Saturday, December 29, 2007

The coming term

I haven't yet brought myself to writing a substantive post, but I figure I can talk about the coming term. I'm going to be TAing for intro to philosophy of science, which I am looking forward to. In addition to that I will be taking a class on Quine and Carnap with Tom Ricketts. This will be good because it will flesh out my background in Carnap and I will see another perspective on Quine, having taken a seminar on his work with Follesdal. I will also be taking a class on the epistemology of perception with McDowell. This could be cool. I don't have a lot to say about this. Perception is all the rage around Pitt this year it seems. Finally, I'm going to do an independent study on algebraic logic using Dunn's algebraic logic book. I am really excited about this. It will, hopefully, help motivate me to write some more posts about logic and get those model theory posts off the backburner. I'm hoping to link this to some things about substructural logic and proof theory, since Restall's proof theory book makes the connection between the two. Somehow this term I've gotten interested in relevance logic, and this will, maybe, connect up to this directed study. In addition to this, I need to start doing work for the grant that I got to study Wandering Significance. Thinking and blogging are mutually reinforcing, so I will probably write some posts on it.

Once I finish up a short paper on Aristotle's logic, I can declare victory over this semester. The first term teaching was rewarding but somewhat rough. Teaching three discussion sections a week takes much more time than I expected. It certainly ate into my time doing my own work. A few ideas I had didn't receive the sort of time I had hoped to put into them.
At the start of the term all the new TAs had to go to several seminars on various aspects of teaching. One thing that we didn't have that, in retrospect, would have been nice to have was a seminar on how to teach and do your own work. I will finish this post with a suggestion I got from someone on how to teach and do your own work: shirk responsibility. Wise words.

Monday, December 24, 2007

Nothing of substance

It turns out that between Aristotle and holiday lethargy I did not get much else done. I probably will continue this trajectory until school starts back up again on the seventh of January. I stumbled across this old quote from an interview with William Gibson, a science fiction author I like a lot, that I think is quite nice, so I thought I would share:
"But it's still the same thing -- I make black marks on a white surface and someone else in another location looks at them and interprets them and sees a spaceship or whatever. It's magic."
Magical but not supernatural. In any case, posting will probably be somewhat light for the next two weeks or so.

Tuesday, December 18, 2007

Other people are interested in Brandom

There is a nice little series of posts on Brandom and Habermas and Brandom on objectivity with further comments. It looks pretty good. I'm hoping to get some comments in soon. I have been bogged down in an Aristotle paper which finally started to warp itself up. Once I get done with this I am going to try to write up some more posts, including some much delayed thoughts on model theory.

Monday, December 17, 2007

Evans link

There has been a buzz about Gareth Evans around here recently. I just found this overview of Evans's Varieties of Reference by Rick Grush at UCSD. It could be useful for those brave souls venturing into the work solo or those of us that might venture into it in the near future. [Edit: The picture of Evans on that page, in fact the only picture I've ever seen of him, is amazing. Oh, to have been a philosopher in the 70's...]

Goldfarb on showing

A couple of weeks ago Warren Goldfarb gave a short talk to our TLP reading group on the notion of showing. Explaining the saying/showing distinction is very important to resolute readers of the Tractatus and it is one of the big ways in which the resolute reading is set apart from the others. The traditional reading takes the talk about showing to indicate that there is some inexpressible reality or truth that statements can gesture towards but not outright say. While these things are nonsense, they are informative nonsense in that they help us see the deep truths. The resolute reading wants to do away with that and say that nonsense is just nonsense. Alright, but what do we make of various places in TLP where Wittgenstein says things like what can be shown cannot be said?
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Goldfarb's idea was to look at all the instances of "show" and its cognates (zeigen in German) in the Tractatus and see if they lend themselves to a metaphysically loaded interpretation. There are around 20 instances in the book and a few relevant passages from the Notebooks. He isolated three versions of showing. One is the sense of showing in which a name shows that it is a name and not a relation and a relation symbol shows that it is a relation. One can't say that something is a name, but that it is a name is apparent from what sort of variable it can be substituted for. This is an idea that Wittgenstein most likely picked up from Frege. The other two senses seem to be original to Wittgenstein in the Tractatus. (I can't find my notes on the talk so this bit might be fixed up later.) The second sense is the way in which a proposition shows that it is logically complex. It can be seen in the proposition that a proposition is logically complex or atomic, but not said according to the Tractatus. The third sense is the way in which propositions show what follow from them, i.e. by combining into tautologies. That p and p->q implies q is shown by (p. p->q)->q being a tautology. I got these two senses confused since they are similar. The important difference is between complexity and consequence. The second step is the former and the third is the latter. All three senses are in play in the finished Tractatus. Going through the text, Goldfarb made a pretty compelling case that all instances of showing in the Tractatus involve only showing logical and categorial features of the propositions involved, which would not necessitate any move to more metaphysically loaded readings. Part of the desire to give a more metaphysical reading depends on the discussion of the mystical, which I will get to below. Goldfarb's talk made it slightly hard to see why people were tempted by the more metaphysical understanding of showing at all. I think that the more metaphysical reading is fairly easy to get on the first read or two. However, examining the specific passages with his distinctions in mind did make it difficult to see the need for a more metaphysical reading of those passages.

There were two further points that were important to his presentation. One was what to make of the 'cardinal problem' letter to Russell. Wittgenstein wrote a letter to Russell in which he told Russell that he had not gotten the message of the Tractatus and he said that the cardinal problem of philosophy was the distinction between what can be said and what can be shown. Goldfarb's take on this was that it was directed mostly at Russell and his philosophy of logic. This was probably the least satisfying part of the presentation since he ended up saying that Wittgenstein was emphasizing the point just for Russell. The idea being that the distinction wasn't the cardinal problem but rather a cardinal problem. I'd like to go back over Goldfarb's take on this in comparison to Kremer's recent paper on the topic, but I'm not sure when that will happen.

The other was what to make of phrase that is translated as "shows itself" in Ogden's translation and as "makes itself manifest" in the Pears-McGuinness translation. The German that these come from is "sich zeigen". They are used in connection with Wittgenstein's discussion of the mystical. Goldfarb's suggestion here is that all instances of "sich zeigen" should be seen as expressing something completely different from what is expressed by "zeigen". This would let the resolute readers try to make sense of the discussion of the mystical apart from the rest of the discussion of showing. I hadn't drawn the connection between the two enough to worry about their relation. It seems like a reasonable enough thing to do. All in all it was a great talk and a delightful way to end the reading group for the term.

Saturday, December 15, 2007

On Brandom's so-called inferentialism

Before getting to the post proper, it will help to lay out a distinction drawn, I believe, by Sellars. The distinction is between three sorts of transitions one could make in relation to propositions, for example if one is playing a language game of some sort. They are language-entry moves, language-language moves, and language-exit moves. The first is made through perception and conceptualization. Perceiving the crumb cake entitles me to say that there is crumb cake there. The second is paradigmatic inferential or consequential relations among propositions. Inferring from p&q to p is a language-language move. The third is moving from a practical commitment or explicit desire to action. Borrowing Perry's example, it is the move from thinking that I have to be at the meeting and that the meeting is starting now to me getting up and rushing off to the meeting.

In Making It Explicit, Brandom distinguishes three things that could be meant by inferentialism. These are the necessity of inferential relations, the sufficiency of inferential relations, and hyperinferentialism. The first is the claim that inferential articulation is necessary for meaning. Representation might also be necessary, but at the least inference is necessary. The second is the claim that inferential articulation is sufficient for meaning. In both of these, inference is taken broadly so as not to collapse into hyperinferentialism, which is the thesis that inference narrowly construed is sufficient for meaning. The narrow construal is that inferences are language-language moves. What does this make the broad construal? According to Brandom, it includes the language-entry and -exit moves. In MIE, Brandom defends, I believe, the necessity of inferential relations, although he says some things that sound like he likes the idea of the sufficiency claim. He doesn't think that hyperinferentialism will work. This is because he thinks that for some words, the content of the word depends on causal/perceptual connections. I think that color terms are examples. Additionally, the content of some words exhibits itself in what practical consequences it has in our action and this exhibition is an essential part of the meaning of the word. My beliefs about crumb cake will influence how I act around crumb cake. Hyperinferentialism cannot account for these because the language-entry and -exit moves essential to their meaning are not things hyperinferentialism has access to.

Brandom's claim then, once things have been unpacked a bit, amounts to saying that the narrowly inferential connections, perceptual input, and practical output are necessary for meaning. This seems to undercut the charge that inferentialism loses the world in a froth of words, which charge is mentioned at the end of ch. 4 of MIE, I think. It is also a somewhat looser version of inferentialism since things that are not traditionally inferential get counted as inferential. The inferentialist could probably make a case that that the language-language moves are particularly important to meaning, but I think Brandom's inferentialism stretches the bounds of inference a bit. I'm not sure an inferentialist of the Prawitz-Dummett sort would be entirely comfortable with the Brandomian version of it. By the end of MIE, Brandom's broad notion of inference encompasses a lot. Granted, it is fairly plausible that much of that is important to or essential for meaning. However, I wonder if it doesn't move a bit away from the motivating idea of inferentialism, namely that inference is what is central.

Wednesday, December 12, 2007

A quirk of philosophical speech

I've noticed a speech pattern that sees a lot of action around here. I don't remember hearing it before coming to Pittsburgh, but I wouldn't trust my memory too much on that matter. The pattern is: well, you might think X. The "well" is optional. It is often used as a way of introducing a view or objection. For example: well, you might think that representation is essential for linguistic meaning. Or, you might think that the conceptual is unbounded, which would lead you to object to bare presences like sense-data contributing any sort of justificatory element. Is this a widespread pattern? I don't think this has crept into my speech or writing.

