special theoretical terms might not determine a single language for physical theory, in our sense of “language”.
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Update: At least one thing is wrong with this ontology. I think the epistemology of analyticity for which I have primarily made use of it is no good. Also, I don't like the ellipticality stuff. If semantic representations are mental representations, then this is way implausible.

On What There Is and What We Can Perceive

Our knowledge of the physical world depends on our perceptual faculties being just about as sensitive as they are. Consider an ideally rational animal, or ideally rational community of inquirers, with only, say, our auditory and proprioceptive faculties. Call it A. It is hard to imagine how A could develop anything we should consider a complete physics. Perhaps I’m wrong – I’m only going on conceivability here – but it sure seems as if the ontology of the theory A would possess at the end of inquiry just could not be the same as any ontology human beings will reach at the end of inquiry.*

A’s theory and ontology would be, in some sense, inadequate. This is because we have all of the evidence A has and more, and A’s theory is inadequate to account for all of our evidence. My intuition is that this inadequacy has some sort of normative force; that is, in some sense, A should adopt a theory that is able to account for our evidence as well as our own completed physics.

Here’s my question: What reason do we have, if any, not to believe that, for all we know, we are in A’s position? More precisely, what reason do we have, if any, not to believe that, for all we know, there is some (perhaps uninstantiated) perceptual faculty, such that our theories should account for the evidence this faculty would furnish for us, were we to have it, in the same sense that A’s theory should account for the evidence furnished by our visual faculties? To be sure, we have pretty good evidence to suspect that none of the animals on Earth have such a perceptual faculty. The question is whether, for all we know, something could have such a faculty, with the world and its contents remaining otherwise entirely as they are.

The only reason I can think of – if it is true – would be furnished by a certain sort of “instrumentalist” meta-ontology. I take instrumentalism to be the view that ontology O is to be preferred over ontology P just in case O is better suited to our purposes than P. Once we have all the evidence in hand, we answer these sorts of “big picture” ontological questions (Carnap might have called them external questions) by recourse to our purposes in theorizing. Suppose our purposes are just to develop a theory with all of the virtues of descriptive adequacy, explanatory power, and simplicity that accounts as well as possible for all of the way things appear to us.** In that case, it is clear that no such troublesome perceptual faculty could exist, because no perceptual faculties other than our own can have any normative bearing on our choice of ontology. Note that this sort of meta-ontology makes it difficult to hold on to the initial intuition I had about A’s epistemic situation – namely, that A should adopt a theory that is able to account for evidence outside of her own perceptual purview. If we think that ontologies are beholden, at last, only to the way things appear to the community of inquiry, then the percepts of outsiders, real or imagined, can have no rational bearing on what exists, in our language.

It’s not clear which I like more – this version of instrumentalism or the offending intuition. Is there some adjudicating evidence that I’ve left out of court? Can anyone point me in the direction of some relevant literature?
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* - I’m assuming here that neither we nor A ever experience any sort of divine revelation or anything like that.
** - This description of “our” purposes is really unsatisfactory to me, but I can’t do any better yet. For what it’s worth, it probably beats Carnap in ESO, where he suggests that the purpose for which he uses the language of serious theory is “the purpose of communicating factual knowledge.”

Confirmation and Relative Frequency

In “Two Concepts of Probability,” Carnap writes: “It is clear that from a probability1 statement [i.e. a statement about degree of confirmation] a statement on frequency can never be inferred, because the former is purely logical while the latter is factual.” (526) For instance, consider the probability1 statement that the hypothesis that any given throw of a die will be a six has a 1/6 probability on the evidence that the die is symmetrical, or P1(h|e) = 1/6. Carnap says that, from this probability1 statement, we cannot infer that the limit of the relative frequency of the six-event is 1/6, or P2(h) = 1/6. My intuition is that this is, strictly speaking, true, but that given both e and P1(h|e) in an adequate inductive logic, the proposition that P2(h) ≈ 1/6 is thereby confirmed to an acceptable degree. If we take an “inference” in inductive logic to be the premises’ conferral of an acceptable degree of confirmation on the conclusion, then, given e and P1(h|e) in an adequate inductive logic, we can infer P2(h) ≈ 1/6. This is not a deductive inference of P2(h) from P1(h|e), but it is enough to suggest that Carnap might have been a little bit confused about the relation between confirmation and relative frequency.

