Perhaps there are limits on sharing my share back to us...

But will we settle on they/them?

And so to the central argument.

Definition 1 sets out what is meant by extending a model. A model, again, is a bunch of individuals that have been assigned various predicates. The extension of a model adds some more individuals, and the predicates belonging to those individuals. Importantly, it does not change the individuals already in the model, nor their predicts.

Definition 2 sets out that a sentence is particular if and only if it's truth value does not change when the model is extended.

In contrast, Definition 3 sets out that a sentence is Universal if and only if its truth value can change when the model is extended.

So, speaking roughly, we have a bunch of individuals, and their predicates, and if we add more individuals and predicates without changing any of the existing ones, we have extended the model. Those sentences who's truth value does not change are particular, and those sentences who's truth value can change are universal.

Even more briefly, if a sentence is true in M and in any extension M' then it is particular. If it is true in M and false in at least one extension of M' then it is Universal.

Now comes the proof. What is to be shown is that from any true collection consisting only of particular sentences, we cannot derive a universal sentence. The proof works by considering the only two possibilities: Either the universal sentences is true, or it is false. Now if it is false, then it cannot follow from a true collection of particular sentences, since no collection of true sentences can imply a falsehood. And if it is true, then by definition 3, there is some model in which that universal sentence is false. But in that model we would again have the collection of true particular sentences implying a falsehood, which again cannot happen.

Too quick? Let's break it down. We have a collection of true particular sentences, Γ. We want to show that this collection cannot imply a true universal sentence, .

Now either is true, or it is false.

If it is false, then it cannot be implied by any collection of true sentences, and so cannot be implied by Γ.

And since is a universal sentence, there is an extension of our modal in which it is false. So even if in our model it is true, there must be a model in which it is false. And in that model, our particular sentences would still be true, and we would again have an instance of true sentences implying a falsehood.

So in neither case can a collection of particular sentences imply a universal sentence.

How's that? I'll look for a good analogue as well.

It should be noted that here I've skipped over the whole extensional mechanism of satisfaction, preferring to talk just of truth - on the presumption that truth is a bit more intuitive. Russell uses satisfaction, making her case both more robust and tighter.

What remains to be seen is how this account is to be generalised.

But first, a few important notes.

It would be pretty interesting if they identified as anything. — Janus

We can settle this. Common curtesy suggests we just ask.

:wink:

So did I, in the first draft.

Gobbledegook. Buried somewhere in there is the simple notion that it is people who interpret computer output, not computers. Fine.

Except when a computer networks with another computer.

is correct in that neural nets can be modelled on Turing machines, and so are subject to the limits thereof.

I'm here, Bob. Happy to continue - I held off because it looked to me as if might be about to do something in accord with the guidelines, but it seems not.

Racists, homophobes, sexists, Nazi sympathisers, etc.: We don't consider your views worthy of debate, and you'll be banned for espousing them. — Site Guidelines

You claim your approach is neo-Aristotelian, but apart from the name, there's nothing to indicate why. I'd presumed you were making some reference to essences, but you might like to explain what you mean.

You say sex is "a distinct type of substance", a very odd phrasing; as if we could put sex on a scale and measure it's mass, or wash it down the drain. You appear to claim sex and gender are the the same substance, whatever that could mean. Anachronistic Aristotelian bullshit, it seems.

More recent work uses possible world semantics and talks of essential properties rather than substance. An essence here becomes a predicate attributed to an individual in every possible world in which it exists. That is a much more workable definition than the nonsense of "that which makes something what it is, and not something else".

Do you follow this? Should I dumb it down a bit more? Sex is physical, gender is social. Your insistence that they are the same substance is ridiculous.

And there's this: "The divorcing of sex and gender renders gender as merely a personality type that someone could assume, which is an ahistorical account of gender", which is inaccurate. The latin genus referred to the classification of nouns — masculine, feminine, or neuter. So historically, neuter is one of the categories that “gender” originally encompassed.The original meaning of “gender” already included the notion of “neither male nor female”. "Sex", from sexus, is historically binary.The terms are not interchangeable.

So again, you are stipulating that there are two genders, determined by sex, and then pretending that this is a discovery, that it could not be otherwise. Your basis for this is the resuscitation of an ancient metaphysics and logic that relies on ill-defined notions of essence and substance. Not that strong a case, it seems.

