• Problem: what are the different kinds of statements about identity?

• e.g. “the sun is the same every day”, “the morning star is the evening star”

• [a continuum: “27 = 27”, “27 = 26 + 1”, “27 = 25 + 2”, “$\sum 1/x^2 = \pi / 6$”]

• Is the interpretation of “a=b” that “‘a’ and ‘b’ designate the same thing”?

• No: then can only generate meta-statements about language and say nothing about the world. “A difference can arise only if the difference between the signs corresponds to the mode of presentation of that which is designated”

• [Compare: “the morning star is [called] Venus”]

• In addition to a referent, ever word has a sense (“mode of presentation”).

• [Is this just sense = intension, reference = extension?]

• “Comprehensive knowledge of the referent would require us to be able to say immediately whether every given sense belongs to it” (27) [i.e. what sense=computation is needed to pick this out?]

• Meta-discussion: how do we then refer to the sense of a word? Quotation marks will do.

• Third piece: conception—internal image, “saturated with feeling”. [q.v. Wittgenstein, “what I experience in a stroke”]

• Sense is speaker-independent, conception is speaker-dependent. [So sense cannot be quite “what computation picks this out”—varies depending on state of speaker knowledge. But OK in the usual model-theoretic sense.]

• [“How do I identify Venus” as part of the definition of Venus, consequently its sense.]

• Vocab: a name expresses its sense and designates its referent.

• What does a sentence refer to? A truth value.

• Replacing an entity sentence with a different part having the same referent is truth-value preserving. But what about replacing subordinate clauses?

• “I concluded that {Pat loves Lou}”

• In this case, the reference of the sentence is preserved when the sense of the clause is preserved.

• What about “He {who discovered the elliptic form of the planetary orbits} died in misery”?

• [There’s no embedded sentence here at all!]

• Bigger worry—what if “He who discovered…” doesn’t refer to anything at all? Top-level sentence doesn’t even have a truth value, b/c it doesn’t compile.

• Frege: indeed, and people should speak in such a way that they avoid presupposition failures.

• [Discussions of various other grammatical phenomena.]

Obviously most of the ideas here are familiar given modern model-theoretic accounts semantics and a better understanding of syntax. At the same time, it’s interesting historically. The version of this paper I have in my head has always just been “nouns denote entities, sentences denote truth values, sense is something else”; it’s impressive to see how omany of the issues with modality, presupposition failure & meta-linguistic discussion already come up here.