I'm now done grading finals for the class I'm TAing, so hopefully I can get back to putting up contentful posts, like that one on Goldfarb on showing I promised recently.

Monday, December 10, 2007

Problems for constructive empiricism

This is a short thing I wrote up for my philosophy of science class on Arthur Fine's criticisms of van Fraassen's position. I liked it, so I thought I'd share. Apparently in that seminar I didn't make it pass the Scientific Image. The problem wasn't solved, but I think I figured out what the problem is. Solving it will probably require figuring out why van Fraassen adopts the epistemological views he does. No mean task, that.

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In his "Unnatural Attitudes," Arthur Fine finds fault with anti-realism in the philosophy of science in its attribution of an aim to science, which, in the case of constructive empiricism, is that science aims at empirical adequacy.
Upon further examination, this objection breaks into two further, related criticisms, one that says constructive empiricism artificially splits the inferential practice of scientists and one that says the constructive empiricist policy about accepting unobservables is unjustified. I will argue that van Fraassen can adequately respond to the latter. The former turns on broader philosophical disputes between van Fraassen and Fine that cannot be resolved here, but I will attempt to give a response that does not rely on these. In the end Fine's criticisms cast some doubt on van Fraassen's view but they are not decisive against it.

Fine initially criticizes anti-realism for the attribution of an aim to science because an aim distorts our understanding of science. The distortion comes from a desire to "interpret science in accordance with a set of prior, extra-scientific commitments." The extra-scientific commitment of constructive empiricism, namely to empiricist epistemological principles, is built into the demand of empirical adequacy, which van Fraassen says is the aim of science. Empirical adequacy comes bundled with a distinction between the observable and the unobservable.

Despite rhetoric to the contrary, the source of Fine's problem does not seem to be that van Fraassen attributes an aim to science, but rather what the aim is. If van Fraassen did not claim that science aims to provide empirically adequate theories, then part of the motivation for the empiricist epistemology is removed. It need not drop out completely, though, as the epistemology is a consequence of, not equivalent to, the aim. Fine's criticism does not essentially involve an aim being attributed to science. Rather, the heart of the criticism lies with the extra-scientific commitments of the empiricist epistemology.

According to Fine, constructive empiricism's unnecessary need to interpret scientific practice comes from a commitment to empiricist epistemology; Fine says this has two primary principles, that belief requires justification and that only experience can justify belief, both of which are important below. The interpretation holds that scientific evidence builds for belief when the statements in question are about observables and for acceptance when they are not. Fine puts the point by saying that the constructive empiricist "can follow the usual lattice of inferences and reasons that issues in scientific beliefs only until it reaches the border of the observable, at which point the shift is made from belief to acceptance. But the inferential network that winds back and forth across this border is in no way different from that on the observable side alone." There is a uniformity in the scientific inferences about microwaves, on the one hand, and about elephants, on the other. Despite the uniformity, the constructive empiricist divides the commitment and supporting evidence into two categories, one for acceptance and one for belief. The inferences drawn by scientists crisscross the epistemological division between propositions about observables and those about unobservables. Thus, the constructive empiricist imposes an unnatural interpretation on science where no natural boundary exists, which is the first criticism of van Fraassen. While constructive empiricism is, rightly in Fine's eyes, set against "the needless multiplication of entities" it does not follow this policy with respect to "the significance of practices". Even though the inferential practices are uniform, van Fraassen draws a line between some of the involved propositions, dividing them into beliefs and mere acceptances. Before getting to van Fraassen's response to this, it will be helpful to lay out Fine's other objection and respond to it.

Fine's first objection leads naturally to his second which is that constructive empiricism's policy of never going for belief in the unobservable is not justified. Fine doubts that van Fraassen's epistemological considerations successfully underwrite merely accepting, and never believing in, unobservables in all cases. He asks, "Why must it be the case, say for electrons, that the complex history of evidence, successful use, and reasoning at the very best supports belief in the observational reliability of electrons and supports our commitment to behave just as though they exist but nevertheless fails to support the belief that they do exist?" Fine thinks that there is no a priori reason to think that the evidence supporting a theory with unobservables, such as electrons, should never support an inference to the existence of them. Constructive empiricism might be a good heuristic, but the details of the specific cases need to be examined to decide the question of belief. Fine thinks that specific cases will disagree the constructive empiricist stance, although some may agree with it. However this would be a conclusion based on a posteriori knowledge, not a priori commitment.

Against this second criticism, van Fraassen has a reply. Given the principle that only experience can justify belief, van Fraassen's policy about belief is justified, but this would be question begging. Rather, a better reply is to focus on Fine's example of the virtues supporting a theory and how this would support belief in the theory's unobservables. Constructive empiricism says that we are not rationally compelled to believe in unobservables but are rationally compelled to believe in observables. Fine's claim that the theoretical virtues and historical details about theories of electrons support belief in electrons is ambiguous. If he means that the extra virtues provide some motivation for believing, then van Fraassen can agree; they may motivate but not compel. Alternatively, Fine may mean that the extra virtues rationally compel us to believe in electrons, although Fine does not say much about rational compulsion. If the belief in unobservables that Fine recommends is justified, it is justified by something outside of experience. Constructive empiricism, according to Fine, includes the principle that only experience justifies belief. This objection is a consequence of Fine's rejection of that principle.

Even without a defense of the epistemological principle, van Fraassen can respond by denying that anything is gained by believing in unobservables. Believing in electrons does not make the theory more vulnerable to refutation or more empirically contentful. As van Fraassen said, "since the extra opinion is not additionally vulnerable, the risk is - in human terms - illusory, and therefore so [are the gains]." This is not a problem that Fine tackles. He could respond that what is gained by the belief is simplicity of our story about science, but this is not justification for a belief to van Fraassen. The van Fraassen ian point is that what is gained is the claim that there are things that do not and cannot figure in our experience of the world. van Fraassen's response and Fine's rejection of the claim that only experience can justify belief bring this exchange to a standstill. A more promising route is for Fine to point to the first problem, the uniformity of inferential practice, as an example of what is gained by believing, maintaining the uniformity, although this is not justification for a constructive empiricist. This leads us back to Fine's first problem for van Fraassen.

The first problem, the uniformity of inferential practice, seems to be the bigger stumbling block for van Fraassen. The epistemological division does not cut at the joints of the inferential practice of scientists. The challenge is to justify the epistemology. Since settling the issue of whether epistemology of science is needed is beyond the scope of this paper, I will focus on the question of what the relation between the inferential practice and justification by evidence is.

van Fraassen only talks about evidence for a theory as a whole. This evidence will be based on the observable, although it will lend support to the statements about unobservables through supporting the theory. Statements about unobservables serve to simplify connections among observables. The inferential connections are among propositions or statements. Whether these propositions are believed or accepted seems to be a separate issue from what inferential connections they have. The inferential connections are determined, at least for the most part, by the theory which receives evidential support from the statements about the observables. The distinction among the types of commitment to propositions that Fine focuses on does not depend on these connections. The types of commitment and the inferential connections are orthogonal. If they are orthogonal, then it is not surprising that they do not naturally line up. The question now is why this should count against van Fraassen's view.

Fine is oddly silent about what the uniformity among inferences is, even though it is, on this reading, central to his criticism of constructive empiricism. The inferences are not epistemologically uniform, since the evidence for them comes in different forms, depending on their subject matter, although all such evidence will be from observables. Inferences about electrons will be based on different things than inferences about elephants, e.g. the former will may be based on voltmeter readings while the latter may be based on tissue samples. They aren't uniform in their subject matter. Fine's point may be that they are uniform in the scientists' commitment to them, in the form of belief in the premises and conclusions. van Fraassen could agree that they are committed but take issue with the further commitment in the form of belief. van Fraassen does not see it as a problem that most scientists take themselves to believe in all the entities they study, because the question is a philosophical one. No matter the actual views of scientists, all that is needed is the commitment to test the theory's empirical adequacy, and this requires no more than acceptance of unobservables and belief in the observable. van Fraassen's view can then maintain a uniformity among the inferences, commitment to using them to test the empirical adequacy of a theory, even though this is likely not the uniformity that Fine points to.

The heart of Fine's criticism is that the epistemological division is artificially imposed on the inferential practices, which are not themselves problematic. A view that adds something artificial to an otherwise unproblematic phenomenon is not thereby refuted by the artificiality. van Fraassen's reasons for drawing the line where it is relies on a criterion, observability, that while artificial with the respect to the inferential practices is not itself ad hoc. In fact, van Fraassen is able to maintain an important, natural uniformity among the inferences, as outlined above. However, given that van Fraassen thinks that being able to make sense of scientific practice without the inflationary metaphysics of realism is reason in itself to choose constructive empiricism, by parity of reasoning being able to make sense of scientific practice without van Fraassen's extra epistemology is reason to choose Fine's view over constructive empiricism. It looks like Fine's criticism should count against constructive empiricism by van Fraassen's own lights.

In conclusion, Fine's objections push one's intuitions against constructive empiricism but they do not decisively refute it. They cast doubt on the necessity of the epistemological distinctions for our understanding of science, undermining the impulse to enrich our epistemology, but they do not provide us reason to think that the epistemology gets things wrong. van Fraassen is able to respond to Fine's criticisms, but the response to the second objection results in both sides digging in their heels. More completely responding to Fine would require a more detailed defense of the empiricist epistemological principles van Fraassen uses. Without that, the responses give on behalf of van Fraassen get him a draw.

