Russell moves from the specific cases so far examined to the general case.

Start with a formal language L, containing a sentence Φ. All the language consist of are symbols and rules for stringing them together. For it to be of use, we give it an interpretation by assigning things to the variables. Each assignment is a model, and there are lots of different ways to make the assignments, so lots of different models - the set U.

And we can have relations between these models - R. The reaction might be having the same individuals up to a certain point, or having the same true sentences up to a certain time, or having the same rows of knitting up to a given row, and so on.

Definition 10 just defines a sentence as being R-preserved if for all models, if it is true in one then it is true in all the others that are related by R. Definition 11 just defines a sentence as R-fragile if whenever there are models in which it is true, there is an R-related model in which it is false.

Note again the lack of symmetry.

The General Barrier Theorem (Theorem 12) says that no R-fragile sentence is entailed by some satisfiable (true in some model) sentences that are all R-preserved.

Both the particular/universal barrier and the past/future barrier are special cases of this general result.

Cheers, Bob.

What is your definition of a chair? If you can't give one because you think it requires essentialism, then I think we need to hash that out first and come back to this. — Bob Ross

It's not that we can't "give a definition" so much as that definitions do not do what you think they do.

Others have carried the point. I'm sorry you can't see it. Read Austin or Wittgenstein some time.

So you seem to have something like

'You cannot skip eating, or you will die.'
Fundamental Purpose = Service Target (One's Own Group) × Final State
therefore, you ought not skip eating.

??

The Axiom of Purpose — panwei

What's that, then? I don't see other mention of it.

But statement A does not tell us what we ought do. It only sets out the consequence of a certain action.

In order to reach the conclusion "You ought not skip eating", one needs an additional premise. Perhaps "You ought seek not to die".

So your argument remains incomplete.

...your gender theory is very much in line with how aristotle may have responded in his time period to more modern and flexible ideas of gender... — ProtagoranSocratist

I'm not so sure. For instance, Martha Nussbaum's response to rigid Aristotelian essentialism would be critical, despite her drawing heavily on Aristotle herself. That cosmic teleology would be dropped. For Aristotle, teleology is immanent in nature itself. It's more Aquinas who would have it enforced by god. But we can do without either.

We're being sold a pup, an Aristotle crafted to suit religious ideology.

2. Humanity is constituted according to a paradigmatic form - a likeness or image that grounds its dignity and capacity for relation to that transcendent source. — Colo Millz

Here again is that presumptive pseudo-Aristotelianism, rife in the forums at present. It smuggles in a theological conclusion under the guise of metaphysics.

You began this discussion by giving your conclusion.

There's the bad faith that continues in your new posts. There's the misapplication of Gadamer. Entering into such a discussion by presuming the human dignity of Genesis is bad faith.

I think you and I are done here. That bit about not providing you with the walls to your self-serving echo chamber.

Look up the definition of a word in the dictionary.

Then look up the definition of each of the words in that definition.

Iterate.

Given that there are a finite number of words in the dictionary, the process will eventually lead to repetition.

If one's goal were to understand a word, one might suppose that one must first understand the words in its definition. But this process is circular.

There must, therefore, be a way of understanding a word that is not given by providing its definition.

Now this seems quite obvious; and yet so many begin their discussion with "let's first define our terms". — Banno

Notice that the dictionary definition, as a description of use, is post hoc? The use precedes the definition.

The question to hand is "which is to be the master?"; and my answer is, the use is the master of the definition. — Banno

There will be amongst us those who hold that there is such a thing as the meaning of a word; and that any worthwhile theory of language must set out, preferably in an algorithmic fashion, how that meaning is to be determined.

There will be others, amongst whom I count myself, who think otherwise, and will go along with quine:

Success in communication is judged by smoothness of conversation, by frequent predictability of verbal and nonverbal reactions, and by coherence and plausibility of native testimony.

If there is a philosophically interesting topic here it may be to compare and contrast Quine's critique of pointing as the source of meaning, with Wittgenstein's. It will not easily be found in a defence of pointing. — Banno

Here's what can be done by way of answering your demand for a definition:

An example of a biological appraisal: This body has two X chromosomes. A biological fact, normatively neutral.