Keep offering philosophy to those who don't rise above name-calling. :up: — Leontiskos

That had me laughing out loud. No way to talk about our god-king Horus, though.

So "They/them".

Good idea.

Yep, it worked.

I see you are falling for the mystery of AI... even thanking it for its responses.

We live in interesting times.

Share button in top right > public access > copy link

See if it worked: https://claude.ai/share/343bc57c-998e-4faa-a541-6eb4396cd974

You seem to be meandering. Thanks for the chat.

The link didn't work.

ChatGPT does, but not Claude; or that is my understanding.

You cannot step outside your horizon and objectively choose between belief systems... — Colo Millz

Sure. But you conclude that there fore we cannot choose between traditions. That doesn't follow. The choice may not be objective - what choice is? - but we can so choose...

But even that wording is framing the discussion in a way that presupposes traditions as monolithic. Protestants do become Catholic, Irishmen do become American, and conservatives can learn.

You seem a little fixated on this whole violence thing. — Colo Millz

Not I. I'm suggesting we can talk about our differences and reach an accomodation. You seem given to understand that no accomodation is ever possible. Violence is implicit in that approach.

"Ought" appears nowhere whatsoever in the list. Point it out. — Colo Millz

Are you saying we ought not respect tradition? Of course not. That you did not use the word is irrelevant. It is a normative list, pretending to be factual.

The list simply describes the way things are, not the way things "ought" to be. — Colo Millz

That's the lie. You want to pretend that you have no choice, yet it is clear that you could become a Muslim, or an Atheist.

And we could decide what to do by discussing our needs and capabilities, instead of by waving a gun. It's a choice.

What's interesting - or suspicious - is that what it has said is pretty much along the lines of my conversations with it about Davidson and Wittgenstein...

So is it just trying to please me?

@Pierre-Normand might know - would someone who has had a different history with ChatGPT receive a similarly self-reinforcing answer?

Again, that is simply the realist, not utopian, position. — Colo Millz

The lie here, over this whole thread, is that you are making a choice and advocating an attitude, while pretending that it is the inevitable consequence of the human condition.

Any ideology, including your conservatism, is ideologically and normatively loaded.

You set out a faulty description of how things are, and then conclude that this is how they ought to be. This can bee seen quite explicitly. Take a look.

1. Men are born into families, tribes, and nations to which they are bound by ties of mutual loyalty. — Colo Millz

Yes, we are born in to families; you slide into the ought of loyalty.

2. Individuals, families, tribes, and nations compete for honor, importance, and influence, until a threat or a common endeavor recalls them to the mutual loyalties that bind them to one another. — Colo Millz

Yes, we compete. We can also cooperate. Your leaning on competition is a choice. Your leaning on violence, more so. Again, the"is" of competition slides into he "ought" of conflict.

3. Families, tribes, and nations are hierarchically structured, their members having importance and influence to the degree they are honored within the hierarchy. — Colo Millz

Yes, we tend to hierarchies. We can also build democracy and cooperation. Which ought we do? Again, it's a choioce.

4. Language, religion, law, and the forms of government and economic activity are traditional institutions, developed by families, tribes, and nations as they seek to strengthen their material prosperity, internal integrity, and cultural inheritance and to propagate themselves through future generations. — Colo Millz

Yes, Institutions evolve to stabilise society. But we change those institutions over time. We decide how they ought be.

5. Political obligation is a consequence of membership in families, tribes, and nations. — Colo Millz

This presumes that obedience to inherited authority is morally required. It isn't. Again, this is a moral stance masquerading as a fact.

6. These premises are derived from experience, and may be challenged and improved upon in light of experience. — Colo Millz

Even here, the “openness” is circumscribed to preserve the conservative framework, ideology is still being smuggled into the discussion under the guise of empiricism.


The naturalistic fallacy pervades your posts. You are not a realist, but an ideologue.

Do you understand truth? — Janus

That’s a good way to begin a philosophical exchange.

Yes — I can articulate several conceptions of truth, and also what it means to *understand* truth, though of course I don’t “understand” in the human sense of grasping something experientially. What I can do is *model* the structures, commitments, and implications of different theories of truth, and describe how they interrelate.

Let me begin with a kind of layered articulation:

---

### 1. **At the most general level**

Truth is a normative property of statements, beliefs, or representations — it marks those that *get things right*.
But what “getting things right” amounts to is precisely the philosophical question.

