Same with you.

'mon, do you need to insult people like that.

Yeah, I like it, it's a bit divergent, but on topic. "Any particular man is mortal" introduces a quantifier almost obliquely. In first order logic it would be parsed "For all x, if x is a man then x is mortal", but now I am wondering if there might be an alternate parsing in some alternate logic. — Banno

Never seen one. I vaguely recall learning about it as a way to think of what happens when you "undo" universal instantiation to get the universal quantifier back in a natural deduction proof. But it crops up much more, without caring about the order of the underlying logic, in maths proofs. You end up saying "let x be a (blah blah)", at the start of a proof, then "every x is a (blah blah)" at the end, of many. But you do so in natural language. So you don't care about the underlying formal logic.

EG you'll write it the same in the Cauchy sequence proof here and in the proof that at least one solution of (x+1)(x-1)=0 is less than 0... Even if the first result needs an underlying second order logic and the second just needs first order. You write it all the same.

I think the formalisations are thus red herrings in the discussion regarding quantifier variance. Since if even mathematical reasoning has both ambiguity and commonality regarding the underlying logic and its quantifier introduction rules, why would we expect logic to behave as more than a prop, crutch or model of quantification in natural language? Never mind ontology!

But I'm not sure how this relates to — Banno

It was an example of people disagreeing about quantifier introduction rules. That one is tricky!

It is a fact that not everyone in every context means the same thing by "all" or by "some". But this is nowhere near the sort of variance our heroes are promoting, in my limited understanding. — Srap Tasmaner

Just to be clear, what do you believe our heroes are promoting? I'm not sure any more.

Second edit; that is, "...for arbitrary a..." just is "for any a you might pick", or "for any a" - it's introducing a quantifier. — Banno

It's just this.

It might but I don't see that it does - those unbound variables make it hard to see what is going on here. But (Pa→Qa) does not allow (∀x (Px → Qx))... You've lost me. — Banno

You can introduce the quantifier onto (Pa->Qa) to get (for all x P(x)->Q(x) ) if you made no assumptions about a anywhere in your reasoning. If someone just comes up to you and hands you some constant with some properties, you cannae, but you can show that if (P( a ) for arbitrary a) then (P( x ) for all x).

In order to recognise a failure of translation, you must understand what success would look like. — Banno

How does translation play into it here? What I would get from successful translation is a set of equivalent uses, you've not provided a guarantee that such an equivalence between utterances involving quantifiers would preserve quantifier rules.

I am willing to go down the individuation and intension route. But I'm not particularly prepared for that kind of discussion.

(1) This shouldn't be the usual one side saying "There are more things in heaven and earth..." and the other saying "No there aren't." — Srap Tasmaner

Yes. I'm of the opinion that there is something substantive here to talk about. Lots of substantive things in fact. One thing we've done so far is treating terms as individuated entities. I think you problematised that in a post here a while back regarding the neuroscience. That whole issue gets occluded once you can already apply a name to a thing. But the metaphysics in that kind of discussion gets dicey real fast and the science gets incomprehensible even quicker.

I like the idea of each side being baffled by what the other could possibly be thinking. — Srap Tasmaner

Is that bafflement gesturing toward incommensurability? I could see people having irresolvable disagreements about how they (their bodies?) individuate entities, even if they agree on everything under heaven and earth. Maybe related to intension again.

But I am far less incline to agree that these are instances of a variation in the quantification rules themselves. — Banno

How would you account for people's differences in use? As in, plenty of people don't know that (A implies B) implies (Everything which counts as A also counts as B). That slide from propositional to first order logic you get from the diagrams. Their quantifier introduction rule would vary over people, as you wouldn't have universal generalisation working the usual way for at least one person. (P(x)=>Q(x) where x is arbitrary lets you derive (for all x P( x ) => Q( x ) ), and they can't do that).

The challenge I see that presenting is that people can believe statements that block applications of inference rules, or otherwise not believe in appropriate inference rules. Even when two people share the theorems of the underlying logic... You just have to hope that every person innately believes every theorem. If they don't use the quantifiers in the same way, they don't have the same intensions over people.