An example of a gendered appraisal: Having two X chromosomes counts as being a woman. A social fact, and normatively loaded. — Banno

Here's why it's relevant to the thread:

The failure of your essentialism is that it mistakes having two X chromosomes for taking on the feminine role. It tries to introduce the normative stuff at the level of biology. — Banno

This is not a chair. — Bob Ross

You have to say that. You have to re-assert your arbitrarily chosen essence, your self- reinforcing monologue.

You do the same thing here:

That is not what bigotry refers to. — Bob Ross

points to the same problem.

You provide the evidence:

From within Caputo’s horizon we learn humility: the human is revealed to be creaturely and continuous with nature. From within the horizon of the Genesis story we learn dignity: the human becomes the bearer of meaning and responsibility. — Colo Millz

In this, you presume the consequence of the dialogue. My point is that your ‘fusion of horizons’ isn’t faithful to Gadamer’s method. Gadamer emphasises openness and vulnerability in dialogue; no horizon should be treated as immune or pre-determining.

But that's how you started.

You've doubled down on the invulnerability of theology. That response reinforces my fear that you are dealing in bad faith.

Show that your faith in Christianity is vulnerable, and you might gain some credibility.

That others have misused Gadamer is no excuse.

It's not AI; but these days, your conclusion is justified. It's "Arm", steam-bent oak, by Clark Bardsley Design, from Auckland, New Zealand.

Nice work, ain't it?

A chair on which one cannot sit. A certain approach to definitions and essences, displaced by a piece of nonsense. For those who can see it.

The barriers to entailment here concern logical implication. →, ⊃, ⊨, ⊢ and that sort of thing.

We can make use of Bayesian methods.

But tomorrow might well resemble today in ways other than the sun rising.

You are actively playing in to the role of victim.

Definitions

Cheers. Don't credit me; it's Wittgenstein, via Anscombe.

In my view, this makes ethics not the negation of science but its completion. — Truth Seeker

Compliment would be better.

To be clear, you are implying that traditional Christianity (viz., roman and orthodox catholicism) are ratshit. — Bob Ross

No. I've said that the arguments for your variant are ratshit.

We can stipulate whatever definitions we want. And provided we keep in mind that they are stipulations, that's fine.

But what I would do is set out for you examples of how the use of "sex" and "gender" differ. That's were your error sits.

...you don't have a chance of persuading others... — Philosophim

No one should be under the illusion that Bob or Leon will change their minds as a result of the discussion here. Our posts are a performance, to an audience. Eventually, as the ineptitude of the response becomes unavoidable, a thread like this becomes too much like kicking a pup. Then it's time to go back to expounding Gillian Russell's text.

Banno, my dear friend, you didn’t answer my question. — Bob Ross

Yes, I have.

You expect me to provide you with essences of sex and gender, failing to see that this very question is dependent on your essentialist framing of the issue.

The meaning of a term is seen in its use, not some abstract expression of essence. I've done what I can for you; its up to you to do the rest.

The difference is in the direction of fit. In science we change what we say to match the way things are. In ethics we change how things are to match what we say. Science tells us how things are, ethics, what to do about it.

It was behind my old thread, Demarcating theology, or, what not to post to Philosophy of Religion. But you might well start a secular version...

In so far as philosophy consists in linguistic plumbing, perhaps some presumption is required - keeping the sewage away from the drinking water.

Just to be clear, if this were my forum, I'd have removed this thread and blocked Bob and Leon.

But this is not my forum. And I have no desire for it to be my forum. This thread is interesting because some folk here have such ratshit ideas; explaining why they are ratshit provides some amusement. Were this my forum, it would be much less entertaining.

To misquote Groucho, I'd not join any forum that would have me as a moderator.

The pretence of victimhood is a cheap rhetorical move.

That wasn't clear from what I have already said?

Meaning is found in use, so there is always some ambiguity. But here we can be pretty explicit.

An example of a biological appraisal: This body has two X chromosomes. A biological fact, normatively neutral.

An example of a gendered appraisal: Having two X chromosomes counts as being a woman. A social fact, and normatively loaded.

The failure of your essentialism is that it mistakes having two X chromosomes for taking on the feminine role. It tries to introduce the normative stuff at the level of biology.