Pitt-CMU conference deadline extension

The deadline for the Pitt-CMU conference was originally today. It is being extended to [Edit: Monday, December 17 (I messed up the date.)]. Please submit if you are interested!

An anecdote

We had the last of the Tractatus reading group meetings on Friday. For our final session, Warren Goldfarb read two short papers on the notion of showing and discussed them with us. I want to write up something about that, but I wanted to mention an anecdote he opened with. He said that he hadn't published much of his stuff on the Tractatus. He then said that at one of his talks he was introduced as, "Warren Goldfarb, whose unpublished work on the Tractatus are de rigueur for any serious student of that work." I found that amusing. Hopefully I will get to the substantive post later tonight or tomorrow.

Monday, December 03, 2007

Van Fraassen on explanation

This is a note I wrote on Salmon and Kitcher's criticisms of van Fraassen's view of explanation in the Scientific Image. It is a little flawed in that the defense I gave in the last third doesn't mesh with what van Fraassen says in the book. I didn't realize this when I wrote it though. Alas. Up until then I think it is not bad though. This is also the thing I tried to post the other day that Blogger kept eating.

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In their article ''Van Fraassen on Explanation,'' Salmon and Kitcher charge van Fraassen with presenting a theory of the pragmatics of explanation that fails to be a pragmatic theory of explanation. This is a hefty charge because van Fraassen denies that there is any sui generis explanatory virtue and defends this claim by providing a theory of explanation that purports to show how explanation is merely pragmatic. In this paper I will present two of Salmon and Kitcher's objections to van Fraassen's theory of explanation. I will then present replies on behalf of van Fraassen and argue that the criticisms do not undermine his project. I will close by presenting what seems correct in Salmon and Kitcher's.

Briefly, van Fraassen sees explanations as answers to questions of the form ''Why is Pk the case?'' A question Q in a given context can be identified with the triple (Pk, X,R), where Pk is the topic of the question, X is the contextually determined contrast class for Pk, and R is the contextually determined relevance relation. An explanation is an answer A to some 'why' question such that the A stands in R to (Pk, X). This makes van Fraassen's theories of explanation and 'why' questions heavily dependent on context. This is explicit at the end of the chapter on explanation in the Scientific Image, where van Fraassen says, ''The discussion of explanation went wrong at the very beginning when explanation was conceived of as a relationship like description: a relation between theory and fact. Really it is a three-term relation, between theory, fact, and context.'' Finally, for evaluating answers we need the background theory K and the part K(Q) that is salient to the question, both contextually dependent. With this background in mind, we will move to the objections to van Fraassen's account.

I will focus on two of Salmon and Kitcher's arguments against van Fraassen which deal with the relevance relations. One is that without any restrictions on what counts as a relevance relation, van Fraassen's account of explanation reduces to triviality. The other is that without any restrictions on relevance relations, van Fraassen's theory of explanation cannot rule out bad explanations without incorporating elements that undermine the claim that explanation is merely pragmatic.

According to Salmon and Kitcher, to reduce van Fraassen's account to triviality, let Pk be a true proposition and X a set of propositions containing Pk and whose other elements are all false. Let R be {( A, ( Pk, X))}U S where S is any set of pairs of the form ( B, ( Y , Z)) where B and Y are propositions and Z is a set of propositions containing Y. Further, S cannot contain any pairs ( B, ( Y , Z)) such that B is true and ( Y , Z)=( Pk, X). Thus, for any true propositions A and Pk, there is a question Q such that A answers Q and Pk is the topic of Q. The conclusion is then: ''If explanations are answers to why-questions, then it follows that, for any pair of true propositions, there is a context in which the first is the (core of the) only explanation of the second.'' Salmon and Kitcher think this is a reductio of van Fraassen's position. They later go on to say that ''if van Fraassen's account does not contain context-independent principles that preclude assigning [trivializing propositions] to K(Q)'' then the above problems will arise. However, a closer examination of their argument will not support the reductio conclusion.

Salmon and Kitcher's argument is not a reductio. Assuming that for each triple of topic, contrast class and relevance relation, there is a context that generates it, then all they have shown is that for each topic and explanation there is a context in which the latter explains the former. What they need for reductio is that for any topic and explanation, the relevance relation for a given context will be the one constructed above. If van Fraassen's account said that any true proposition were an explanation for any question topic in a context, then it would be trivial. However, this is not the case. Some propositions will not explain some question topics in a given context although they could explain the topic in other contexts as the relevance relation of the context would be different. Thus, their reductio fails.

To see why their argument fails, it is helpful to note that the construction above does not invoke context. The contrast class X, the relevance relation R, and the background theory K are all determined by the context, not by the theorist. Formally van Fraassen leaves open the possibility that there are contexts such that for any true proposition they provide contrast classes and relevance relations such that the proposition explains the topic at hand, but this is, prima facie, not different than other theories of formal pragmatics. For example, David Kaplan's theory of indexicals allows contexts in which the speaker is not at the location of the context or at the time or even in the world. These are in a way deviant contexts, but they are formally allowed. Kaplan suggests a natural way of restricting attention to non-deviant contexts. Turning back to van Fraassen's theory, the possibility of unusual contexts is not a reductio of his position. The claim that there is no context in which a certain proposition would explain a given topic is quite strong, and various science fiction examples should provide inductive counterevidence to this claim.

One of Salmon and Kitcher's criticisms of van Fraassen's theory, and a possible reason why they do not mention context in formulating this objection, is that van Fraassen does not indicate any way in which the contrast class or the relevance relation are to be read off of the context. Looking again to Kaplan's theory of indexicals, the formal contexts are quadruples ( cA,cT,cL,cW) of a speaker, a time, a location, and a world. It is fairly straightforward to figure out which formal context corresponds to which concrete context. The speaker cA will be the person talking and cT will be the time that person is talking. There are some complicating details, such as the extent of the location region. Ignoring these for the moment, the formal contexts are comprised of features that are easily read off of a concrete context. Returning to van Fraassen's theory, a difference emerges. The contrast class and relevance relation are less straightforwardly read off the concrete situations. We will return to this point in the conclusion.

The other objection of Salmon and Kitcher to be discussed is that without any formal requirements on relevance relations, van Fraassen's account allows bad explanations and the only way to rectify this makes explanation cease to be merely pragmatic. Their examples follow a pattern, so we will focus on their example of the astrological explanation of the date JFK was assassinated. The setup is that the contrast class is the set of propositions saying that JFK died each day in 1963 together with one saying that he survived 1963. The topic Pk is that he died on 11/22/63. Salmon and Kitcher stipulate that R is the relation of astrological relevance in which the answer stands to the contrast class and the topic. The answer consists of the conjunction of a true description D of the positions of the heavenly bodies, the proposition that if D then Pk, and the denial of everything in the contrast class except Pk. Salmon and Kitcher claim that van Fraassen's theory says this is an explanation. Further, they think that van Fraassen cannot rule out the answer as being astrological because it invokes only facts that are part of the background theory K, i.e. astronomical facts. The only way out of this predicament, according to Salmon and Kitcher, is for van Fraassen to make it so that the relevance relations are not determined solely by merely subjective factors. They say, ''[van Fraassen] ought to be equally serious about showing that relevance is not completely determined by subjective factors. If we are talking about distributions and redistributions of personal probabilities, they must be subject to some kinds of standards or criteria.... To be scientifically acceptable, the redistribution of probabilities must involve differences in objective probabilities...'' However, the move to more objective determinations of relevance and to objective probabilities introduces a non-pragmatic aspect into explanation, undermining van Fraassen's claim that the explanatory virtue is just pragmatic.

Van Fraassen has two responses available, both rejecting excessive assumptions Salmon and Kitcher need for their arguments but to which van Fraassen is not committed. The first of these is that the background theory K includes only contemporary science, possibly with some additional factual information. Thus, in their example given above, the astronomical information is part of K but the astrological beliefs that the agents have and that make it a good explanation to them are not. This provides space for including suspect relations as relevance relations and getting around van Fraassen's admonition that explanation shouldn't rely on old wives' tales. This allows enough space between K and the agents' beliefs to allow Salmon and Kitcher's problems to enter.

Van Fraassen should reject this construal of the background theory. Van Fraassen says, ''[K] is a factor in the context, since it depends on who the questioner and audience are.'' Since it involves who the questioner and audience are, it would seem that van Fraassen means to include in K at least some of the beliefs of the agents in question. There is nothing to debar them from having mistaken or misguided beliefs, e.g. that astrology is true, which are part of K. Since K is not restricted to just contemporary science, van Fraassen has a response to their argument. He should deny that there are no astrological propositions in K. One of the agents involved in the exchange takes the explanation to be good precisely because they have astrological beliefs, so they should figure in K. If van Fraassen is entitled to claim that explanation should not be based on old wives' tales then this will provide a way for him to rule the astrological explanation out as an explanation.

Van Fraassen has another response to Salmon and Kitcher's argument. They assume further that the only solution to the problem is to make the relevance relations more objective and the probabilities involved into objective probabilities. This is a crucial step toward their conclusion that explanatory virtue is not just pragmatic. If the account must involve these objective features then it looks like explanation is not just pragmatic as it latches on to objective features of the world, above and beyond what van Fraassen thinks explanatory virtue involves.