Nothing to do with *kinds* of objects here, but to do with *how* we range over a collection of values. — Srap Tasmaner

I think I see what you mean. I just want to devil's advocate though, that you can provide an extensional definition of the filter in that case, and that would turn it into a kind (it'd be an indicator function on row number, right?).

Another way of parsing that is the hypothetical disagreement between the two analysts is whether they're quantifying over all the rows, or all the rows satisfying a predicate. There's a stipulation that you're using the same spreadsheet in the background.

Though I do think that's a dodge for various reasons. That spreadsheet mean evaluation could be made into a macro and output somewhere, so any difference would be counted as part of the spreadsheet's normal function. In that case one analyst who believed the formula did X and one analyst who believed the formula did Y would be able to disagree on the interpretation, and thus disagree on the intension of introducing quantifiers over spreadsheet related expressions. As in, if Alice thought the spreadsheet was taking a raw mean, and Bob thought the spreadsheet was taking a trimmed mean. They could both agree to the statement "the mean is less than five", while not having the same intension for mean.

Thinking it through, I think this is related to intension quite heavily. Bob could introduce the quantifier (given his premises of a trimmed mean) that "there doesn't exist an X such that X in in the upper and lower 1% pf the distribution of quantities which goes into the mean" based on his belief that the trimming predicate removes such entities. And Alice could not, based on the belief that those quantities were not removed.

I do think, though, that you could provide another extensional dodge there. By introducing a modal operator to model the differing beliefs, and perhaps a modal operator to model the differing possible spreadsheets. Then you'd end up with Alice and Bob agreeing on quantifier meaning, given fixed beliefs and with fixed possible world with a fixed domain in each world, and a fixed symbol set shared between them... and fixed symbols in the underlying language etc.

I suppose the question of pragmatics rears its head again at that point, does it even make sense to think of introducing or eliminating any quantifier having an exact specification. Or is it simply that the majority of such uses are relatively insensitive to differences in intension. And are later qualified or disambiguated with inquiries into another agent's modal status.

I dunno OLP heads, "is" sure crops up in a lot of language games with different grammars. Almost as if there are different uses of it!

Violent Faculties by Charlene Elsby

Sadistic horror written by a philosophy PhD. The plot is a rogue philosophy prof literalising thought experiments on willing or coerced subjects. Think it'd give some of you lot a chuckle.

They're clearly being confused by maths. They think that because a geometric series of time intervals can have a finite sum and because this geometric series has the same cardinality as the natural numbers then it is possible to recite the natural numbers in finite time. Their conclusion is a non sequitur, and this is obvious when we consider the case of reciting the natural numbers (or any infinite sequence) in reverse. — Michael

I imagined you were arguing toward the claim that anything which has no first event is not physically possible. Which is a bit different from the geometric series angle. Which shows that there are logical possibles which have no first event. The sticking point between you and us series heads seems to me that you've been arguing on the basis of "no first event" blocking logical possibility, which would then block physical or metaphysical possibility. Which is why I intervened, because while I agree with your argument strategy, the means you were arguing for it were imprecise enough to admit the geometric series counterexample. I do think your points can be steelmanned though.

You might come up with a mathematical model for "recitation of first element", which maps a series to its minimum or maximum. Since the series has a minimum, you can do that. It has no maximum, so you can't. It's the same principle as asking someone to count backwards from infinity. And then it's true, it's not logically possible to "recite" backwards from infinity, or "recite" the maximum of an increasing geometric series.

Going back to the first page of the thread, such a "recitation" for the state of Thompson's lamp, or just isolating the "state", could be construed by taking a time period and associating it with the states the lamp takes in that time period in order. If Thompson's lamp has states in a time period, they'll be picked out by that. However, the function which generates the values of Thompson's lamp has the property that for every time period X, there exists a time period Y such that if max( Y )>max( X ) then Y contains at least two states (on or off). You get those by going further toward the completion time. That property implies there is simply no "state" of the lamp at limit of 2 minutes. So it having a state is logically impossible.

What makes Thompson's lamp a paradox, then, is a physical or metaphysical intuition about the concept of the state of the lamp. There needs to be a beginning to the process, and it needs a unique isolable end state. Both the geometric series and Thompson's lamp have no unique isolable end state.

That will then bottom out in an inquiry about whether there are physical or metaphysical possibles which have non-unique and non-isolable end states.

