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A topic that recurs in the interviews with Quine is his views on analyticity and how his views have changed since “Two Dogmas”.

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Things are rather busy around here between the end of term, prospectives visiting, and me trying to finish up my model theory work from last semester. I’m having some trouble posting because of this. Some ideas are bouncing around, but I haven’t yet posted them. Here’s a short bit on one of them.

Several philosophers have leveled objections against parts of Carnap’s logical syntax project. Among these include Goedel, Kleene, Friedman, and Beth. Their objections focus on the Carnap’s views on foundational issues in the philosophy of math. This comes out especially in the Goedel and Beth objections (the latter of which I want to discuss in more detail later). The Friedman (primarily in his “Tolerance and analyticity in Carnap’s philosophy of mathematics”) and Kleene objections find tension between the principle of tolerance and foundational issues. All of these objections share a common move, and it is this theme that some of the responses, such as Ricketts’s and Goldfarb’s, want to dispute. The move is to saddle Carnap’s logical syntax project with more interest and involvement in foundational issues than Carnap had.

It sounds weird, in a way, to deny that Carnap had foundational aims. He talks about logicism a lot and seems to adopt that thesis. He wrote a pamphlet entitled “Foundations of Math and Logic.” Nonetheless, there is something to the response of denying these foundational aims to Carnap. Carnap’s logicism is different from Frege’s and Russell’s. Carnap doesn’t try to reduce math to logic in Frege’s sense. I’m not sure why exactly he is a logicist. He wants the mathematical part of any language to be valid or contra-valid, but this is not a reduction to logic. The pamphlet mentioned does not really address foundational issues in the way that Frege or Brouwer did. The parts that talk about foundations are surprisingly short. They seemed to be more interested in dismissing the questions than resolving them.

I wasn’t looking for Carnap’s discussion of foundational issues in Logical Syntax when I read it However, I was looking for the discussion of foundational issues in “Foundations.” From the little bit that was there, it seemed consistent to deny that Carnap wanted to engage in the foundational debates of his time. He rather wanted to sweep them aside with the invocation of his principle of tolerance. I haven’t gone back to LSL to check this, but I’m expecting to see a similar pattern there. Are there any places in LSL that are particularly hard to read as anything but Carnap engaging in foundational debates?

It might help to clarify what I mean by “foundational debates.” An example would be the disagreement between the intuitionists and the classical mathematicians. The intuitionists, roughly, wanted to reject certain forms of mathematical reasoning and the results that followed from them. The classical mathematicians wanted to keep all of classical mathematics since they regarded it as coherent and correct. Classical math provided more tools, and possibly essential ones, for scientific inquiry. The intuitionists provided arguments that classical math was incoherent (or bad or…) and the classical mathematicians provided responses. By denying that Carnap was engaging in foundational debates, one is denying that Carnap wanted to provide arguments against intuitionism and for classical math. One is denying that he wanted to adjudicate the dispute and settle who had the better arguments. Instead, he invoked the principle of tolerance to sidestep the issues entirely. This is not to say that he doesn’t have sympathies. He preferred classical math, at least from LSL. This was not the product of a settled foundational debate though.

I read Alexander George’s “On Washing the Fur without Wetting It” today. The assessment of he gives of the analyticity debate is very appealing. He gives some arguments that the standard interpretation of the debate is incorrect since it makes out Quine’s arguments to be too weak or Carnap to be too dense. I need to think about it some more before I can comment on the reconstruction, but I did want to comment on the moral that he draws. The big contribution of the paper is an explanation of how the different takes on analyticity change what is at stake in the debate. As George puts it:
“[F]or this distinction between kinds of truth is of a piece with one between kinds of difference, and so differences over anlyticity must affect how those very differences can be conceived. This is no doubt a source of the difficulty in obtaining a satisfactory perspective on the dispute…: for there appears to be no way even to judge what kind of dispute it is without thereby taking a side in it. To try to determine the nature of a disagreement over the nature of disagreements without taking any kind of position on that disagreement is just to try to wash the fur without wetting it.”
The last sentence was included to explain the title. I don’t think the last sentence is correct in general. George makes a case that it applies to the different stands on analyticity in particular, which is all that is needed. Read the rest of this entry »

This week in the Quine and Carnap class we’re talking about the analyticity debate. I’ve read most of the Carnap pieces for it and wanted to write a short note on them. It is a rough note. One thing that surprised me in Carnap’s response to Quine’s “Carnap on Logical Truth” was how little weight he seems to place on analyticity. Carnap says that if there is a change of meaning of a term along the lines that Quine discusses, then the analytic truths change as well. They change because we have changed languages, from Ln to Ln+1. I had thought that there would be more stability in languages and analytic truths. Rather than switching the whole language and with it the analytic truths, one would just change part of the language, leaving the analytic truths as is.

I’m not sure if I think this is a good response. It trades a difference in meanings for a difference in languages. it makes it hard to see what the the distinction is between speaking a language in which the meanings change and switching between speaking different languages. This seems reasonable enough. I’m not sure what sort of pragmatic ground one could supply for opting for the one rather than the other. I had thought that analytic truth supported the former but Carnap seems to say no.