The second response is to deny their crucial premises that the relevance relation and explanation must reflect objective probabilities. Constraints can be put on relevance which do not require tying it and explanation to objective probabilities. Van Fraassen says that ''observable is observable-to-us,'' so it is to be expected that relevance would be relevance-to-us. The relevance relation should depend on K, which van Fraassen would allow to include the beliefs of the agents, as well as current science, to give content to van Fraassen's claim that good explanation should use good science. This ties relevance to subjective factors, in the sense of relying on the subjects involved, possibly including personal probabilities. However, this need not count against it since the subjects and their beliefs are things science investigates, and so, in a sense, objective. Salmon and Kitcher have given no reason to demand more objectivity than that.

Without Salmon and Kitcher's crucial premises concerning relevance, the pressure on van Fraassen's theory to give up the claim that explanatory virtue is just pragmatic disappears. Salmon and Kitcher's argument that van Fraassen's theory requires explanation to have its own non-pragmatic virtue does not work against van Fraassen's position. However, part of their criticism still stands.

At the heart of Salmon and Kitcher's criticism is the charge that van Fraassen does not place any formal constraints on what constitutes a relevance relation while also claiming that not all relations between a proposition and a suitable ordered pair count as genuine relevance relations. This makes the relevance relation an unexplained explainer. It does a lot of the work in van Fraassen's account of explanation, but there are no constraints on it or indications of what counts as a relevance relation.
As was said above, the relevance relations are less straightforwardly picked out of a concrete context than the speaker. Van Fraassen needs to give an account of how the context determines the relevance relation. Without such an account, van Fraassen has just shifted the focus from problems of explanation to problems of relevance.

While Salmon and Kitcher's arguments do not work against van Fraassen in the way they claim, they do highlight demands on the relevance relation. The relevance relation should be tightly connected to the background theory. It should involve the beliefs and intentions of the agents involved in the explanation. Salmon and Kitcher supply a promising suggestion: isolating what look like relevance relations for different sciences at different times and generalizing from there. They have not shown that no account of relevance can be given and the pressure is on van Fraassen to supply such an account. If one cannot be given, then Salmon and Kitcher's arguments will need to be reevaluated.

Wednesday, November 28, 2007

Technical difficulties apparently, and LaTeX bonus

Blogger is keeps eating a long post I have on van Fraassen's view of explanation. I don't have the patience to mess with it any more tonight, so I wll simply point out that recently (since February 2007 I guess) a very easy installer for LaTeX has been available on Mac. MacTeX offers a painless installation of LaTeX, the TeXShop front end, and the Excalibur spell checker wrapped up in a 700 mb .dmg file. I recently put LaTeX on a friend's computer and walked them through using it, and it was the easiest installation of it I've done. Heads and shoulders above the old i-Installer way, although that was kind of neat in itself.

Saturday, November 24, 2007

Scattered thoughts on a vague distinction in the philosophy of language

This may be quite naive and rambling, but I'll go ahead. There is a difference in views of language that I've been somewhat puzzled by for a while. One approach takes linguistics fairly seriously and focuses more speaker intuitions. These two parts may not be intimately related. Philosophers falling into this camp are, say, Jason Stanley and Francois Recanati. Another camp tends not to pay that much attention to linguistics. There is, maybe, a tendency to view language through the lens of first-order logic, broken into terms and predicates. Philosophers in this camp are, say, Sellars and Dummett. I think Davidson might be read as being on each side at different points in his writings. As it stands, I've drawn nothing resembling a clear line. This may even play out in different approaches to semantics. Why one might concentrate on, say, meaning in terms of reference or meaning in terms of inference. As an aside, I once asked one of my linguistics professors at Stanford what linguists thought something like conceptual role semantics. He said that they didn't really think about it because it was a different sort of project than what they were interested in. He pointed me to this little explanatory piece by Ned Block. That helped put things into perspective, but I digress... I almost want to say that the integration of philosophy of language into other areas of philosophy also cuts along these lines. However, I am fairly sure that is false and more a product of selective memory. People on both sides are interested in integrating philosophy of language into other areas, such as philosophy of mind or of action. In any case, I came across a footnote in van Fraassen's essay on Putnam's paradox which exemplifies one side (It is left as an exercise to the reader to guess which)(The context is a discussion of translation and knowledge of meaning):
"For the sake of example I am here pretending that Dutch and English are two separate languages in actu. I usually think of one's language as everything one has learned to speak, and of natural language as consisting in all the resources we have for speaking and writing."
This, by itself, probably does not force van Fraassen into one or the other grouping, although it seems to lend itself to fitting into one group rather than the other. This idea, it seems, lends itself to viewing language more expansively than usual for linguistic semantics. Interestingly, I think that Lewis in "Language and languages" could be on board with this completely even though he is someone I would usually situate in the first group. I must go ask some linguists what they think of this...

This was a little rambling, but, I am currently stuck on a paper idea. What better way to pass the time than ramble on about approaches to the philosophy of language? Probably doing those model theory proofs now that I think about it... But, I'm pretty sure people that would naturally place themselves in one or the other camp read this, so hopefully someone is interested.

Friday, November 23, 2007

On a distinction I don't quite get

Occasionally I see a distinction drawn in philosophical literature. I think it is usually drawn in terms of entities. The distinction is historical versus essence-bearing. The idea is that if something has an essence, then there is a clearly demarcated core of things to know about that entity. These things are objective, transcend paradigms, or are not dependent on any specific conceptual frames or theories. I think it usually goes along with this view that knowledge about the essences yields necessary truths about the thing and, possibly, that this knowledge can be gotten a priori. I'm not sure since I don't think I've seen this laid out and defended anywhere.

The contrast is entities that are historical. These things have no essences. Their properties are entirely contingent. Their properties are dependent on how they develop over time, a development which could have been otherwise. There is no necessity in their being so. Because of this, possibly, they are not as open to a priori investigation. Knowledge of their properties yields no necessary truths. Arthur Fine has one version of this view in his "Unnatural Attitudes": "But the description of science as an historical entity was intended precisely to undercut at least one version of that idea, the idea that science has an essence. ... If science is an historical entity, however, then no such grand enterprise should tempt us, for its essence or nature is just its contingent, historical existence."

I've seen versions of this distinction used by many philosophers. Ones that spring to mind are Brandom, Rorty, and Fine. I feel like there should be something along these lines in Marx, Nietzsche, Hegel, Quine, Davidson, McDowell, and Kripke, but no instances are forthcoming. [Edit: McDowell, Davidson, and Hegel probably shouldn't be in the list. Kripke is mainly there to endorse the essence side of the distinction. I 'm not really sure if he talks about the other side.] As I said above, I don't think I've ever seen an explicit laying out of this distinction and what it entails. I'm not even sure what sort of distinction it is. Is it a distinction of sorts of aims, looking for essences versus looking for historical developments? Is it a distinction among entities, the essence-haves and -have-nots?

At least at times it has a bit of an intuitive pull. There does seem to be some general distinction, however blurry, that it is rightly drawing. But, this is terribly hand-wavy. A more pointed question is: is the distinction rightly drawn in the exclusive terms I gave above? Is there a helpful sense in which we can understand historical entities as having essences of some sort (barring 'historical' as an essential feature,I suppose)? Are these two categories orthogonal ones? Getting clear on this would help illuminate the claims that people who use it make. For example, if they are orthogonal, then Fine would be wrong to say that viewing science as historical should tempt us away from viewing it as having an essence.

Tuesday, November 20, 2007

Non-philosophical content

I've heard that in the university in Goettingen, there is a room called Hilbertsraum, which is a play on Hilbert's room and Hilbert space. I think that is kind of clever.

In the Cathedral of Learning in PIttsburgh, most the philosophy seminars occur in the Wilfrid Sellars Seminar Room, which is named, *drum roll*, the Space of Reasons. I also think that is kind of clever.

Friday, November 16, 2007

Brandom versus Habermas

A few years ago there was an exchange between Habermas and Brandom about the status of facts and norms in Brandom's Making It Explicit. I have yet to finish either of their papers, but it looks like a pretty solid exchange. Grundlegung posted a link to what looks like a very good summary and explanation of the debate. Maybe this will help me to finish those papers...

In which I toot my own horn

I found out that I got a small grant to pursue a project on the relation between the philosophy of language and philosophy of science, concentrating on theory change and Mark Wilson's work in Wandering Significance. I'm supposed to write a paper or two over the course of the grant period, so I'll probably be putting some things of that sort up here over the course of the next several months. Which, if you don't get excited by the Brandom and Tractatus stuff that has been dominating lately, will serve as a nice change of pace.

Wednesday, November 14, 2007

Aristotle and indexicals

In the Topics, Aristotle describes accidents as "now belonging, now not belonging." This is an interesting thing to note since, at least how the translation renders it, it looks like it is part of one sentence. Clearly if you are saying this, it would be spread out over time and would be evaluated in slightly different contexts. The time parameter would have shifted. Considered as written and as a type, rather than a token, it seems reasonable to deny that there is a principled reason to shift the context. The whole thing would be evaluated relative to one context. In that case though what Aristotle says is false and can't be true. It would require something to be both P and not P.

I mention this because one of the features of Kaplan's setup for indexicals is that he evaluates types in context. This is because types, not being spread out in time, can be evaluated relative to one context. This lets us get at the logic of the terms rather than getting bogged down in details about tokenings. Aristotle's example seems to be one place where this supposed virtue breaks down. In order to understand it and properly evaluate it we must consider both the type and the tokenings as temporally spread out.

