Resolving Frege-Geach?
I've set out to expose Frege–Geach as a category error. Details to follow.
I’ve been miffed by the Frege-Geach problem since I first encountered it, however many years ago. In February, I published an essay, effectively dissolving it as a category error. I returned to the essay and revised it this week to soften the claim to ‘misplaced confidence in what natural language syntax can deliver’.
Read more of my journey here: The Demise of Frege–Geach
I published version 1.1, When Syntax Is Asked to Bear Too Much: The Frege–Geach Problem and the Limits of Linguistic Invariance, but was still unsatisfied. I still feel that a category error is at the heart of the problem, so I engaged with several LLMs to determine if I might solve it.
My starting position was that moral language is categorically different to the quotidian variety, but this was part of the case I was already making. Analytical philosophers would not likely accept this carve-out. I needed to demonstrate that this grammatical behaviour wasn’t limited to moral utterances.
It turns out that my Language Insufficiency Hypothesis (LIH) had already argued a general case for Contestable terms that acted like Bernard Williams’ thick terms. Moral terms are functionally ‘thick’ in the sense that matters here: they carry multiple context-sensitive functions that resist invariant embedding. LIH illustrates how these terms are lossy.
My new task became to double down on the category error. My intuition was (read: is) that the error is overlooked because the category has yet to be defined. What’s a bloke to do?
Define a new category for these cases. I call them ‘recruitable expressions’ – though ‘performance-sensitive expressions’ is still in the running.
Using a well-worn example in the case of Frege–Geach, here’s a quick illustration:
1. Murder is wrong.
2. If murder is wrong, then getting your brother to murder is wrong.
3. Therefore, getting your brother to murder is wrong.
For those not in the know, Frege–Geach argues against ascriptivism and non-cognitivism generally. The emotivist version, via Ayer, holds that moral claims are not truth-apt and might effectively be recast as ‘boo to murder’ – I don’t like murder.
Frege–Geach takes the emotivist at their word and asks what happens when we substitute:
Boo to murder.
If boo to murder, then getting your brother to murder is wrong.
Therefore, getting your brother to boo to murder.
The sentences stop making sense.
But I argue that equivocation is happening between instance 1 and 2. I might map it as follows:
X.
If x, then getting your brother to X.
Therefore, getting your brother to X.
Notice the lower case ‘x’. I might as well have used X₁ and X₂. My paper will discuss this in more detail and with non-moral examples.
Essentially, X is (effectively) assertorial and x is an antecedent to a conditional. The syntax changes the semantic load. The category error is assuming that lexical recurrence entails functional identity – that because the same words appear in both contexts, they must be doing the same work.