Gillian Russell

Gillian Russell (Washington University - St. Louis) is "presenting" her paper "One True Logic?" The two invited commentators for her paper are JC Beall (University of Connecticut), and Jonathan McKeown-Green (University of Auckland).

Download gillian_russell.pdf
Download mckeowngreens_commentary_on_russell.pdf
Download ocp-beall-russell.pdf

Comments

[Gillian Russell]

Hi Jonathan,

Thank you for your comments - there's a lot to think about in there. It made me smile to think of you doing experimental logic on your students and colleagues.

In response to the last paragraph on your page 2, I quite agree that a 2-dimensional descriptivist about names like can avoid my argument against arguments being composed of sentence-proposition pairs since they can deny that "Hesperus is bright" and "Phosphorus is bright" express the same proposition. Like you, I'm not tempted by the 2D view, but I wonder whether a point similar to the one I made about the equivalence thesis at the topic of page 6 can re-used here: if an answer to the question "what hypothesis about what we normally take the constituents of arguments to be makes the most sense of our actual practice"? - has a substantial consequence in the a controversial debate in the philosophy of language, I'm inclined to think that that is a point against it.

[Gillian Russell]

Hi JC,

Thank you for the comments - I really am grateful that you took the time to do this when you're so busy.

I'm very taken by your "rock" argument to the conclusion that the view I suggeset at the end of the paper could only be a very cheap (in a bad way) kind of logical pluralism, since it would turn out that every object in the universal (not just the things we normally think of as uninterpreted sentences) would be valid in some sense (for example, when we take the object to express the proposition that snow is white or snow is not white) and invalid in others (e.g. when we take it to express the proposition that snow is white.) That isn't a very attractive consequence of the view.

I can think of a possible line of response: one might say that you can distinguish two forms of logical pluralism: a cheap, and a not so cheap. On the cheap way, when you consider whether an object (e.g. set of marks on the board, rock, abstract structure...) is valid in some sense, you get to attach any meaning you like to it. On the not so cheap way, the same object can come out valid in one sense and not valid in another even when you don't consider every possible meaning that could be attached, but only think about the meanings that can get attached to it relative to an actual language.

Maybe I could push something in that direction, but, in truth, I'm not sure I really want to do so, for two reasons: 1) I think there's something fundamentally right about your suggestion that the view is not really a form of logical pluralism. In truth (as you might be able to tell from the progression of thought through the paper), logical pluralism has a lot to do with with the etiology of and inspiriation for the view, but my main goal is to push the view itself, rather than its classification as a form of logical pluralism. I suggested at the end of the paper that there's a way to think of the view whereby it might be described as a kind of logical puralism. Your rock argument might be a a good reason to let that construal go.

[Angel Pinillos]

Hi all,
I enjoyed the paper and the comments. I have a couple of questions.

(1) There is an INVALID argument we may express with "Hesperus is a planet therefore Hesperus is a planet". This would happen if the speaker has a "Paderewski" case with respect to the single name "Hesperus". For instance, she could think that there are two objects named "Hesperus" and that if one is a planet then the other must be too (because she believes that they have similar properties). Hence she intends the argument to be an inductive argument. Arguably, the premise and conclusion are identical in syntax, character and proposition expressed; and yet it is invalid! This single case seems like enough to give all the counterexamples to the cases Gillian went through and more. What do you think about it?

(2) Second, I was a bit surprised to find little discussion concerning the notion of logical form. Isn't there some truth to the idea that logic is after validity due to form and not just validity (simpliciter)? Hence, I am wondering about Gillian's first claim that logic is the study of validity. After all, is logic concerned with 'All bachelors are unmarried'?
(For this reason, I find the claim that "I am here now" is a logical truth a bit puzzling)

[patrick allo]

As I see it, your emphasis on the nature of the truth-bearers used in arguments points to an aspect of logical pluralism that, while already present in the exposition of Beall and Restall, is not made explicit in their defence of logical pluralism.

While you point to an inherent ambiguity in the level of discriminatory power of truth-bearers, it seems that Beall and Restall's 'case-plurality' can equally well be understood in terms of an ambiguity in the level of discriminatory power of the logical vocabulary. A relevant consideration in that context is that "deductive strength varies inversely with discriminatory strength" (see e.g. Humberstone on "Logical Discrimination). Basically, a system L' has a higher discriminatory strength than L iff it judges some L-equivalent formulae as being not L'-equivalent.

A more elaborate argument can be obtained by comparing classical to relevant logic, and specifically by evaluating the latter in terms of a language containing both extensional and intensional operators. Thus presented, we notice that if an argument is invalid in the classical (minimally discriminating) sense, it is also invalid in each more discriminating (that is: relevant) sense. Conversely, if an argument is valid in the relevant sense, it is also valid in the classical sense. In summary: increasing the discriminatory power of the logical vocabulary preserves invalidity, while decreasing its discriminatory power preserves validity.

Formally this can be made precise in terms of infomorphisms between languages, but a simple figure (fig1) equally does the job: http://homepages.vub.ac.be/~pallo/Figures/fig1.jpg

granting Beall and Restall their response to the Quinean objection that "a difference in logical principles marks a difference in language," we should say that our choosing of a specific class of 'cases' is somehow encoded into the discriminatory power of the logical constants (but does not alter their core meaning). For all I know, the distinction between Carnapian tolerance and logical pluralism is not threatened by the adoption of both extensional and intensional connectives.

If correct, this way of rephrasing 'case' pluralism at least suggests that 'truth bearer' pluralism about logical consequence is a genuine pluralism on the condition that 'case' pluralism is itself a genuine pluralism. That is, if there is no single answer to the question which connectives correctly formalise the argument:

p AND (NOT-p OR q) therefore q

there is no single answer to the question what the correct logic might be, and this conclusion does not seem radically different from the view that different kinds of truth-bearers can be used to make the precise structure of arguments apparent. As I see it, we might have good reasons to disambiguate a specific instance of DS as p \otimes (~p \oplus q) rather than p \otimes (~p \sqcap q); but totally lack a reason to chose p \otimes (~p \oplus q) above p \wedge (¬ p \vee q). If we use the more discriminating connectives, we obviously can make the relevant distinctions, but if we use the less discriminating classical connectives, we lack such capacities.

Therefore, if pluralism about deduction can be understood as a pluralism about discrimination, it seems to me that the pluralism you're investigating is by no means more modest than Beall and Restall's.

Also, the fact that we can conceive more ambiguous languages which validate very little arguments shows that there is even more room for variation (fig 2 &3).

http://homepages.vub.ac.be/~pallo/Figures/fig2.jpg
http://homepages.vub.ac.be/~pallo/Figures/fig3.jpg

On the whole, I am quite sure that your examples can be examined along similar lines. This would show that single-language pluralism is compatible with allowing differences in the discriminatory power of truth-bearers.

[Ajf 6]

The hope of green fields, we yearn for the dream!