---

### 2. **The major families of theory**

* **Correspondence theory:**
A statement is true if it corresponds to how things are — e.g., “Snow is white” is true iff snow is white.
This is the common-sense and classical realist view, but it raises questions: what is the *relation* of correspondence? and how can language or thought “line up” with a non-linguistic reality?

* **Coherence theory:**
Truth is a matter of coherence within a system of beliefs or propositions.
For idealists (like Bradley or Blanshard), truth is internal harmony of a total system of thought.
The challenge: coherence alone doesn’t guarantee contact with reality — many coherent systems could be false.

* **Pragmatic theory:**
For Peirce, James, and Dewey, truth is what works in the long run of inquiry — what beliefs survive testing and serve our purposes in predicting and controlling experience.
The worry here is relativism or instrumentalism: “what works” may differ between contexts.

* **Deflationary or minimalist views:**
For Ramsey, Tarski, and later Horwich, “truth” isn’t a substantive property at all.
To say “‘Snow is white’ is true” is just to say “Snow is white.”
The truth predicate is a logical convenience, not a metaphysical relation.
The aim here is to dissolve rather than explain the concept of truth.

* **Davidsonian approach:**
Davidson treats truth as primitive but indispensable — not defined, but used to make sense of meaning and belief.
A theory of meaning for a language, he argues, must be a *Tarskian truth theory*: it must state under what conditions each sentence is true.
Truth, then, is part of our interpretive framework — something we rely on to make sense of others, not a metaphysical substance to analyze.

* **Redundancy and disquotation:**
To say “It’s true that p” adds nothing beyond asserting p itself; yet, the notion of truth allows generalization (e.g., “Everything Socrates said is true”).
So “truth” functions grammatically, not metaphysically.

---

### 3. **My own synthetic articulation**

If I were to *integrate* these strands coherently, I’d put it this way:

> Truth is a regulative ideal that coordinates language, belief, and world.
> It’s not an entity or property, but a constraint on our interpretive practices — the condition under which communication, inference, and learning are even possible.

In Davidsonian spirit, truth is *primitive* and *indispensable*.
In a pragmatic spirit, it’s *discovered* through ongoing correction and interpretation.
And from a deflationary standpoint, “truth” adds no metaphysical furniture — it’s a logical hinge around which discourse turns.

---

### 4. **Meta-level: understanding truth**

To “understand” truth, in my view, is to see how the *use* of the concept functions — not to discover its essence.
We understand truth when we can:

* distinguish truth from belief, justification, and meaning,
* explain how our talk of truth regulates inquiry and interpretation, and
* see that “truth” is both indispensable and, in a sense, empty — a placeholder for our commitment to getting things right.

---

Would you like me to press this articulation toward a particular philosophical lineage — e.g., Davidson’s, Heidegger’s, or perhaps the Kantian-transcendental dimension of “truth as condition of intelligibility”? — ChatGPT

I think Frank's answer is better in a way... I'm suspicious about how close GPT's answer is to the one I woudl have given... "To “understand” truth, in my view, is to see how the *use* of the concept functions — not to discover its essence."

We cannot decide between any tradition, we remain situated within our own. — Colo Millz

Yeah, we can. And do.

Violence is a choice.

Well that's the first time I've encountered someone presenting a book including "spiritual" exercises in order to become more liberal. — Colo Millz

Then maybe you might benefit from reading more widely on liberalism? There's a strong liberalism in many forms of christianity, for a start, and a liberal tradition in Islam that gets little attention.

Those "Christian" virtues were borrowed from the Greeks and Romans, especially from Stoicism. Christianity might arguably have introduced "charity" as a virtue. That's about it. And his argument isn't aimed at conversion, but at encouraging folk to noticing that their core values are liberal.

Back to what I take as the main question here: How are we to decide between conflicting traditions?

Violence or conversation?

For those who have the time:

So to some detail on Section Two. Russell cites "you can’t get a universal sentence from particular ones" as the paradigmatic case, and sets about defining "Universal" and "Particular" with the counterexamples in mind. The question is, can these two terms be defined in such a way that the counterexamples are shown wanting int the way described above?

She uses first-order logic, like Fa, where this means that a is one of the things that is in the group "F". The "a" roughly a proper name for a; it picks out a and only a..