(I added the italicised "your" because there are variants of essentialism that do not promulgate the incoherence seen in your account)

...historically in the West negative attitudes towards homosexuality predominated prior to Christianity. — Count Timothy von Icarus

That does not match my understanding.

Latin culture worship the phallus, denigrating the passive participant in intercourse. It wasn't being homosexual that was mocked, but being penetrated. The dogma that same sex acts were sinful in themselves enters from Leviticus. It was Christianity that invented the notion of such acts being "against nature"

In fact, I haven't received a single private message complaining about this discussion. — Jamal

You will ruin the pretence of victimhood saying things like that.

Taking on the extreme, as is my want:

Reasoning employed in service of a prior commitment doesn't count as philosophical reasoning. For Christians philosophy is just commentary. Christians enter into philosophical discussions in bad faith.

In my understanding of Gadamer, a "fusion of horizons" is only available when the discussion proceeds in good faith; when the participants are open to the conclusion that they are wrong. Christian faith forecloses on that. A faithful Christian cannot engage in hermeneutical reasoning. Attempt to use Gadamer to blend theology and philosophy begins by misunderstanding him.

The whole enterprise of this thread is fatally flawed.

In knitting terms, the set up hasn't changed much. Each row is a time t, and has a colour, p, and the row you are presently knitting is row n, but the garment - a scarf? - goes forever in both directions.

The rather scary looking Definition 5 just asks that we consider two scarves, identical right up to an including the row we are presently knitting, but differing thereafter. The one is a future-switch of the other.

And we can add the notion of preservation and fragility. A row that is already knitted is preserved - no further knitting will change it. A row that has not yet been knitted is fragile - it might change.

And extending those terms to the temporal case, a sentence is preserved if true in M, and true in all future-switches of M (Definition6). It is fragile if true in M, but there's some future-switch where it's false (Definition 7).

And a sentence that is future-switch preserved is Past, (Definition 8), while one that is future-switch fragile is Future (Definition 9)

In the first-order argument, we found that we could not derive sentences about all the individuals from any set of sentences about some of the individuals. Here, we find that we cannot derive sentences about the future from sentences about the past. We are now well-positioned to construct a general account of barriers to entailment.

Now some considerations of the model - how the logic is to be interpreted.

There is a sequence of times, t₁, t₂, t₃... forming a set T, with one of them nominated as "now", n. There is a binary relation "<", understood as "t₁<t₂" means t₁ occurred prior to t₂.

"<" is

• Transitive: if t₁<t₂ and t₂<t₃ then t₁<t₃.
• Dense: there is a time between any other two times.
• Extendable: Any time has a time before it, and a time after it.
• Total: given two times, one is before the other.

So time flows in one direction - the breach of symmetry again. And it is continuous, goes forever into the past and the future and there are no gaps.

Yep, the set T is analogous to the real numbers. Russell chose this set up from among a number of alternatives, She might have chosen a different set, with beginnings and ends or analogous to the natural numbers rather than the reals, and achieved much the same outcome. Nothing in particular hangs on the choice of temporal formalism.

Every atomic sentence in the model is assigned either a 1 or a 0 (roughly, true or false) at each time by a function I, such the same sentence may be true at some time yet false at some other. So I may assign 1 (true) to p at t₁, and 0 (false) to p at t₂, and so on. I(p, t) = 0 means 'p is false at time t.

As for your question - whether I’m a moral realist - the answer depends on what kind of realism we mean. — Truth Seeker

If I may, there's an ambiguity in "realism" that needs sorting. There are varieties of moral realism which suppose that moral facts are much the same as physical facts, found lying about the place. That's hard to support. Other varieties just point out that there are true moral sentences. The problem is with the notion of realism, not the ethics.

The article now turns to applying this schema to other examples, starting with temporal logic - the grammar of time.

Some explanations.
P - past existential, so Pp is read "p was true (at some time) in the past"
F - future existential, so Fp is read "p will be true (at some time) in the future"
G - future universal, so Gp is read "p is going to be true in (all of) the future"
H - past universal, so Hp is read as "p has historically (always) been true"

In the particular/universal first order logic case, the model was extended by adding more individuals and their predicates. Here, the model is extended by changing a future. The mooted barrier becomes "No set of premises about the present or past entails a sentence about the future".

