The Demise of Frege–Geach?

4–5 minutes

Journal Entry

I published an essay on the Frege–Geach problem in February. I published an update yesterday. I still wasn’t satisfied, so I engaged with several LLMs. This was my approach.

The involved LLMs were:

  • Claude
  • Grok
  • ChatGPT
  • Gemini
Audio: NotebookLM summary podcast of this topic.
(This summary misses the mark in some ways, but it brings up some interesting observations along the way.)

First, I fed them some documents in no particular order, my goal being to share my own knowledge and position on the purported problem.

I started with Gemini. This was my prompt:

I am interested in resolving the Frege–Geach problem, but it seems I can only dissolve it. This doesn’t appear to be adequate for some analytical philosophers. How might I get closer to resolving it? My main argument is that they are assuming that language is stronger than it is, and they don’t agree with my argument.

As the prompt notes and by design, many analytical philosophers are reluctant to grant the degree of insufficiency I take to be constitutive of natural language, especially where logical embedding is concerned. Evidently, that counts as my not wanting to play their game. From my perspective, they are committed to a different ontological grammar. What this means practically is that I need to present my solution proposal in their terms. This doesn’t mean their terms are right; problems are only relevant in their dialect, even though my argument is that all dialects are lossy – mine included.

Part of the challenge is that formal logic was invented precisely because ordinary language is imprecise, yet its standards are often retrofitted back onto natural language as though they revealed what language must have been doing all along.

Without sharing the entire play-by-play of the transcripts, I established my course of action. I’d dissolved the problem, but I hadn’t yet resolved it.

My initial intuition of several years ago was to argue that they were expecting too much from grammar. I’ll use a well-worn example. Follow these statements:

  1. IF ‘Murder is wrong.’
  2. THEN ‘If murder is wrong, then getting your brother to murder is wrong.’
  3. SO ‘Getting your brother to murder is wrong.’

According to them, the embedded ‘murder is wrong‘ doesn’t make sense. Here’s their logic:

According to Ayer, moral statements are simply emotive. When one utters, ‘murder is wrong‘, they are really saying ‘Boo, murder‘ – ‘I don’t like murder‘.

If ‘murder‘ is defined as ‘killing disallowed by the state‘, then murder is wrong might be translated into ‘killing disallowed by the state is wrong’ or ‘what the state declares is wrong is wrong’, but we also know that the state makes many pronouncements, many of which carry no moral weight and others which are counter to expected moral positions – law does not equal moral, and vice versa. Let’s move on and revisit our statements:

  1. IF ‘Boo to Murder is wrong.’
  2. THEN ‘If boo to murder is wrong, then boo to getting your brother to murder is wrong.’
  3. SO ‘Getting your brother to murder is wrong.’

My intuition was that the embedded clause does not perform the same linguistic act as the standalone assertion, even if the lexical material is repeated. We’re committing a category error. More crucially, the category it belongs to doesn’t exist, so it’s unspecified. It needs to be invented.

Although I struggled to find apt nomenclature, I settled on performance-sensitive expressions.

A parallel challenge is that the solution can’t be a simple carve-out for moral language. Whilst I feel that moral language does use its own grammar and semantics, I don’t expect analytical philosophers to accept this assertion, so the solution should be more generalisable. I’d need to demonstrate where else this conditional logic fails in the same manner.

ChatGPT had this to say in response to a draft:

The comparative-cost section is good, but one sentence should be added to pre-empt the “your account also uses theory-laden notions” objection.
A critic may reply: your own terms, like “coherence zone” and “synchronisation protocol,” are also theoretical machinery. True enough. The difference is that your machinery is independently motivated and not introduced solely to patch Frege-Geach. You imply this already, but it would help to say so directly.

It offers clearer language:

Embedded moral predicates are not semantically identical to their unembedded counterparts, but neither are they inert; they are performance-sensitive expressions whose full evaluative load is attenuated under embedding while a thinner inferential profile remains available for reasoning.

In any case, I am still polishing the essay, dotting Is and crossing Ts. I think I’ve got the main argument and some examples. One of my weaknesses may be that I rely heavily on my own theories, but these are published and debatable on their own merits.


Two Valleys Diverged in a Mountain Range

(Or: What I Learned When I Learned Nothing)

NB: This is the first of a parable triptych. Read part 2, The Tunnel.

Two valleys diverged in a mountain range, And sorry I could not travel both And be one traveller, long I stood And looked down one as far as I could To where it bent in the undergrowth of reeds and optimism;

Then took the other, just as fair, And having perhaps the better claim, Because it was sandy and wanted wear— Though as for that, the passing there Had worn them really about the same,

And both that morning equally lay In fog no step had trodden black. Oh, I kept the first for another day! Yet knowing how way leads on to way, I doubted if I should ever come back.

—Except I did come back. And I met someone coming the other way. And we stood there in the clouds like a pair of idiots trying to explain our respective valleys using the same words for completely different things.

Audio: NotebookLM summary podcast of this topic.

Image: NotebookLM infographic of this topic.

