Posts on: Conceptual Analysis
Philosophers (and linguists) often appeal to judgments about the
validity of general principles or arguments. For example, they judge
that if C entails D, then 'if A then C' entails 'if A then D'; that
'it is not the case that it will be that P' is equivalent to 'it will
be the case that not P'; that the principles of S5 are valid for
metaphysical modality; that 'there could have been some person x such
that actually x sits and actually x doesn't sit' is an unsatisfiable contradiction; and so on. In my view, such judgments
are almost worthless: they carry very little evidential weight.
Okay. Here are some thoughts on a talk Frank Jackson gave last week on Williamson on thought experiments.
The question is what Gettier discovered in his famous article. According to Frank, he revealed a fact about our concept 'knowledge': that it is not the same as our concept of justified true belief. According to Williamson, Gettier has revealed a fact about knowledge itself: that it is not justified true belief. A discovery merely about our concepts, Williamson says, "would show little of philosophical interest"; it would be "of significance primarily to theorists of concepts, not to epistemologists". For "the primary concern of epistemology is with the nature of knowledge, not with the nature of our concept of knowledge". (All of these are from p.206 of The Philosophy of Philosophy.) Frank disagrees. He thinks that results about the key concepts of a discipline are quite important to that discipline.
Daniel Nolan and I once suggested that talk about sets should be analyzed as talk about possibilia. For simplicity, assume we somehow simply replace quantification over sets by quantification over possible objects in our analysis. This appears to put a strong constraint on modal space: there must be as many possible objects as there are sets.
But does it really? "There are as many possible objects as there are sets." By our analysis, this reduces to, "there are as many possible objects as there are possible objects". Which is no constraint at all!
Here is a short paper version of my GAP.6 talk "Modal metaphysics and conceptual metaphysics", to appear in the GAP.6 proceedings. It has a lot less formulas than the talk.
I distinguish two metaphysical projects: modal metaphysics and conceptual metaphysics. I show that the two projects really are distinct, and that Frank Jackson's argument for the opposite conclusion doesn't work. Then I have a closer look at how the projects come apart, and suggest that when they do, the modal project always becomes metaphysically uninteresting. Thus the term "metaphysical modality" is a misnomer: metaphysical entailment only matters for metaphysics insofar as it coincides with conceptual entailment.
I suppose I should say a little more on what I call "modal back-reference", and on the sense in which what a sentence expresses can be conceptually independent of how things are in the actual world: doesn't what a sentence express always depend on what the sentence means? Unfortunately, I don't have a simple and uncontroversial answer to that, so I just ignored this point. Hopefully no-one will notice.
To be an electron is to roughly satisfy our electron theory;
to be a banana is to roughly satisfy our banana theory. To say
that electrons or bananas are such-and-such is equivalent to saying
that things (roughly) satisfying a certain theoretical role are
such-and-such.
Thus our Total Theory of the world is arguably a priori equivalent
to its "electron" ramsification or its "banana" ramsification, in
which all occurrences of "electron" and "banana", respectively, have
been replaced by existentially bound variables. What Total Theory adds
to those Ramsey sentences is only the Carnap sentence for "electron"
and "banana": the material conditional with the Ramsey sentence in the
antecedent and Total Theory in the consequent. And this conditional is
arguably analytic.
In section 24.D of his "Replies and systematic expositions" in the Schilpp volume, Carnap argues that every theory can be split into a component "representing the factual content of the theory", and another component serving as "analytic meaning postulates [...] for the theoretical terms". In fact, he doesn't speak about every theory, but it seems that what he says is true in general.
Take everything you believe about water, and call that your water theory. Your theory presumably contains things like "water fills our lakes and rivers", "water boils at around 100 °C under normal conditions", "water consists of H2O", and so on. All that is plainly empirical. Now the factual component of your theory, according to Carnap, is its Ramsey sentence: the theory with all occurrences of "water" replaced by a variable and prefixed by an existential quantifier binding that variable. The analytic meaning postulate then is the material conditional of the Ramsey sentence as antecedent and the theory itself as consequent. Let's call that the Carnap conditional of the theory.
Long ago, I worried about how the Ramsey-Carnap-Lewis account of theoretical terms could be applied to predicates. I noticed two reasons why Lewis's proposal to just turn the predicates into singular terms ("Instead of [...] 'F ---', for instance, we can use '--- has F-hood'", HTDTT p.80) is no good: first, it entails that completely false theories, say about witches or gods, leave their theoretical predicates undefined, whereas in fact those predicates are clearly empty (and thus defined); second, the proposal can turn consistent theories into inconsistent theories. This second problem can be generalized: For many predicates, there is no corresponding property that could be denoted by a singular term. Exactly which predicates these are depends on one's theory of properties, but "having parts", "being self-identical", "being a set" and "being a property" are generally good candidates, besides of course "not instantiating oneself".