Just as a particular fact will remain true when the model is extended, a past fact Pp will remain true into the future. And even as ∀xFx can become false by adding more individuals, Fp may become false if the future turns out differently than expected.

So we have a structure similar to the previous first-order logic example, but in the place of extending the model we have what Russell calls "future switching", switching amongst alternative futures.

For the purposes of this temporal logic, sentences about the present behave in the same way as sentences about the past, so we can consider the "P" operator to also apply to them.

So your overall point is that those five interactions didn't "contend with (your) view"?

I don't follow that at all. They might not be what you were expecting, but they form a neat dialogue on your claim.

Again, your "epistemic symbolism of society’s understanding of the ontological reality of sex" just seeks to collapse gender into biology, which is again no more than your failure to recognise the distinction between sex and gender.

It's bang on.

Yes, I did:

You still haven't contended with the revised version I asked you to. — Bob Ross

Yes, I did:

What a terrible argument. A woman wearing a dress is not like a triangle's having three sides. There are no triangles that do not have three sides, but there are women in trousers. — Banno

And so on. I'm sorry you haven't been able to follow these connections. This is how threads of this sort become echo chambers, one party repeatedly demanding accounts the other has already given because they do not match the expected response.

The fact of the matter is that no one from the opposition, expect perhaps Jamal, has even tried to contend with the OP — Bob Ross

That's an extraordinary claim.

Taking on the role of the victim in the face of overwhelming critique is a cheap, purely rhetorical move.

Of the very same post:

↪Banno - A substantive post. :up: — Leontiskos

I don't see how these comments help forward the conversation. — Bob Ross

So it was a substantive post that did not help forward the conversation.

Perhaps the problem is not with my post?

To be honest, this thread is revealing itself as liberals being incapable of discussing an alternative gender theory. Virtually no one has even quoted or tried to contend with the OP so far: instead, they are trying to cancel me. — Bob Ross

Well, again, that's because you are not discussing an alternative to gender studies, but foreclosing on it. Your claim that gender is just biological sex has been thoroughly debunked.

Banno, why do you straw man me? — Bob Ross

If you think that my interpretations of your claims is a straw man, one possibility worth considering is that your account is not as coherent as you suppose.

Here's my critique in outline.

1. Aristotelian essences are hollow.
2. There is a usable and interesting distinction to be made between biological sex and socially inaugurated gender.
3. You account of Aristotelian ethics is shallow. Other Aristotelian theorists, such as Nussbaum, do not reach the conservative conclusions of your account.
4. In claiming that certain gender traits are biologically determined, you move form an is to an ought, a logical error.
5. I hold that the stance you take concerning issues such as sexuality and abortion to be immoral.

It might not be obvious where this break of symmetry originates. It is built in.

In the knitting analogue, we only ever add rows, never deleting them. There's the broken symmetry.

Atomic Existential statements, such as Fa or "Row three is green", once made, are never taken back. This goes for all particular statements - it's the definition of "particular".

But universal statements, once given, can be made false by new particular statements. That's the definition of "universal".

The intuition sometimes has to give way to the logic; but with practice the intuition can change to match the logic.

The definition of a particular sentence is that it can't change when we knit more rows.

The negation of the particular sentence "Row one is green" is the particular sentence "Row one is not green". However, the negation of the universal sentence "All rows are green" is the particular sentence "Not all rows are green". This break in symmetry is central to what comes next.


Contraposition
∀xFx ⊨ Fa, by contraposition gives ¬Fa ⊨ ¬∀xFx. This looks like particular ⊨ universal... but it's not, because ¬∀xFx is particular, not universal. Negating the universal in this case yields a particular.

In terms of our knitting,

∀xFx ⊨ Fa. if every row is green, then we can conclude that row one is green. A universal implying a particular.
¬Fa ⊨ ¬∀xFx. If it's not true that row one is green, then it's not true that every row is green. A particular implying another particular. Contraposition doesn't generate counterexamples to the particular-universal barrier thesis, because the barrier only blocks inferences from particulars to universals, and ¬Fa ⊨ ¬∀xFx is an inference from a particular to another particular. Note the broken symmetry.