Sunday, November 11, 2007

And now for something completely different

This term I'm TAing for intro to ethics. For the last part of the course we are reading chunks of Bernard Williams's little book Morality. I was just reading through the preface, which, because unassigned, will likely go unread, and came across this hilarious quote: "This sad truth [that writers on moral philosophy either are hard to take seriously or refuse to write about anything important] is often brought forward as a particular charge against contemporary moral philosophy of the 'analytical' or 'linguistic' style: that it is peculiarly empty and boring. In one way, as a particular charge, that is unfair: most moral philosophy at most times has been empty and boring… Contemporary moral philosophy has found an original way of being boring, which is by not discussing moral issues at all."
Granted, the particular sort of moral philosophy he is talking about has come and gone. However, it is still about as amusing as Anscombe's long list of ad hominems in her essay "Modern Moral Philosophy".

Saturday, November 10, 2007

Kremer's point on the Tractatus

I'm participating in a TLP reading group this term. We're going to make it through the end of the 3's by winter break. One point that I've made several times to individuals, and which came up again in discussion on Friday, is something that I thought would be worth putting online. It is originally due to Michael Kremer, in his excellent "Mathematics and Meaning in the Tractatus." Many people think that in TLP, there is a very strict two part distinction: sentences have sense while names have meaning (Bedeutung). Names have no sense; they just mean the objects to which they refer. The objects are the meaning of the names. This is a pretty natural reading to get out of the 3's. However, sentences also have meaning. Wittgenstein uses "meaning" in two ways throughout TLP. Sometimes he means the stricter sense to characterize the relation between names and objects, and sometimes he uses it in a more general way to talk about whatever significance linguistic units have. The textual evidence for this comes from 4.4241: "When I use two signs with one and the same meaning, I express this by putting the sign '=' between them. So 'a = b' means that the sign 'b' can be substituted for the sign 'a'." The signs used there are the ones normally used as names, lower case letters from the early part of the alphabet. However, combine this with 5.254: "An operation can vanish (e.g. negation in '∼∼p' : ∼∼p = p)." We clearly have propositional signs flanking the '='. This means the two signs have the same meaning. However, they aren't names. Therefore, Wittgenstein has two senses of meaning in place in TLP. This is a fairly straightforward point but it is missed by a lot of people.

Wednesday, November 07, 2007

Proofs and provability

Earlier today I had a thought about proof theory. Proof theory is, roughly, a formal investigation of the properties of proof systems. (I sort of dig proof theory.) Provability logic is an interpretation of modal logic. It has its own axiom set distinct from S5 and it was, I believe, originated by Goedel and greatly elaborated by Los and Boolos. It assigns the interpretation "is provable" to the box instead of the normal alethic interpretation. So, '[]p' is read as 'p is provable'. Now, the question I have is: what is the relation between proof theory and provability logic? The contexts in which I've seen provability logic didn't connect it to proof theory and those in which I've studied proof theory didn't connect to provability logic. It seems like a big flaw for at least one of the two if there is no connection. Glancing at the SEP reveals that there is at least one article on this topic: Beklemishev, L.D., “Parameter-free Induction and Provably Total Computable Functions,” Theoretical Computer Science, Vol. 224 (1999): 13-33. I haven't tracked this down yet, but I'm going to venture a guess that it isn't too philosophical. (Of course, I could be wildly wrong on this count.) In any case, at the moment I'm not sure what the relationship between provability logic and proof theory is and I have no idea what it should be.

Friday, November 02, 2007

These people are not me

This is kind of funny. If you do a Google image search on my name in quotes(*cough*vanity search*cough cough*), no pictures of me come up. However, pictures of the following do come up: Aidan, Nate, Nate's cat, Bertrand Russell, Goedel, Robbie Williams, and John Perry on the cover of the collection in his honor Situating Semantics. No pictures of me though.

[Edit: As Kenny points out, if you turn off moderate safe search, then you'll get a picture from a few years ago of me with my friend Megan in Coupa Cafe in Palo Alto, CA. You will also get a picture of Trogdor.]

Thursday, November 01, 2007

What's so great about the observable?

This is part of a paper I wrote that I liked. I'd prefer to break it up with most of the post under a fold, but I can't get that functionality to work. If you have any advice, apart from Blogger's help site, let me know and I'll try to apply it here.

In his "Ontological Status of Observables," Paul Churchland charges van Fraassen with being selectively skeptical about the unobservable. He draws our attention to a three-part distinction: (1) the observed, (2) the unobserved but observable, and (3) the unobservable. It would be crazy to only believe in (1), the actually observed things. Churchland thinks van Fraassen does not give a principled reason why his constructive empiricism says to believe in (1) and (2) but not (3). Without the principled distinction van Fraassen's position is unstable since his reasons for not believing in (3) seem to apply also to (2). van Fraassen's view either ends up coinciding with the crazy view or it looks like a form of realism. Churchland's challenge can be posed as: what is the principled reason for believing in (2) but not (3)?
Read more

To press his point, Churchland lists several factors which could contribute to something not being observed. These include: spatiotemporal position, spatial dimension, duration, energy, wavelength, and mass. If any but the first are the reason for being unobserved, then the processes or entities in question will be neither observed nor observable. If something has too great a spatial or temporal distance from us, then it will likewise be unobserved, but it will be observable. Churchland thinks there are practical reasons for privileging spatial and temporal location while labeling things that fail the requirements of the rest of the list "unobservable." He thinks this is due to greater control over our location rather than our sensory make-up. However, practical reasons, he thinks, are not enough to dictate what we should believe in. Churchland's challenge can also be put like this: what principled reasons are there for privileging, with respect to what we should believe in, the first item on the list over the others? Churchland thinks that anything that counts against the other items on the list will count against spatial and temporal distance. Not believing in something due to a failure of anything on the list would be the ludicrous view endorsing only the observed whereas admitting things regardless of which items of the list were violated would be endorsing the unobservable, a form of realism. Van Fraassen has a response to this and the previous form of Churchland's challenge, but before getting to the reply, I will need to present some of van Fraassen's view and make some comments on it.

There are two important things I want to note about Churchland's challenge. The first thing is that the observable/unobservable distinction is not the same as the observable/theoretical distinction. As van Fraassen points out, there are many theoretical entities that are observable and must be described in theoretical terms, like DVD players. The second thing is that the observable/unobservable distinction is an empirical one, the point to which will turn next.

The observable is that which we, some portion of the epistemic community we belong to, can observe while the unobservable is that which we cannot observe, so they are modal notions. van Fraassen sees science as drawing this line of possibility, not philosophy. What we can observe is a matter of the physics and biology involved in being human. For example, there is a fairly constrained spectrum of light that human eyes can pick up and a fairly limited range of sizes that human eyes can see. Humans are physical systems that act as a measuring device. The capabilities of humans as measuring devices will be determined by physics and the other sciences as one sort of measuring device among others. The limits of these devices are to be drawn through scientific investigation and not philosophical speculation and argumentation. Since the line is an empirical matter and not a philosophical one, it is subject to change. Our epistemic community could change, either by welcoming in other species or through the processes of evolution changing some or all of our epistemic constraints. If the standards of observability change, then then accepting a theory as empirically adequate would bring correspondingly different commitments with it.

Van Fraassen gives some examples to illustrate the observable/unobservable distinction. One is the moons of Jupiter, which are observable both with a telescope and without one. A mu-meson in a cloud chamber is unobservable although it is detected by means of the cloud chamber. Observation must be unaided by an apparatus while detection allows the use of one. This is one of the places that Churchland's challenge will be pressed later: if humans are measuring devices, then it seems that we should allow that these measuring devices may be combined with other measuring devices to create a more complex system capable of more measurements.

Churchland's challenge, in its second form, can be met by using some of van Fraassen's distinctions laid out above. To see why spatial and temporal location have a privileged status, we should turn again to van Fraassen's description of humans as measuring devices. Measuring devices will function the same if they are moved in space or in time, that is, their measuring mechanisms will be unaffected. It is assumed here that the idea of measuring mechanism is intuitive and unproblematic. A more thorough response would have to explain this notion in greater detail. A microscope in Pittsburgh will work the same in Buenos Aires and on the moon. Similarly, a voltmeter working yesterday will work also today and in the year 2046. Assuming that the structure of space and time is such that it allows for these sorts of translations of measuring devices without altering their basic measuring mechanisms, the privileging of space and time, in the way Churchland notes, makes sense. A human could be shifted in space or time without the physics and biology of her measuring capacities being affected. If all that separates an observer from a potentially observed event or entity is a spatial or temporal distance, then, using the assumption, the observer could be shifted to a spatiotemporal location that allows her to observe the relevant event or entity.

This response will not work for the other things in Churchland's list. Changing the wavelength observable by the human eye is changing the biology and physics of the measuring device. It is, in effect, made into a different sort of device. Shrinking a human to a size comparable to that of, say, an electron would drastically change at least the biology involved in observation. For example, the biological mechanisms involved in visual perception would have to change to accommodate the comparatively large size of photons at that scale (if perception of that sort is even possible on that scale).

The above considerations lead to the response on van Fraassen's part that it isn't that space and time have a privileged position because we have more control over them, rather it is because we can change along those dimensions without changing the sort of measuring mechanisms we are, biologically and physically. Churchland's example of the fir trees that make observations illustrates this point. While the trees themselves are not capable of locomotion, moving them in space and time wouldn't change the biology and physics of their observational mechanisms. If this line of thought is correct, what is relevant isn't that we can control certain sorts of variation but that certain sorts of variation don't result in altering the sort of measuring device we are.