Peter Menzies and Huw Price, in their forthcoming "Is Semantics in the Plan?" have spotted a mistake in Lewis's "Psychophysical and theoretical identifications". But they don't spot that it's a mistake, and rather think it shows that the Ramsey-Carnap-Lewis-account of theoretical terms is severly limited.
The mistake is that Lewis identifies "theoretical role" with "causal role":
Some people intuit that
- the subject in a Gettier case has knowledge;
- Saul Kripke has his parents essentially;
- "Necessarily, P and Q" entails "Necessarily, P";
- whenever all Fs are Gs and all Gs are Fs, the set of Fs equals the
set of Gs;
- the liar sentence is both true and not true;
- the conditional probability P(A|B) is the probability of the
conditional "if B then A";
- it is rational to open only one box in Newcomb's problem;
- switching the door makes no difference in the
Monty Hall problem;
- propositions are not classes;
- people are not swarms of little particles;
- a closed box containing a duck weighs less when the duck inside
the box flies;
- spacetime is Euclidean;
- there is a God constantly interfering with our world.
They are wrong. All that is false.
Call an expression E scrutable with respect to a class of expressions C iff it is a priori that all true sentences involving both C and E are a priori deducible from all true sentences involving only C. Equivalently, E is scrutable with respect to C iff there are no worlds w1 and w2 of which exactly one is in the 1-intension of some C+E-sentence, whereas all 1-intensions of C-sentences contain either both worlds or neither.
Is every expression scrutable with respect to some class of expressions to which it does not belong? If the relevant language has synonyms for all expressions, that's trivial. We should better ask about families of expressions: what classes of expressions are scrutable only with respect to expressions containing other members of their class? Call such classes indispensible. Large classes of expressions like the class of all expressions are obviously indespensible, as is probably the class of indexicals and the class of quantifiers. Dave Chalmers would also add the class of phenomenal expressions. As a type-A materialist, I would rather not.
I keep wavering between two different uses of "analytical". This entry is meant to remind me of the difference and of why I should prefer the one over the other.
On the first use, a sentence is analytical if it has a universal A-intension. On the second, a sentence is analytical if one can't understand it unless one believes it (this is what I, unoriginally, proposed last year). The first is the better explication.
Philosophers like to paraphrase away ontological or ideological commitment: how can there be a lack of wine if there are no such
entities as lacks? Because "there is a lack of wine" is only a loose way of saying "there is not enough wine".
So do we suggest that "there is not enough wine" somehow gives the
underlying logical form or linguistic structure of "there is a lack of
wine"? One might think so: if there are no lacks, we can't honestly
use lacks as semantic values in our linguistic theory. So if 1) our
linguistic theory says that sentences of the form "there is an F" are
true iff the relevant semantic value of "F" is non-empty, and if 2)
"there is a lack of wine" has the form "there is an F", and if 3) the
members of a predicate's semantic value are things that (in some
intuitive sense) satisfy the predicate, then, given the truth of "there is a lack of wine", it follows that there are things satisfying "is a lack of wine". Which presumably we wanted to deny. Rejecting (2) seems to be a good way to block the argument: "there is a lack of wine" is
not really a sentence of the form "there is an F"; really, it
is a sentence of the form "there is not enough G".
I've written a little paper in German about the connections between metaphysical (modal) and analytical implication for the Olaf Müller-Kolloquium here at Humboldt University: "Fundamentale Wahrheiten" (PDF). It brings together some things I've already written about here. The main ideas are entirely due to Lewis, Jackson and Chalmers.
Since I haven't slept last night and feel unable to do anything productive, here is an abbreviated translation.
Metaphysical debates about causation, consciousness, chance, change, mathematics, or modality have a lot in common. In all cases, metaphysical theories try to tells us what, if anything, makes a certain class of statements true. Among the possible answers, we usually find suggestions to reject the alleged phenomena, to declare them as primitive, and to reduce them in various ways to something else. But on closer inspection, there appear to be big differences, in particular with respect to what is required for a reduction.
Serious Metaphysics, in Jackson's sense, tries to identify a limited set of truths (i.e. true sentences) that entail (i.e. strictly imply) all truths. So what about
*) Everything is just as it actually is?
