Friday, August 26, 2016

EN 005 Kripke's Frege: The "Frege Principle"

# EN 005
Kripke's Frege:

Once more I would like to reiterate the purpose of this particular thread of commentaries. I do not wish to maintain that what Kripke says is wrong, or that his observations lack worth, but I would like to draw attention to some of shortcomings of the direction in which he takes his inquiry.

I certainly know of some articles favorable and unfavorable to Kripke's proposal and it is clear that I am acquainted with only a tiny fraction of what has been written about it. So with few exceptons I will essentially ignore the literature dealing with "Kripke's Frege". What I pretend to do here is pick out a few topics that are important for understand the logic and philosophy of language of Frege and see how well Kripke's treatment of it allows the topic to still fit into Frege's general view of things.

One main hypothesis (against e.g. Dummett) in Kripke's exegetical remarks is that Frege's treatment of indirect discourse compels him to accept an infinite hierarchy of indirect senses. I will skip this point, at least for the moment, as this would be a consequence Frege himself clearly did not draw in his writings and hence is beyond the purpose of these observations.

One item which is well within our topic, however, and which stands out in Kripke's account is, what is frequently called─following Davidson, I believe─the "Frege Principle":

Krikpe attributes to Frege adherence to the following principles:

The first [principle] is that the referent of a whole is a function of (or is determined by) the
referents of its parts. 

The second principle analogously replaces “reference” by “sense”. (Kripke 2011, 269)

And he adds: "What these principles mean is that if in any piece of language one replaces some significant part by one with the same referent (sense), the referent (sense) of the whole is unchanged." (Kripke 2011, 269/70). Then he introduces─in the words of Dummett (1973)─a "reverse principle" to the two principles just mentioned [references for this thread are summarized in a separate post without number]:

The sense of a complex is compounded out of the senses of its constituents. (Dummett, 1973,
p. 152; original emphasis) [Quoted as per Kripke (2011, 270)]

There is another famous principle that stands out in Frege and which the logician from Wismar states himself in prominent places in Grundlagen der Arithmetik, though never again explicitly afterwards, a fact that has led to some controversy as to whether Frege adhered to it after introducing the distinction between sense and reference (or rather meaning) in his original doctrine about judgeable contents. The principle I refer to is the "Context Principle". Kripke is largely mum on this other principle.

But since I believe that it is impossible to reach a correct understanding of Frege's treatment of compositionality while ignoring the importance of contextuality, we will have to view Kripke's discussion of the topic largely under the light of an aspect which he largely ignores or deals with lightly.



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