Here’s what they don’t tell you about Frost’s poem: the two paths were “really about the same.” He says it right there in the text. The divergence happens retroactively, in the telling, when he sighs and claims “that has made all the difference.”

But he doesn’t know that yet. He can’t know that. The paths only diverge in memory, once he’s committed to one and cannot check the other.

Here’s what they don’t tell you about political disagreement: it works the same way.

Video essay of this topic. Another NotebookLM experience.

The Actual Story (Minus the Versification)

Once upon a time—and I’m going to need you to suspend your allergy to fairy tales for about eight minutes—there was one settlement. One people. One language. One lake with drinkable water and fish that cooperated by swimming in schools.

Then mountains happened. Slowly. No dramatic rupture, no war, no evil king. Just tectonics doing what tectonics does, which is ruin everyone’s commute.

The people on one side kept the lake. The people on the other side got a rain shadow and a lot of bloody sand.

Both sides adapted. Rationally. Reasonably. Like competent humans responding to actual material conditions.

Lake people: “There’s enough water. Let’s experiment. Let’s move around. Let’s try things.”

Desert people: “There is definitely not enough water. Let’s ration. Let’s stay put. Let’s not waste things.”

Neither wrong. Neither irrational. Just oriented differently because the ground beneath them had literal different moisture content.

The Bit Where It Gets Interesting

Centuries later, two people—one from each side—decide to climb the mountains and meet at the top.

Why? I don’t know. Curiosity. Stupidity. The desire to write a tedious blog post about epistemology.

They meet in the fog. They speak the same language. Grammar intact. Vocabulary functional. Syntax cooperative.

And then one tries to explain “reeds.”

“Right, so we have these plants that grow really fast near the water, and we have to cut them back because otherwise they take over—”

“Sorry, cut them back? You have too much plant?”

“Well, yes, they grow quite quickly—”

“Why would a plant grow quickly? That sounds unsustainable.”

Meanwhile, the other one tries to explain “cactus.”

“We have these plants with spines that store water inside for months—”

“Store water for months? Why doesn’t the plant just… drink when it’s thirsty?”

“Because there’s no water to drink.”

“But you just said the plant is full of water.”

“Yes. Which it stored. Previously. When there was water. Which there no longer is.”

“Right. So… hoarding?”


You see the problem.

Not stupidity. Not bad faith. Not even—and this is the part that will annoy people—framing.

They can both see perfectly well. The fog prevents them from seeing each other’s valleys, but that’s almost beside the point. Even if the fog lifted, even if they could point and gesture and show each other their respective biomes, the fundamental issue remains:

Both are correct. Both are adaptive. Both would be lethal if transplanted.

The Retreat (Wherein Nothing Is Learned)

They part amicably. No shouting. No recriminations. Both feel they explained themselves rather well, actually.

As they descend back into their respective valleys, each carries the same thought:

“The other person seemed reasonable. Articulate, even. But their world is completely unworkable and if we adopted their practices here, people would die.”

Not hyperbole. Actual environmental prediction.

If the lake people adopted desert-logic—ration everything, control movement, assume scarcity—they would strangle their own adaptability in a context where adaptability is the whole point.

If the desert people adopted lake-logic—explore freely, trust abundance, move without restraint—they would exhaust their resources in a context where resources are the whole point.

The Bit Where I Connect This to Politics (Because Subtlety Is Dead)

So when someone tells you that political disagreement is just a matter of perspective, just a failure of empathy, just a problem of framing—

Ask them this:

Do the two valleys become the same valley if both sides squint really hard?

Does the desert get wetter if you reframe scarcity as “efficiency”?

Does the lake dry up if you reframe abundance as “waste”?

No?

Then perhaps the problem is not that people are choosing the wrong lens.

Perhaps the problem is that they are standing in different material conditions, have adapted rational survival strategies to those conditions, and are now shouting advice at each other that would be lethal if followed.

The lake-dweller says: “Take risks! Explore! There’s enough!”

True. In a lake biome. Suicidal in a desert.

The desert-dweller says: “Conserve! Protect! Ration!”

True. In a desert biome. Suffocating near a lake.

Same words. Different worlds. No amount of dialogue makes water appear in sand.

The Frostian Coda (With Apologies to New England)

I shall be telling this with a sigh Somewhere ages and ages hence: Two valleys diverged on a mountainside, and I— I stood in the fog and tried to explain reeds to someone who only knew cactus, And that has made… well, no difference at all, actually.

We’re still shouting across the mountains.

We still think the other side would be fine if only they’d listen.

We still use the same words for utterly different referents.

And we still confuse “I explained it clearly” with “explanation bridges material conditions.”

Frost was right about one thing: way leads on to way.

The valleys keep diverging.

The fog doesn’t lift.

And knowing how mountains work, I doubt we’ll meet again.


Moral: If your political metaphor doesn’t account for actual rivers, actual deserts, and actual fog, it’s not a metaphor. It’s a fairy tale. And unlike fairy tales, this one doesn’t end with reunion.

It ends with two people walking home, each convinced the other is perfectly reasonable and completely unsurvivable.

Which, if you think about it, is far more terrifying than simple disagreement.

Read part 2 of 3, The Tunnel.