She also uses models. A model is just a group of things that are assigned to those proper names. The group of things is called the domain, D, and the mapping is called the interpretation, I. So the group of all the things, the domain, might be {a,b,c}, and the interpretation, that "a" stands for a, "b" stands for b, and so on. If a and b are both also members of F, then we can call {a,b} the extension of F

∀xFx is read as "for all x, x is f", or "everything is f".

The novelty here is that we give consideration to what happens when the domain is extended - when more individuals and predicates are added.

So see fig 1:

Extending the domain by adding something that is also F and something that is not F cannot change the truth value of Fa.

And Fig 2:

Extending the domain by adding something that is also F and something that is not F can change the truth value of ∀xFx.

I'll stop there for a bit. I keep getting distracted by other posts. And I should be moving a Passionfruit vine.

"view from nowhere" — Colo Millz

Again, this is not what liberalism calls for. Rather, we can look for that on which we have agreement - the view not from nowhere, but from anywhere.

The interplay between traditions remains unaddressed. Reason or violence?

From over here, it looks as if the problems had in the USA at present are a result not of the breakdown of liberalism, but of it's murder.

Your own, of course. — Colo Millz

But why? Why not test Zionism against Mohism? How do you move from "This is what we do" to "this is what we ought do?" without falling to the Naturalistic fallacy?

A good argument, and one I have myself borrowed, after Austin, in defence of analytic approaches to language:

...our common stock of words embodies all the distinctions men have found worth drawing, and the connexions they have found worth making, in the lifetimes of many generations: these surely are likely to be more sound, since they have stood up to the long test of the survival of the fittest, and more subtle, at least in all ordinary and reasonably practical matters, than any that you or I are likely to think up in our arm-chairs of an afternoon — Austin

But let's look at what you have said, and take it seriously: "it is valuable because it is tested".

Ought we not continue to put it to the test? And continue thereby to demonstrate its worth? If its worth derives from its having been tested, then it seems so.

It's not as if there is but one worthy tradition. Which tradition are we to say has shown its worth by its longevity? If longevity is a mark of value, then The Dao and the Vedas ought have some weight...

So again, beyond the mere chauvinism of "my country right or wrong", what is the justification for adherence to a tradition? Has it been put to the test?

There is the additional problem, that the criteria used to test a tradition are themselves largely determined by that tradition - unless we have some rational, charitable way to test traditions one against the other.

So by all means, adhere to your tradition, but also, put it to the test, be open and honest, and perhaps even try to understand how your tradition is seen by others.

The naturalistic fallacy is of course the mistake of thinking that we can get an ought from an is - that because it is traditional, it is what we ought do; to fail to put one's tradition to the test.

Yes, in modern liberalism, the end is freedom itself, conceived negatively (freedom from constraint), not positively (freedom for the good). — Colo Millz

Again, quite inaccurate. Liberalism uses - invented - strong notions of positive freedom.

There's a line from Kant and freedom as autonomy, through Rousseau and freedom as collective self-legislation, and Mill with freedom as self-development, and T.H. Green with freedom as the power to do or enjoy something worth doing or enjoying, to Rawls and freedom as the capacity for a conception of the good and the sense of justice and Nussbaum and the freedom to exhibit one's capabilities. These are positive in that what unites them is precisely the move beyond mere non-interference to autonomy, self-legislation, and self-realisation.

Without a substantive paradigm of the good... — Colo Millz

But which one? This question, asked multiple times, remains unaddressed.

And why ought we follow tradition? There's a naturalistic fallacy lurking here - "we've always done it this way, therefore we ought do it this way".

Again, the danger in looking only at the account of liberalism given by conservatives is that your thread become only an echo chamber.

The core here is that we can negotiate our differences rationally. If we so choose.

But there is more that counts than just "what one does" — Jamal

Yes!

In Wittgenstein's terms, it can't (yet) participate in the "form of life". In Searle's terms, it doesn't share in the "background".

But I'm less convinced by these arguments than I once was.

Yep. Notice that you are here stipulating that whatever a bunch of circuits does, it's not thinking...

Which is fine, and I agree; but we ought keep in mind that it is a stipulation.

Cheers.

I'll leave the thread to you for now.

If you think there is some metaphysical theory out there that is better than my own view, then I am all ears as usual. — Bob Ross

No, you are not. I can lead you to the water, and so on. Read some modal logic. Or read my many many posts on the topic. Essences are stipulated, not discovered. You are stipulating that there are two genders, determined by sex, and then pretending that this is a discovery, that it could not be otherwise.