This line of response would likely not satisfy Churchland although it does provide an answer about why van Fraassen thinks we should believe in the unobserved observables and what is distinctive about the observable. We should believe in more than just the observed because the unobserved observables are those things that we could possibly observe if we had been shifted along dimensions that don't affect how we as devices make our measurements. The unobservables are what we could not observe without changing the sort of measuring devices we are. One line that Churchland should press in response is what makes our current biological and physical mechanisms so special, since, viewed simply as measuring devices, there would not be anything suspect about combining one device with another, e.g. a human with a microscope. This would make van Fraassen's constructive empiricism look like realism.

Unfortunately, van Fraassen doesn't say much positive about this. What is special about our biological and physical mechanisms seems to be that they are ours, and not any other feature. What counts as evidence for us will be determined by these mechanisms. They can change, as mentioned above, but this seems to be fairly restricted. There does seem to be a way to rule out the measuring device composed of a human plus a microscope. First, let us assume that that the microscope uses different physics than our eyes, say, by interacting with light differently. Suppose the former uses diffraction alone while the latter uses refraction alone. The combination of the two requires a different physical mechanism than the eye alone. Further, let us assume that a magnifying glass uses just refraction and allows us to see things that are impossible to see with the naked eye. The combination of an eye with a magnifying glass would result in legitimate observations, as there is no modification to the physical mechanisms involved; it is all refraction. It is unclear whether van Fraassen would agree, but I don't see a way for him to consistently deny this and maintain a principled distinction in the face of Churchland's criticisms.

Grrr argh!

I just spent the last 30 minutes or so trying to follow the directions on Blogger's help page about getting partial posts or folds activated. I followed the directions they gave with weird results. For some reason adding code to the template that doesn't involve changing the font resulted in a page with a different font size. To make this worse, the fold capability doesn't seem to work. I was hoping to post a longer thing I wrote on van Fraassen on observation, but I really don't want to if I can't break it up with a fold. Is it really this hard to get this simple functionality?

[Edit: Hat tip to Daniel for the help. I think it is kind of silly that this functionality requires the user to go in and modify their template code rather than having a built in widget or something to take care of it automatically.]

Tuesday, October 30, 2007

Get thee to a punnery

Why are there not more discussions of the instrumental value of music? *drum roll* But seriously, Aristotle seems to want to say that music isn't final without qualification because it has some instrumental value.

I'm not sure if that is a standard pun among ethicists and other value theorists, but I hadn't heard it before. I think it is a shame, if not.

Monday, October 29, 2007

This is neat...

I just stumbled across this repository of online .pdfs. Apparently Stanford is putting online the text of their CSLI lecture notes and other books as well. There are some things that look nice in there. Among the things I found were Barwise and Moss's Vicious Circles, Troelstra's Lectures on Linear Logic, and Link's Algebraic Semantics in Language and Philosophy. Best part: they're all free.

Saturday, October 27, 2007

Pitt-CMU conference update

We've lined up our faculty speakers, Gordon Belot and Peter Machamer. They will be giving talks in addition to the keynote by Bas van Fraassen. The submission deadline is December 10, 2007. For more information, see the website.

The limits of the first-order

Why has standard first-order logic occupied philosophers so much? In particular, why take it as the basis for forays into the foundations of math or the nature of language or metaphysics? It has its good points to be sure. It is complete and compact. The negative that I'm thinking of is non-trivial though. First-order logic (with identity) has some pretty large expressive limitations. In particular, it cannot express the general concept of finitude. It can express trivial finiteness conditions, e.g. "there are exactly n things that are such and such" or "there are at least m things that are so and so". It cannot express "there are finitely many things that are so and so", so it also is incapable of expressing "there are infinitely many things that are so and so". Of course, if we want we can make up our own quantifiers that express infinitude. This comes at the expense of some of the niceties of first-order logic; in this case the Loewenheim property. If finite sentences are too limiting, we can always add infinitary conjunctions or disjunctions. These force us to give up standard forms of compactness. However, these seem like good moves to make in many applications. Why would we saddle ourselves with expressive limitations from the outset?

Wednesday, October 24, 2007

Van Fraassen's Manifest Image

I had a thought about how to motivate van Fraassen's constructive empiricism (the view that we need only accept theories as empirically adequate, that is, believe what they say about observables and be agnostic about what they say about the unobservables) since anti-realist views can seem at times, unmotivated. The thought I had was that he is responding to Sellars's Philosophy and the Scientific Image of Man. (Apologies for poor Sellars reconstruction.) In that essay, Sellars contrasts two images of man, the manifest and scientific images. The manifest one is, roughly, the commonsense conception of ourselves and the world. The scientific image is that which contemporary science gives us. I think it is roughly the difference Eddington finds between the everyday idea of tables and chairs and the view of them as composed mostly of empty space and composed of small, small particles and fields, etc. Sellars thinks that one important job of philosophy is to spell out the relation between the images. In the end, he says that they don't need to be reconciled but that the manifest image needs to be joined to it. Sellars is also a realist of a rather extreme kind. He was also van Fraassen's teacher at Pitt.

Now, my crazy idea is that van Fraassen's constructive empiricism is an attempt to go the other way. It is an attempt incorporate the scientific image into the manifest. The manifest image seems to roughly correspond to the sort of thing that van Fraassen views as observable. Especially when viewed through empiricist lenses, the macroscopic level at which we normally find ourselves lends itself to being viewed as the world of the manifest image. Of course, van Fraassen doesn't talk much about intentions and norms that Sellars's manifest image also concerns itself with. Putting that aside for now, if one is agnostic about everything that is not observable, in van Fraassen's sense, then one is agnostic about the traditional way of understanding the scientific image. Eddington gets just the manifest table. Constructive empiricism says to be agnostic about the scientific table. Everything science says about the observable is incorporated into our beliefs about the world of the manifest image. This seems like it is one way of cashing out the relation between the relation between the two images of man. The scientific image helps us to understand the manifest image, but we need only believe in the world of the manifest image.

I floated this in my philosophy of science class today. A couple of good points were raised against it. One is that apart from the title, van Fraassen doesn't really mention the Sellars piece. Another is that what I have been calling the manifest image in van Fraassen's book is somewhat different than the manifest image in Sellars's essay. This is true, but it doesn't seem that far from what you'd get if you took Sellars's manifest image and tried to cast it in an empiricist vein. Depending how exactly observable gets spelled out in the end, this might not be tenable at all. I think that if the idea of observable is constrained to the roughly medium-sized macroscopic things and processes, then it is a possibility.

Saturday, October 20, 2007

Are there any software platonists?

A formulation of mathematical platonism is that mathematical entities exist independently of us and when we do math we are exploring the realm of the mathematical entities and discovering new things about them. This is a fairly basic or naive formulation of it, but it gets the flavor roughly right. A software platonist would think that programs exist independently of us and when we do computer science or programming (not sure which would be the better formulation) we are exploring the realm of programs and discovering new things about them. A mathematical platonist would say that the natural numbers would exist even if humans never did and a software platonist would say, e.g., that LISP or Apple OS X would exist even if humans never did. Further, the natural numbers were around long before there were humans, and, similarly, LISP and Apple OS X were around long before there were humans. We started exploring the natural numbers a long time ago but only recently started exploring LISP and even more recently Apple OS X.

It seems to me that software platonism is nuts. There is a fairly strong sense, I would think, in which Apple OS X would not have existed were we (broad, inclusive 'we') not around to create it. It was created by engineers and is changing over time. But, it is still just a program. However, as such, there is a Turing machine equivalent to it. Now, LISP was also created by a computer scientist, but it is a bit more abstract and so the platonist intuitions are maybe stronger for it. Engineers have changed LISP over time, and I don't know how a software platonist would explain what links the various versions of LISP (or, for that matter, how programs of any sort run on hardware, but that might not be so different than us counting with the natural numbers). LISP has, I believe, been shown to be able to compute the same functions as Turing machines; the term is Turing-complete, I think.

The question is: are we creating or exploring an antecedently existing realm of programs? There is a related question: are we creating or exploring an antecedently existing realm of Turing machines? I'd hope the two fall together, given the tight connection between programs and Turing machines. However, there seems to be a little bit of room to drive a wedge between the two. I suppose that would allow one to be a Turing machine platonist without being a software platonist. Although, one could try to use the Turing machines, which may be able to draw on mathematical platonist leanings, to argue for platonism about programs.

I don't have any worked out ideas in this area, but it does seem to me that software platonism is hopeless. Are there any software platonists?

Thursday, October 18, 2007

Structure is as structure does

Philosophers like structural comparisons for various reasons. Establishing these are often important. For example, in the Tractatus, Wittgenstein seems to be trying to set up an isomorphism between language and the world. In other contexts, philosophers try to establish that structures are isomorphic. It seems like outside of model theory the only notion of structural comparison that gets any play is isomorphism. The model theory class I'm taking has started making me wonder why this is. There are lots of other interesting and useful sorts of comparisons: back-and-forth games, bisimulation, homomorphisms of various sorts, etc. We could even through out a lot of the homomorphisms, the ones that are one-way. I'm not sure why the others don't see more philosophical action. Bisimulation is the key notion of modal logics, at least in the Amsterdam school. Yet, philosophical discussions of modality don't mention it as far as I know (which, admittedly, isn't very far). Back-and-forth games (meant here in a more general sense of games of any finite length) seem like they would be fruitful and usefully combined with ideas from computability theory. This is because they emphasize the idea of being able to differentiate two structures using only a certain number of checks. The two structures could be non-isomorphic, but discovering this fact could take an infinite number of checks, something that finite little agents could not do. What lead to the popularity of isomorphism? It often seems a little heavy handed. Is it just that it gets covered in the standard logic classes, like induction, and so is the tool of choice amongst philosophers?