((p)(p <-> actually p), or (x)(F)(Fx <-> actually Fx))
(*) is true. It entails all other truths: whenever S is true, then so is "necessarily, if (*) then S". And it is fairly simple and economic: for instance, it doesn't contain macrophysical or phenomenal terms. Still, it's not serious metaphysics. What's wrong?
Apropos conceptual differences, Lewis didn't seem to care much about whether his
analyses exactly matched other people's semantic intuitions:
In "Veridical Halluzination and Prosthetic Vision", he claims that
prosthetic vision is properly called "seeing". He continues:
If you insist that "strictly speaking", prosthetic vision isn't really
seeing, then I'm prepared to concede you this much. Often we do leave
semantic questions unsettled when we have no practical need to settle
them. Perhaps this is such a case, and you are resolving a genuine
indeterminacy in the way you prefer. But if you are within your
rights, so, I insist, am I. I do not really think my favoured usage is
at all idiosyncratic. But it scarcely matters: I would like to
understand it whether it is idiosyncratic or not. (p.280 in Papers
II)
Another example: In Convention, he suggests that a regularity to dress in a particular way doesn't count as conventional if many people conforming to the regularity want others not to conform (so that they can poke fun at them). Realizing that this classification isn't obvious he notes:
If the reader disagrees, I can only remind him that I did not
undertake to analyze anyone's concept of convention but mine. (p.47)
He speaks of reminding the reader because he had already mentioned in the introduction that there might be no clear common concept of
convention. But, he adds, "what I call convention is an important
phenomenon under any name" (p.3).
A few more comments on why I think the setup of Weinberg, Nichols and Stich's experiments on intuitions is unfortunate. The problem seems particularly obvious in the experiments on semantic intuitions reported by Machery, Mallon, Nichols and Stich, but I think it carries over to many (though perhaps not all) of the experiments of Weinberg, Nichals and Stich. Here is one of the questions Machery, Mallon, Nichols and Stich asked:
I don't understand what's so bad about admitting that people may use and understand the same words in slightly different ways.
Suppose there is a community of Martians who have a word for true
justified belief, but no word for knowledge. When these Martians learn
English, they might at first take "knowledge" to be synonymous with
their word: the difference hardly shows up in ordinary contexts. So when they use "knowledge", they mean true justified belief.
Suppose we want to know whether some thing A has the property of representing B. The first thing to do is to ask what exactly is meant by "representing" in this context. That is, we must inquire into the general conditions under which it would be true that some x represents some y. Then, in a second step, we have to find out whether these conditions are satisfied by A and B.
When I say that semantic properties aren't primitive I mean that there must be an informative answer to the first question for semantic terms. That is, it must be possible to spell out general conditions under which something represents or means or denotes y. And the answer must be specifiable in non-semantic vocabulary. We can do better than saying that x represents y iff it represents y. The answer needn't be simple, nor immediately obvious. As usual, the best approach might be to use thought experiments: if such-and-such were the case, would x represent y? If yes, "such-and-such" can be added as a disjunct to the conditions under which x represents y.
Question: What exactly is wrong with something like this as a (physical-cum-indexical) conceptual analysis of "pain" (in my idiolect)?
the state I am in now
One obvious problem is that it's too unspecific: pain is not the only state I am currently in. But that's not the only problem. What else?
Is it a priori that I feel pain now? Or does my knowledge that I feel pain depend on empirical information? Could it turn out that I don't feel pain? Could it have turned out?
Suppose theory 1 says that entity x has certain properties, and theory 2 says that entity y has those properties. If we believe both theories, should we conclude that x=y?
It depends. Sometimes we not only should but must conclude that x=y, for example when theory 1 says that x is the planet Venus and theory 2 says that y is the planet Venus. In other cases, there is little reason to draw the conclusion, as when the theories merely say of x and y respectively that it is some planet or other. In yet other cases, the conclusion can be motivated by methodological considerations. For instance, whoever first realized that Hesperus is Phosphorus probably realized that the identity makes for a simpler overall theory.
Here comes the promised reply to Sam's
reply to my previous
posting. In that posting, I first suggested that some sentence S (in a
given language) is analytic iff you can't understand it unless you believe
it. Then I said that, "put slightly differently", S is analytic iff it is
impossible to believe that not-S.
As Sam notes, the first definition implies that even very complicated
analytic truths have to be believed in order to be understood, which might
be somewhat unintuitive. I'm not sure how bad this is for lack of a clear
example. Sam uses "the sum of the digits of the first prime number greater
than 1 million is even", but this is not analytic, so here I can perfectly
well admit that you may understand it without either believing or
disbelieving it. He also mentions infinitely long sentences, but I don't
believe there are any of those in ordinary languages.