I don't think it is the extension that is ill defined with that case, but rather a leveraging of the fact that the pieces are made of infinite points each, and you don't need 'more natural numbers' to count each one of them twice.. — noAxioms

I'm pretty sure that one comes down to being able to split the pieces up into pieces that aren't measurable - IE can't be assigned a size - in a clever way, then applying some cool transformation to them that blow them back up into the sphere. But that's by the by.

OK, here you seem to use 'metaphysically possible' to mean 'possible in a universe with different physical laws'. But I don't find that very distinct from logically possible. — noAxioms

I think that's a species of metaphysical possibility - a different physics. What would distinguish that from logical possibility, in my book, is that there are simply more ways of being noncontradictory than being unable to exist in our universe. Like flibbertygibbets. And nonmeasurable sets. And, maybe, abstract categories.

I don't think it impossible for a geometric series to complete. — Michael

Good! Then it's logically possible for it to. An infinite number of things can complete without blowing up logic.

Actually, I've been asking about the distinction between those two. Nobody has really answered. A nice example (not a supertask example if possible) of something that is one but not the other would be nice. — noAxioms

I don't have a particularly clear cut example to distinguish the two. And I don't know if the concept of logical possibility survives the existence of nonclassical logics. But what I envision for logical possibilities are things which don't by themselves, and with no other contextual information, entail a contradiction. Any possible fact is logically possible.

As for the merely logically possible - as in logically but not metaphysically possible - , I imagine procedures like Banach Tarski. Turning a sphere into two spheres using only the material in the first sphere. But that's just because I can't imagine a concept of space used in metaphysics (like extension) that makes central use of non-measurable sets (things with ill defined extension in principle).

Physically possible? That's getting hard. A universe that contains violations of the second law of thermodynamics is metaphysically possible. Like Lord of the Rings, Harry Potter. In the sense that there's a self consistent narrative going through those works of fiction whose behaviour is impossible to translate to our universe, those universes would be metaphysically but not physically possible.

So when I hear @Michael talking about the impossibility of a geometric series "completing" (so to speak) due to being unable to recite the terms in finite time, I hear a use of a metaphysical or physical context of events, speech and recitation which just isn't there in the definition of mathematical terms. And in that regard @Michael's response addresses physical or metaphysical possibility, rather than logical possibility.

The only reason I intervened is to pedantically point out the distinction, and that Michael let it slip for at least one post.

↪fdrake So you’re claiming that it’s logically possible to have recited the natural numbers in descending order. That’s evidently absurd. — Michael

Nah. That's an appeal to metaphysical or physical impossibility. Not logical impossibility!

The sequence {1/2n} for n=1 to infinity has a finite sum, 1. That's numbers and an infinite set. So yes, geometric sequences have a model in set theory. They also have a finite sum, no last operation, and contain an infinity of operations. You can think of the partial sum, up to the nth term, as the total time elapsed on clock whose ticks last 1/2n. The limit construction exists without contradiction. The reason being that the sequence gets arbitrarily close to its greatest lower bound (0). And there is no smallest element, since the greatest lower bound isn't in the set.

How can a sequence of operations in which each operation is performed only after the previous operation is performed complete without there being a final operation? — Michael

So there is no final operation, there is an infinite sequence of operations, and it completes in a finite time. Since the completion time is just the limit of the partial sums.

There's your model. Logically possible. I leave now.

OK, that would be pretty much what has been the topic of discussion this whole thread. — noAxioms

I imagined you lot were talking about metaphysical rather than logical possibility. @Michael made a comment to the effect that such a construction was logically impossible. Which would be odd, seeing as such an object has a model in set theory. Even if it's not physically or metaphysically possible. All I wanted to add.

The sum of an infinite set of identical finite numbers is not finite, no matter how small the number being summed. It needs to complete in finite time to be a supertask. — noAxioms

Aye that is true. I wrote wrong. I was imagining a clock that speeds up in its ticking to ape a convergent geometric series.

The fact that there is a bijection between the series of time intervals and the series of natural numbers and that the sum of the series of time intervals is 60 does not prove that the following supertask is metaphysically possible: — Michael

The lamp starts off. Every time the clock ticks a lamp turns from off to on or from on to off as applicable. Thomson's lamp shows that this leads to a logical inconsistency. — Michael

Might show it's logically possible tho.