Nevermind, for now, how to extend the basic moral here to cases in which the “≈” won’t work. Am I missing something?

"Grue" and "Third Child" Are Sometimes Projectible

The observation that some batch of emeralds is green is evidence for the hypothesis (K) that all emeralds are green, and is not evidence for the hypothesis (H) that all emeralds are grue. But this need not be the case. Suppose we lived in a world in which the spectral reflectance curve of everything that comes into existence, after a certain length of time n, shifts some specified amount. In particular, the shift is such that, after a duration of n, everything that comes into existence as a green object becomes blue. Suppose, further, that no emeralds naturally form in this world. Then, at time t – n, Jack synthesizes the first batch of emeralds ever to come into being in this world. Jack observes that the emeralds are green.

Isn’t it the case, here, that Jack’s observation is evidence for H, but not for K? Isn’t it the case, here, that “grue” is projectible over objects created at t – n?

A similar and perhaps slightly less ridiculous imaginary case would be a nearby possible world in which birth order strongly impacted the way we form friendships, so that people with the same number of older siblings were much more likely to be friends. Then if friends are more likely to be amongst one another than with others, then the observation that five people in a room of thirty are third children is evidence for the hypothesis that (at least most of) the other twenty five are also third children.

What are the consequences of this? Well, if “grue” and “third child” are projectible when we have certain background information or given certain background conditions* and unprojectible when our information or conditions are otherwise, then we sometimes need certain information about our own information or the condition of the world in order to determine whether a hypothesis or predicate is projectible. If we want to maintain that claims about the projectibility of a hypothesis or predicate are a priori, then we will have to relativize “projectible” to a specification of the condition of the world or our own information (and even that might not work). Otherwise, we will have to say that claims about the projectibility of a hypothesis or predicate are a posteriori, and that the information about our own background information or about the condition of the world is somehow evidence for the projectibility claim. Either way, the most important consequence is that the best theories of projectibility cannot distinguish the projectible from the unprojectible solely on the basis of necessary or irreducibly monadic features of given hypotheses or predicates.

Note also that, in Jack’s world, in populations of objects existing for a duration of n or longer, then we can only project normal color predicates (e.g. “green”/“blue” – not “grue”/“bleen”) from samples. So, in this case, even within a given world, sometimes “green” will be projectible and sometimes “grue” will be projectible. This seems to have nothing to do with how entrenched “green” and “grue” are in the world.
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* - I say “background information or given certain background conditions” because it is not clear what is making “grue” and “third child” projectible in these scenarios – that they have certain weird features or that we know they have the weird features.

An Unnecessary Criterion of Adequacy for a Definition of "Confirmation?"

One of Carl Hempel's criteria of adequacy for a general definition of "confirmation" in his "Studies in the Logic of Confirmation" (1945) is that it must apply to sentences of any logical form. According to Hempel, a general definition of "confirmation" cannot state only what sorts of sentences confirm, say, universally quantified sentences with a single variable.

Maybe I'm missing something, but I think this is not a good criterion. As far as I can tell, as long as we define “confirmation” for, say, universally quantified sentences of single variable (with negation), then, if we accept Hempel’s “equivalence condition”*, we have a general definition of “confirmation.”

Can’t we eliminate any existential quantifier in terms of a universal quantifier and negation by means of the logical equivalence (Ex)(Fx) <=> ~(Ax)~(Fx)?

Isn’t it true that, for any n-adic predicate R, for any place pi in the predicate, for any ordered set of objects {x1, x2, …, xi-1, xi+1, …, xn} occupying the other places in the predicate, we can define a monadic predicate R`, such that R`xi <=> Rx1,x2,…xi-1,xi,xi+1,…xn?

And, at least in languages without empty names, isn’t it true that Fa <=> (Ex)(x = a & Fa)?

So, if we allow ourselves to define somewhat contrived predicates and help ourselves to languages non-free logics, isn’t every sentence logically equivalent to some sentence in universal form with one variable? This is not, of course, to say that we could actually get by in science or daily life without sentences of more complex logical forms; this is a claim only about what a definition of “confirmation” needs to be truly general. As usual, I reserve the possibility that I’m totally mistaken about the logic here.
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* - The equivalence condition states that "If an observation report confirms a hypothesis H, then it also confirms every hypothesis which is logically equivalent with H."