Wednesday, October 17, 2007

Call for papers: Pitt-CMU philosophy grad conference

I'm pleased to announce the 2008 Pitt-CMU Graduate Philosophy Conference.

Keynote speaker: Bas van Fraassen
Theme: Relativism and rational reflection
Facutly speakers: TBA
When: March 1, 2008
Where: The University of Pittsburgh

Call for papers: The deadline for submisisons is December 10, 2007. More information can be found here.

Tuesday, October 16, 2007

We are sorry to inform you...

I just came across a wonderful link again. This is a page of rejection letters of famous papers. It includes papers by Turing, Shannon, and Dijkstra. I will quote the Turing letter for those that don't want to click through:
""On Computable Numbers, with an Application to the Entscheidungs Problem." This is a bizarre paper. It begins by defining a computing device absolutely unlike anything I have seen, then proceeds to show—I haven't quite followed the needlessly complicated formalism—that there are numbers that it can't compute. As I see it, there are two alternatives that apply to any machine that will ever be built: Either these numbers are too big to be represented in the machine, in which case the conclusion is obvious, or they are not; in that case, a machine that can't compute them is simply broken!
Any tabulating machine worth its rent can compute all the values in the range it represents, and any number computable by a function—that is, by applying the four operations a number of times—can be computed by any modern tabulating machine since these machines—unlike the one proposed here with its bizarre mechanism——have the four operations hardwired. It seems that the "improvement" proposed by Turing is not an improvement over current technology at all, and I strongly suspect the machine is too simple to be of any use.
If the article is accepted, Turing should remember that the language of this journal is English and change the title accordingly."
I love the last line. Turing should remember that the journal is in English, so he shouldn't call the Entscheidungsproblem by its German name. I wonder how amusing this will be when I start sending things to journals...

How fast does time go?

I seem to have fallen off the blogging bandwagon for a bit. A combination of recent events conspired to eat up time that might otherwise be used for writing, but there shouldn't be much to prevent me from writing about things in the nearish future.

The title of this post comes from a question I always thought was a little weird, namely what is the rate at which time passes. I've always liked the uninformative answer of one second per second. Often it seems like it goes much faster, like the lightning quick weekend I just had. Other times it slows down. For example, recently I went skydiving and I was warned that during the free fall it feels like time stops. I was looking out for this, so I was concentrating on it as I jumped out of the plane. Time really does seem to grind to a halt for those, apparently, 50 seconds. I'm not quite sure what to make of the feeling of time stopping together with my seeming ability to entertain thoughts at that point. The kantian in me is very confused by this since time is the form of inner sense and it seems like stopping that would interfere with inner sense. Nonetheless, it certainly seemed like time stopped then it started again. Truly odd. This ends my rambling on time perception. I'd like to return to the philosophy of time at some point since I really dig on McTaggart. I'm not sure when that will be. I promise to try to avoid further forays into phenomenology though. (Bonus points to anyone that caught the underlying motivation for this post.)

From the looks of my posts, one would think that I've spent most of my time thinking about Making It Explicit and the Tractatus. This is in part true. I've been thinking about other things but these haven't yet made their way into posts. This will hopefully change this week.

For those interested in the Pitt-CMU grad conference in the spring, the website is up but the new call for papers isn't done yet. Bas van Fraassen is the keynote speaker, which should be pretty sweet.

Sunday, October 07, 2007

Making It Explicit: Incompatibility problems

Throughout MIE, we are told what incompatibility is. Two claims are incompatible when commitment to one precludes entitlement to the other. We are also told that incompatibility is a modal notion. In fact, it plays are rather central and rather modal role in the later part of MIE and Brandom's later work. Now, my problem is I don't understand where the modality comes from. Commitment and entitlement are normative but they aren't, at least at this point in the story, modal. The preclusion isn't modal either; it is just straightforward non-modal precluding.

There is a modal sense of incompatibility that is used in other philosophical papers. This is, I think, a sense in which two propositions are not jointly possible; non-compossible is the term I think. This is clearly modal. If that is what Brandom means, then there should be some demonstration that this sort of incompatibility and the kind defined in MIE coincide. There isn't any such demonstration, which makes me think that this is not on the right track. However, if it isn't on the right track, then I don't know how in the world incompatibility is modal. If it is on the right track though, then I'm also not sure how the argument is supposed to run since these two notions don't seem coextensional. I'm doubtful that the latter implies the former either, but then this is just denying that I'm on the right track.

Saturday, October 06, 2007

Semantic Externalism

You know you've had a cultural impact when your ideas make it into a dinosaur comic. Hilary Putnam must be proud of this.

Tuesday, October 02, 2007

Making It Explicit: Notes on reading ch. 4

I want to write some in depth posts about the material in chapter 4, but I have precious little background in the philosophies of action or of perception. Instead, I will try to sort out a few things about the structure, mostly in an expository vein, mostly sketching some of the major themes. The chapter covers a lot of ground; in particular, action, perception, and epistemology. Most of the epistemological background in the book is in the chapter, preceding the perception stuff. The perception and action sections are supposed to present the theories of the book on those topics. It seems like neither is entirely satisfactory and a lot more could be said about all three parts.

The perception section bears most of the weight. Conceptually, action is identified with (I think that is right) language-exit moves while perception is identified with language-entry moves. Perception bears most of the weight because the model for perception is reused for action. The order of things is just, in a sense, reversed.

The model of perception is what Brandom calls the two-ply account. It consists of having an appropriate reliable differential responsive disposition and applying the appropriate concept. There is a two part structure here to reflect the interactions of the causal order of things and the rational order of things, with dispositions for the former and concepts for the latter. For action, instead of passively accepting a stimulus, the causal side of things is motivational. There is a further story to tell on the action side about practical reasoning and practical commitments, but this leans heavily on the established ideas of doxastic commitments, theoretical reasoning, and the two-ply model for perception.

Brandom is primarily concerned with materially good practical reasoning, like theoretical reasoning. This means that the inferences will in general be non-monotonic. Similarly to his views on material inference in the theoretical case, the practical case features multiple sorts of formal goodness. Whereas the different sorts of conditionals express different sorts of endorsements of inference on the theoretical side, the different sorts of oughts (instrumental, unconditional, etc.) express different sorts of endorsements of practical reasoning on the practical side. In a big way, the account of action is what you get if you take the structure for the theoretical side, i.e. inference, logic, perception and the rest, and change as few bits as possible to make it about action. The symmetry is both lovely and kind of creepy.

Friday, September 28, 2007

Making It Explicit: Brandom's problem with commitment

Near the start of chapter 3 of MIE, Brandom tells us that the primary normative concept for inferential articulation is commitment. When we move to the social picture involving more than one agent, there is a shift to multiple primary concepts. They are commitment and entitlement. These are two sides of one coin, to use a phrase that Brandom likes a lot. Surprisingly, he thinks that commitment can be understood entirely in terms of entitlement. In what sense is commitment needed then? Commitments have a sort of double life. Not only are they undertaken, but they are also what one is entitled to. To put it awkwardly, one can be committed and entitled to commitments. There is a status sense and a content sense of commitment it seems. (I think this point is one that MacFarlane hammers on in his excellent "Inferentialism and Pragmatism", available on his homepage.)

If commitment, in the status sense, is fully understandable in terms of entitlement, then it would stand to reason that incompatibility should be too. Incompatibility is defined as commitment that precludes an entitlement to something else. This would go something like: p is incompatible with q just in case p authorizes the removal of or the preclusion of entitlement to q. That doesn't sound that bad. Brandom should probably have said that the fundamental normative status for the game of giving and asking for reasons is entitlement and commitment takes on its content role. There are two problems with this that I don't have responses to. The first is that I'm not sure he's allowed to appeal to the idea of content at this point in the book. The second problem is that if commitment isn't a fundamental normative status, then it is difficult to see why inference must be the bridge to semantics. Any sort of doing should work to connect the praxis to the semantics.

(The people that are in the Brandom seminar are probably tired of the joke in the title in its various incarnations, but I find it funny nonetheless.)

That seemingly magical fact

[Edit: I'm trying out using the html for the math symbols and Greek letters since Blogger won't do LaTeX markup. Let me know if they are not rendering correctly in your browser.]
Sometimes you read that that natural deduction systems are more appropriate for intuitionistic logic while sequent calculi are more appropriate for classical logic, e.g. in Hacking's article "What Is Logic?", whence the title. While reading a defense by Peregrin of why intuitionistic logic best characterizes the logic of inference, I came across a line that caught my eye. Peregrin comes to the conclusion that intuitionistic logic is the logic of inference as long as we restrict ourselves to single conclusion inferences. He goes on to say that he has written elsewhere about why we should restrict ourselves in that way. The interesting bit is the restriction to single conclusion inference.

One of the first lessons learned when studying the sequent calculus is that you get classical logic from the intuitionistic rules by allowing multiple conclusions. Going back over my notes from proof theory last year, it seems that you can also get classical logic if you keep the single conclusion by add a reductio rule, Γ, ∼φ ⇒ ⊥, so Γ => φ. This requires giving up the subformula property, so the multiple conclusion formulation is usually opted for.