The relativization to a language prompted the question, legitimately or not: What is the difference between the predicates ‘analytic sentence’, ‘true’ and ‘logically true’? In a way they are similar; they are relativized to a language. Truth doesn’t have a lot of weight put on it by Quine. (I might be wrong here. I’m going to talk to someone about that tomorrow.) He mentions the use of it to generalize about linguistic items. Analytic sentences are a genus of the species of truth, as Quine says, as are logical truths. Logical truths are true in virtue of logical form though. Analytic truths are true in virtue of meaning, which surely means that they are true in virtue of the meanings in that structural configuration. Not all sentences with those meanings are true nor are all sentences with that structure true.

What extra do we signify when calling a sentence analytic? It isn’t a greater commitment to its truth. That can be abandoned readily. Carnap says the analytic sentences aren’t ones that must be held come what may. If there is recalcitrant experience we can always switch our language to a similar one in which certain sentences are no longer analytic. A change in analytic sentences is a change in meaning though, so it doesn’t seem like much can be made of truth in virtue of those meanings; they are too fluid.

At this point I’m a little confused about what Carnap is maintaining in opposition to Quine. In “Carnap, Quine and Logical Truth,” Isaacson gives an interpretation of the analyticity debate that puts little distance between Quine and Carnap’s ultimate positions. When I read it, this seemed rather surprising. After reading Quine and Carnap’s contributions, it seems pretty close to the truth.

In Logical Syntax, Carnap says that he has shown that one can talk about the logical form of language and that this is a counterexample to Wittgenstein’s dictum that you cannot talk about logical form, as it can only be shown. There is something that seems odd about this. From the little bit of secondary literature I’ve read, no one really seems to say much about this, although some of Carnap’s contemporaries seem to embrace Carnap’s claims. It seems like Carnap is talking past Wittgenstein. The problem with fleshing out this claim is that I have to flesh out one of the difficult doctrines in the Tractatus. (As opposed to the simple ones, I guess.) I’m going to attempt to sketch an answer. Read the rest of this entry »

In his article “Present State of Research into the Foundations of Mathematics,” Gentzen briefly talks about Goedel’s incompleteness results. He says that it is not an alarming result because it says “that for number theory no adequate system of forms of inference can be specified once and for all, but that, on the contrary, new theorems can always be found whose proof requires new forms of inference.” This is interesting because Gentzen worked with Hilbert on his proof-theoretic projects and created two of the three main proof-theoretic frameworks, natural deduction and the sequent calculus. The incompleteness theorems are often taken as stating a sort of limit on proof-theoretic means. (I’m treading on shaky ground here, so correct me if my story goes astray.) That is to say, any sufficiently strong proof system will be unable to prove certain consequences of its axioms and rules. Adding more rules in an attempt to fix it can result in being able to prove some of the old unprovable statements, but new ones (maybe just more?) statements will arise. Read the rest of this entry »

In Brandom’s Locke Lectures, he quotes an odd line from Sellars: “the language of modality is a transposed language of norms.” Part of the point of the lectures is to give some clearer content to that claim. Brandom does it with his analysis of pragmatic metavocabularies and such. I had thought that this idea of a transposed language was original to Sellars. He is a fairly colorful writer, which sometimes obscuring his points.

In reading Carnap’s Logical Syntax, I came across something similar. At the start of section 80, “The Dangers of the Material Mode of Speech,” Carnap says that the material mode is “a special kind of transposed mode of speech.” This is glossed as “one in which, in order to assert something about an object a, something corresponding is asserted about an object b which stands in a certain relation to object a.” He goes on to say that metaphor is a transposed mode of speech. Looking back at the Sellars quote, this seems to be the sort of thing he meant. I don’t know if an idea of transposition was common in the first half of the 20th century, but I’ve not come across it elsewhere.

This lead me to a question. To what extent were Sellars’s ideas a reaction to or an offshoot of Carnap’s? It is clear that Sellars read a lot of Carnap. His article on the role of rules of language (an article whose title I’m blanking on) [Edit: “Inference and Meaning”, thanks Rick] directly deals with Carnap. Sellars made a contribution to Carnap’s Schillp volume. According the SEP article on Sellars, Sellars was deeply influenced by Carnap, focusing mainly on their engagement with science and epistemology. It doesn’t seem to mention views on language, although the article on rules [Edit: “Inference and Meaning”] definitely lays out stuff on material inference and inferentialism, as it is retroactively called.

Why would this matter? An apparently hot topic is the influence of Carnap on Quine. Carnap also had a big influence on Sellars, whose views on a great many things are different than Quine’s. Looking at what they were reacting to in Carnap and what their ultimate reactions were could probably indicate further territory to explore. Especially since Sellars was fairly heavily influenced by Wittgenstein and Kant in ways that Quine was not. To strain a metaphor to the breaking point, it would be like triangulating the shadows of giants. While on their shoulders. In any case, it is starting to seem like a non-terrible idea to look into this. There is some material on the influence of Carnap on Quine, and possibly some on Carnap and Sellars. I don’t know if there is much on Sellars and Quine since they didn’t seem to engage each other much. Although, books on roughly inferentialist ideas, like Brandom’s Making It Explicit and Peregrin’s Meaning and Structure discuss them together, though not Carnap to my memory. It seems like it could be fruitful to bring all three into the picture together.

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Shawn Standefer, recent Ph.D. in philosophy from Pitt. (More about me)

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