Some expression can't be properly understood unless one believes certain
things: In some sense you don't understand "irrational number" unless you
believe that no natural number is irrational; You don't understand "grandmother"
unless you believe that grandmothers are female; Maybe you don't understand
"cat" unless you believe that cats are animals.
This is all quite vague because "understanding" and "believing" are vague.
I now want to suggest that a sentence is analytic iff you can't understand
it unless you believe it. Analyticity is also vague, so the vagueness of
the explicans is fine for this purpose.
Suppose some theory T(F) implicitly defines the predicate F. If we want to
apply the Ramsey-Carnap-Lewis account of theoretical expressions, we first
of all have to replace F by an individual constant f, and accordingly
change every occurrance of "Fx" in T by "x has f" etc. The empirical
content of the resulting theory T'(f) can then be captured by something
like its Ramsey sentence 
f T'(f), and the definition of f
by the stipulation that 'f' denote the only x such that T'(x), or nothing
if there is no such (unique) x.
In the previous three entries, I've tried to argue that there are no
genuinely implicit definitions: Whenever a new expression is introduced via
an alleged implicit definition, either there is no question of definition
at all, as in the case of new expressions used as bound variables in
mathematics, or there is an explicit definition nearby.
This latter fact, that sometimes explicit definitions are only
nearby, provides a partial vindication of implicit definitions. For
example, let's assume that folk psychology implicitly defines "pain". But
folk psychology itself is not equivalent to the nearby explicit definition.
To get an explicit definition, we have to turn folk psychology into
something like its Carnap sentence. So the theory itself could be called a
genuinely implicit definition.
I've said that an explicit definition introduces a new expression by
stipulating that it be semantically equivalent to an old expression. If
there are no non-explicit definitions, this means that you can only define
expressions that are in principle redundant. Aren't there counterexamples
to this claim?
Consider the definition of the propositional connectives. We can
explicitly define some of them with the help of others, but what if we want
to define all of them from scratch? The common strategy here is to
recursively provide necessary and sufficient conditions for the truth of a
sentence governed by the connective: A 
B is true iff
A is true and B is true.
Scientific theories are often said to implicitly define their theoretical
terms: phlogiston theory implicitly defines "phlogiston", quantum mechanics
implicitly defines "spin". This is easily extended to non-scientific
theories: ectoplasm theory implicitly defines "ectoplasm", folk psychology implicitly defines "pain".
The first problem from the mathematical case applies here too: Since all
these theories make substantial claims about reality, their truth is not a
matter of stipulation. For example, no stipulation can make phlogiston
theory true. That's why, according to the standard Ramsey-Carnap-Lewis
account, what defines a term (or several terms) t occurring in a theory
T(t) is not really the stipulation of T(t) itself, but rather the
stipulation of something like its 'Carnap sentence' x T(x) 
T(t). All substantial claims in T(t) are here cancelled out by the
antecedent.
I vaguely believe that there are no implicit definitions. So I've decided
to write a couple of entries to defend this belief. The defence may well
lead me to give it up, though. Anyway, here is part 1.
Explicit definitions introduce a new expression by stipulating that it be
in some sense synonymous or semantically equivalent to an old expression.
For ordinary purposes this can be done without the use of semantic
vocabulary by stipulations of the form
Christian has to write an introductory paper on Quine's "Two Dogmas". I
wouldn't like to do this. I think "Two Dogmas" is excessively overrated,
and should only be read in courses on the history of American philosophy.
Unfortunately, Christian seems to agree with most of my misgivings.
Maybe I find some opposition here.
"Two Dogmas" consists of three parts: §§1-4, §5 and §6. In §§1-4 Quine
argues that there is no distinction to be drawn between analytic and
synthetic statements. His argument appears to be as follows:
Hereby I stipulate that "fb13" is to denote the first human born in the
13th century. Hence it might seems that "fb13 was born in the 13th
century" is analytically true, true by definition. But if analytic truths
are closed under logical implication, "somebody was born in the 13th
century" would also be analytically true. Which it is not.
I don't think tinkering with closure under logical implication will help.
Hereby I stipulate that "fb23" is to denote the first human born in the
23rd century. However, if recent progress in civilization continues, there
might well be no humans in the 23rd century. And if no humans are born in
the 23rd century, "fb23 is a human born in the 23rd century" is false. So
it cannot be true by definition.