Natural deduction systems only allow for one conclusion for each inference. This doesn't mean we don't have natural deduction systems for classical logic. We do, but they involve a reductio rule, from ∼∼φ to φ. How would this square with being more appropriate to intuitionistic logic? There seems to be a sense in which the reductio rule is really a multiple conclusion rule. In a standard multiple conclusion sequent calculus formulation, proving the reductio rule requires using multiple conclusions. Alternatively, we can prove that a formula is provable in a classical natural deduction system with reductio iff it is provable in the multiple conclusion sequent calculus. Given that this is "iff", why should the sequent calculus version be privileged? The sequent calculus version has the subformula property and cut elimination. This puts really strong restrictions on the structure of proofs. In particular, the subformula property requires that only the things in the bottom line of the proof appear in the preceding steps of the proof. This restriction is strong enough to simulate, in a way, semantic effects (See Jeremy Avigad's work for more on this). Put in a more philosophical way, it requires us to make explicit everything that goes directly in to the proof.

This explicitness requirement does the work. The sequent calculus version shows us that the reductio rule is really a multiple conclusion wolf masquerading in single conclusion sheep's clothing. It is apparent that none of the other rules require multiple conclusions. These correspond to the intuitionistic sequent calculus rules and they go over directly to natural deduction systems. Classical logic with its reductio rule can go over too, but along the way the reductio rule assumes the appearance of a single conclusion rule. Natural deduction is natural for single conclusion inference and the sequent calculus is natural for multiple conclusion inference (I haven't really defended the latter claim here). There is a sense, then, in which natural deduction is more natural for intuitionistic logic.

Sunday, September 23, 2007

All the benefits of links over honest posting

There is what looks to be a good entry on the Stanford Encyclopedia of Philosophy on the Frege-Hilbert correspondence and disagreement. It is interesting because it makes Frege seem slightly reasonable even though he ultimately loses. When I had read the correspondence a few years ago (I think I only read Frege's contributions), Frege seemed rather unreasonable. It is nice to know I was incorrect.

[Edit: There is a new article on the philosophy of math up on the SEP. It looks like a nice little overview, especially the computation section at the bottom.]

I've discovered that it is difficult to juggle teaching with doing your own work (shocking, I'm sure). I have a paper due in a few days that is eating my free time. I hope to put up a new post either tonight or tomorrow. I keep meaning to write something on a topic other than Wittgenstein or Making It Explicit, but I have done an exceptionally poor job of thinking about other things.

Friday, September 21, 2007

An interesting historical note

Apparently the first use of schematic letters in the history of logic was Aristotle's Priori Analytics book 1 chapter 2. Even though I recently read that chapter several times, it didn't even occur to me that it was the first such usage. I gather Quine was quite fond of schematic letters in his teaching of logic. A tip of the hat to James Allen for pointing this fact out to me.

Sunday, September 16, 2007

On setting the bar low

I didn't realize how odd the preface of the Tractatus is until last week during the PItt reading group. In particular, the following:
"If this work has a value it consists in two things. First that in it thoughts are expressed, and this value will be the greater the better the thoughts are expressed. … On the other hand the truth of the thoughts communicated here seems to me unassailable and definitive."
I think the latter bit, after the ellipsis, gets the most focus usually. The truth of the thoughts is important. But, what struck me in a way it hadn't before was the first bit. The work has value insofar as it expresses thoughts? That seems to set the bar low as it isn't that hard to express a thought. The interesting thing is combining this with 6.54, which says that anyone who has understood the propositions of the book will recognize them as nonsense. This would make it a little harder to take Wittgenstein as expressing thoughts. In the preface he says that he doubts he has done it well. This might be literary self-deprecation, but that seems a bit unlike Wittgenstein.

We should note that Wittgenstein doesn't say what thoughts are, or are supposed to be, expressed in the book. Just that some thoughts are. The truth of these thoughts he thinks is clear. Michael Kremer says some interesting things about different senses of truth in his paper on solipsism that I suspect are important for understanding Wittgenstein here. In short, he thinks there is a non-propositional sense of truth. This is not the ineffable sort of truths that some realists ascribe to the TLP. It is more like the sense of truth expressed when people say things like "the truth in beauty" or "the truth in solipsism" (to use Kremer's title). Taking the preface to be meaning truth in this sense would go some ways towards making it consistent with the end of the book. The problem would probably come from the expression of thoughts. This would, it seems, have to be thoughts in a sense distinct from the Tractarian view of them, i.e. as significant propositions. Otherwise, taking a non-propositional view of truth would be a non-starter. There isn't a corresponding idea of thought developed in Kremer's paper. He says some possibly relevant things about solipsism among other "ways of thinking" which might be fleshed out appropriately, but it would result in interpreting the preface in such a way that it resembles the body of the book very little. That might not be a bad thing though. I don't have a well-developed idea here, but I think there is some promise to making sense of the preface along these lines.

(Running a quick search on Kremer's article, it seems that he talks about the preface. However, he doesn't talk about the part I am talking about. He concentrates on the early part of the preface which discusses drawing a limit to thought.)

Friday, September 14, 2007

Dear Blogger, What I really want is LaTeX

Why on earth doesn't Blogger support LaTeX markup like wordpress does? There seems (from my naive point of view) to be no reason for this deficiency.

Dear Blogger, please fix this glaring hole so your philosophical blogging community, among others, can use pretty symbols to represent what we mean perspicuously.

Making It Explicit: logical expressivism

One of the novel features of MIE is Brandom's philosophy of logic. He calls this the expressive theory of logic. On this view, the primary purpose of logic is to express certain things. It privileges the conditional and negation. The conditional expresses the acceptance of an inference from premises which form the antecedent to the conclusion which forms consequent. The conditional lets you say that a certain inference is acceptable. Of course, conditionals in different logical systems express different sorts of acceptance. Classical conditionals express a weak form of acceptance, intuitionistic conditionals a stronger acceptance in the form of saying there is a general method of transforming justification for the premises into justification for the consequence, and so on. Negation expresses incompatibilities, generally in the presence of a conditional so as to allow one to say that certain inferences are not kosher. Incompatibility can be used to create an entailment relation defined as inclusion on sets of incompatibles. Brandom suggests taking conjunction and disjunction as set operations on those sets of incompatibilities. This would work for languages with a conditional and negation. If one does not have negation, then, I suppose, come up with the sets of incompatibilities although one couldn't say that the incompatibilities were such. Barring defining conjunction and disjunction in terms of incompatibilities, I'm not sure exactly what they would be accepting. Conjunction might express the acceptance of both conjuncts. Intuitionistic disjunction might express the acceptance or ability to demonstrate one of the disjuncts and you know which one. I'm not sure what classical disjunction would express exactly; possibly that one accepts one of the disjuncts although no further information is given about which.

There is nothing in Ch. 2, where logical expressivism is introduced, about quantifiers. At this point in the book, nothing has been said about objects, so I'm not sure what the quantifiers express since it is likely to be tied in with theoretical claims about objects. Modal operators aren't addressed in MIE, although they are tackled in the Locke Lectures. I don't remember that terribly well, although I think for the most part Brandom sticks to alethic modalities in S4 and S5. I could be wrong on this. I am almost positive he doesn't get to non-normal modal operators (to use Restall's terminology) such as the Kleene star. I currently have no idea what the Kleene star would express. I'm similarly unsure about intensional connectives as in relevant logic's fusion. It might be an interpretation similar to Restall's of application of data in the form of propositions to other data, although this is really speculative. There might be something in this.

Something that I'm a little more immediately curious about is the status of translations of formulas. There are certain systems of logic that can be translated into others, e.g. S4 into intuitionistic logic. The conditional in S4 is classical, but the translation (in Goedel's translation at least) of the intuitionistic A->B looks like [](A'->B') where A' and B' are the translations of A and B. The classical conditional then will express a weaker acceptance of an inference but it will be modified in some way by the necessity operator in front. If the view of logic is right, one would expect the translation to preserve what is expressed in some form. I will have to track down the relevant part of the Locke Lectures in order to further test this idea.

Thursday, September 13, 2007

Making It Explicit: Norms again

The comments on the last post were helpful, so I'm going to take another stab at figuring out how implicit norms are supposed to get around the rule-following problems that are supposed to undermine explicit rules. I think I was wrong to attribute the thesis that implicit rules are too much like explicit norms. Looking back at Ch.1, a difference emerges. Implicit rules are supposed to be exemplifications of a practical ability, applying practical rules and standards. They are a form of know-how. Explicit rules are linguistic, propositional things. They are a form of know-that.

Brandom denies that know-how is reducible to know-that. Instead, I think he thinks the converse is true, know-that is reducible to or at least depends on know-how. Consequently, I'm doubtful that it is correct to say that implicit rules can be made explicit without remainder. The reason is that there is a change in kind, from know-how to know-that. Since implicit rules are exemplified in the normative attitudes held by and sanctions performed by the critters in question, there is not the threat of a regress developing. This is because there is nowhere for the interpretive regress to get started.

This is, at least, the start of the answer. It is much like the previously suggested Kantian strategy of using the faculty of judgment. Something different in kind than the explicit rules is brought in to ground the explicit rules and prevent the regress. More details need to be supplied, but I think that is roughly how the start of the story goes. The rest of Ch. 1 supplies some of the details. Brandom leans on the idea of sanctions quite a bit and more needs to be said about them. They are important and in some cases non-normative, but I don't have much to say about them at this point.