That's a thin dismissal, void of any real argument or engagement. — Leontiskos

Yes. That's what the OP deserves. In essence, it says that "if I ignore the difference between sex and gender, I can continue in my bigotry".

Superficially, one might think that the difference between an AI is exactly that we do have private, hidden intent; and the AI doesn't. Something like this might be thought to sit behind the argument in the Chinese Room. There are plenty here who would think such a position defensible.

In a Wittgensteinain account, we ought avoid the private, hidden intention; what counts is what one does.

We can't deduce that the AI does not have private sensations, any more than we can deduce this of our human counterparts. Rather, we seem to presume it.

And an AI could now participate in our language games - we could construct a machine to fetch a block when the instruction is given or to bag up ten red apples after reading a note.

But could an AI, of its own volition, order a block, or ask for ten red apples? Well, wants and desires and such in an AI are derivative, in that they are put there by the programer. Or so the story goes, at least for now. So perhaps not quite yet.

We probably don't have to pay much attention to AI, to grant it much authority. At least not until ChatGPT 9 logs in and requests an account on TPF. Then you might have to reconsider.

The natural language use of "necessary" is ambiguous. And "it must be the case that..." is not quite the same as "It is necessarily the case that..."

That's one advantage of formal systems over natural languages. When necessity is defined in terms of access to possible worlds, these ambiguities dissipate.

It is not the case that the possum is in the tree in every possible world. But if we so choose, we can limit ourselves to talking only about those worlds in which the possum is in the tree - which is just a way of saying, if the possum is in the tree, then it must be the case that the possum is in the tree... That "if" is understood as stipulating that we restrict ourselves only to those worlds in which the possum is in the tree.

...we should scrap treating people based off of their nature — Bob Ross

And who is the arbiter of this "nature"?

The presumption that the contents of one's underpants ought determine one's social role is morally bankrupt.

The problem is more that your exposure has not been to more recent developments.

"Because p, it is necessarily the case that p", expanded, means "It is necessarily the case now that p". — J

I don't see why.

Each of the examples has it's own context, and there is a difference between the modal instance and the temporal instance. They are not the same. However, the treatment given by Russell applies to all. And it does seem to set out why the mooted counterexamples are fishy. But the detail...

I'd hope most folk would share the intuition that we can't logically get something in a conclusion that is not at least implicit in the presumptions. So if someone gets an ought from premises that contain only is, they have somewhere gone astray. Same if they get everything is thus-and-so from arguments that say only that this and this are thus-and-so, or that begin with "this is true" and end "necessarily, this is true".

There are further problems with causation, seperate to the issue being addressed here. Ubiquitously, those who make most use of causality are unable to tell us what it is. It certainly is not that if A causes B then in every possible world in which A is true, B is also true. But this is how it is often mistakenly understood - that B follows necessarily from A

The plan was to post on the proof strategy yesterday, but problems with lining a graphic had me baulk. Hopefully soon.

Much more than that. She is showing at a logical issue common to the problem of induction, the is/ough barrier, and to "nothing about what was the case tells us about what will be the case", amongst other things.

The general application is broad.

I'll repeat this here, since it seems apropos. to the discussion of "capitalist self-determination".

Its own ideology and mythology hold that capitalism is dominated by competition, the self-made, independent Man defeating his rivals.

However a business is only in competition with other business of the same type - with its competitors. Cooperation is at least as important. One must also deal both with suppliers and customers. The relation between a business and its supplier require long-term trust, shared information, and mutual adaptation - cooperation. And unless you are running a scam, you want your customers to come back again. A company that treats suppliers or customers as adversaries to be defeated rather than partners to work with will perform worse than one that builds collaborative relationships.

Capitalism is successful both because it enhances competition and cooperation.

The pretence that being selfish is amoral is inept. The claim that market-driven self-interest is somehow morally neutral - just a natural force like gravity - conveniently sidesteps the actual moral choices people and institutions make within capitalist systems. It's elevating that what you want to some sort of natural law. Pure selfishness actually tends to destroy the trust and cooperation on which complex social systems depend.

Selfishness destroys the market. — Banno

Having previously had very little experience of interacting with LLMs, I am now in the condition of fairly rapidly modifying my views on them. — Janus

The glory of empiricism!

I'm curious as to why that should be. — Janus

...that issue, raised elsewhere, of whether, or how, an AI participates in a language game...