It is often said, correctly I think, that there are contingent but a priori
sentences, e.g. "water is the dominant liquid on earth". Are these
sentences analytic or synthetic? That is, what puts you in a position to
know these sentences? Does understanding suffice, or do you have to invoke
some other a priori means, like Gödelian insight? To me this seems
wildly and unnecessarily mysterious. Of course understanding suffices, at
least in ordinary cases. So there are contingent but analytic sentences. I
wonder why this is hardly ever said. Does anyone really believe that those
statements are synthetic a priori?
Dave Chalmers kindly explained his views on deducibility to me. He thinks that anything one could reasonably call non-deferential understanding of the fundamental truths would suffice for being able in principle to deduce macrophysical facts, provided that these fundamental truths, unlike my P, contain phenomenal facts and laws of nature. He also notes that I shouldn't have called these restrictions (to non-deferential understanding and the rich content of fundamental truths) assumptions, since they are really just restrictions. I'm still not sure if any kind of non-deferential understanding would suffice, but with the restrictions in place it's not as easy to come up with counterexamples as I thought.
Back to the question of deducibility.
According to the deducibility thesis, the fundamental truths (plus
indexicals, plus a 'that's all' statement) a priori entail every truth.
More precisely, when P is a complete description of the fundamental
truths and M any other truth, then, according to the deducibility thesis,
the material conditional 'P M' is a priori.
Dave Chalmers agrees that any concept can be explicitly analyzed by an
infinite conjunction of application-conditionals. But he wants to
restrict 'explicit analysis' to finite analyses. That certainly makes
sense, but I doubt that there are any concepts for which the
application-conditionals cannot be determined by finite means. For
example, I think it will usually suffice to partition the epistemic
possibilities into, say, 50 zillion cases and specify the extension in
each of these cases. Admittedly, I can't prove that, but the fact that concepts can be learned and our cognitive capacities are limited seem suggestive.
Dave Chalmers told me to
read some of his
papers. I have, and I'll probably say more on the
deducibility problem soon. Here is just a little thought on conceptual
analysis.
Chalmers suggests that we don't need explicit necessary and sufficient
conditions to analyse a concept. Rather, we can analyze it just by
considering its extension in hypothetical scenarios. What is it to
consider a hypothetical scenario? The result seems to depends on how the
scenario is presented. For example, 'the actual scenario' denotes the same
scenario as 'the closest scenario to the actual one in which water is H2O'.
But the difference in description could make a difference for judgements
about extensions. Chalmers avoids such problems by explaining
(§3.2, §3.5) that to consider a scenario is to pretend that a
certain canonical description is true. Hence to analyze a concept, we
evaluate material conditionals of the form 'if D then the extension of C is
E', where D is a canonical description. (Are there only denumerably many
epistemic possibilities or can D be infinite?) Now fix on a particular
concept C and let K be the (possibly infinite) conjunction of all those
'application
conditionals' (§3) that get evaluated as true. Replace every
occurrence of 'C' in K by a variable x. Then 'something x is C iff K' is
an explicit analysis giving necessary and sufficient conditions for being
C.
There may not always be a simple, obvious, or finite
explicit analysis, but at least there always is some explicit
analysis. If moreover satisficing is allowed, it is very likely that we
can settle with something much less than infinite.
When I tried to spell out the 'modus tollens' I mentioned on monday, I
came across something that may be interesting.
Frank Jackson argues that facts about water are a priori deducible from facts about H2O:
1. H2O covers most of the earth.
2. H2O is the watery stuff.
3. The watery stuff (if it exists) is water.
C. Therefore, water covers most of the earth.
1 and 2 are a posteriori physical truths, 3 is an a priori conceptual
truth.
Here are, very quickly, some more thoughts on the matters I talked about here
and there, inspired by another discussion with Christian.
You don't have to know much about plutonium to be a competent member of our
linguistic community. One thing you have to know is that plutonium is the
stuff called 'plutonium' in our community. Maybe that alone suffices.
Of course, if noone knew more about plutonium than this, the meaning of
'plutonium' would be quite undetermined. To fix the meaning, it would
suffice if a few persons, the 'plutonium experts', knew in addition
that this element (where each of the experts points at some
heap of plutonium) is plutonium.
If you're asked to explain how your preferred theory of everything -- that is, your brand of physicalism -- can accomodate some entity X, the first thing to try is the Canberra Plan. It goes as follows: First, collect features that could be said to characterise X. If you're lazy, simply collect everything the folk says about X. Next, say that since these features comprise the essence of X, whatever physical entity has (more or less exactly) those features is X. Finally, explain that of course there is such a physical entity, since otherwise statements about X wouldn't be true.