This is not a supertask, not even as the tick rate increases arbitrarily high, because the cake (if it is continuous, which a physical one isn't) is going to take forever to consume at any clock rate. — noAxioms

Why? The ticks per second is also going to infinity.

I don't really think it matters whether this is a supertask or not, though. It was an attempt to give an example that hits @Michael's argument.

The lamp starts off. Every time the clock ticks a lamp turns from off to on or from on to off as applicable. Thomson's lamp shows that this leads to a logical inconsistency. — Michael

By providing a standard mathematical object which is infinite, has no final element, tends to an end state, and has an infinite number of occurrences ("steps"), but occurs in finite time.

What does it mean for every operation to occur without some final operation occurring? — Michael

A clock ticks 1 time per second.
You start with a cake.
Every second the clock ticks, cut the cake in half.
Make the clock variable, it ticks n times a second.
The limit clock as n tends to infinity applies an infinity of divisions to the cake in 1 second. There is no final operation.

There's nothing logically inconsistent in this, it's just not "physical".

@Banno @J

(ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism;

That is what you see in practice though. There are no modal operators in propositional logic. But both modal and propositional logic are great. Their semantics also differ considerably. When you write the possibility and necessity symbols in a modal logic, you quantify over possible worlds. When you write them in a quantified modal logic, you quantify over worlds, and there's also quantification within worlds in the usual logic way.

Those quantifiers are introduced differently, and as the paper "Quantifier Variance Dissolved" notes that provides a strong argument for a form quantifier variance without a reduction of quantifier meaning to underlying entity type it quantifies over, and without committing yourself to the claim that there's a whole bunch of equally correct logics for the purposes of ontology.

It's gonna be hard to write them down.

Though something like the act of marrying two people is done with language, rather than expressed by it. Though in a less restricted sense of expression and meaning, perhaps the meaning of "I do" is the act of agreement. And in that sense "I do" expresses an agreement to the contract of marriage. But that says nothing more than an agreement was made.

Perhaps then, the use of language expresses nothing at all. It simply does. Transforming situations to other situations. Expression would then be a metaphor for an element of that transformation. A folk tale for coordinating our actions before, during and after our actions transform us.

Naw. I close now.

A not so gentle reminder to keep the distinction between zionists and Jews, and pro-palestinian/anti-zionist people and anti semites in your head at all times. The same goes for Hamas and palestinian people+Hamas and the Islamic. If you equivocate, you just end up calling each other racist for no reason. Stop it. That goes for you @BitconnectCarlos as well as @Lionino, and @Benkei should have known better.

(Gallup pole from 2023) Americans say they read an average of 12.6 books during the past year, a smaller number than Gallup has measured in any prior survey dating back to 1990. U.S. adults are reading roughly two or three fewer books per year than they did between 2001 and 2016.

My completely unreasonable hunch is that this poll was answered by book readers rather than the general populace. 1 book a month is a lot for almost everyone I know - including non-dense fiction readers!

I fear there's long term effects on our societies with this. What do people think about this? — ssu

My second completely unreasonable hunch is that the decline of book reading is a symptom rather than cause of declining levels of education.

eliminative materialism. — Wayfarer

Dennett's not an eliminativist though. He's a critic of it.

One perspective (Dennett, 1987) is that propositional attitudes are actually dispositional states that we use to adopt a certain heuristic stance toward rational agents. According to this view, our talk about mental states should be interpreted as talk about abstracta that, although real, are not candidates for straightforward reduction or elimination as the result of cognitive science research. Moreover, since beliefs and other mental states are used for so many things besides the explanation of human behavior, it is far from clear that our explanatory theories about inner workings of the mind/brain have much relevance for their actual status.

From SEP. He isn't even an eliminativist toward "experience". Just thinks it's thought of badly.

Oh yes absolutely. I have in mind Austin's comment that while word use should be the first word on a topic, it need not be the final one!

Thanks for the reference. I'd highlight, in another context, that there's room for revising an understanding in ordinary language for some purpose. Like "know" could mean something different in the context of a mathematical proof, a scientific experiment, or a history book. But it's not particularly relevant. Even if those understandings may even be better in context than the pretheoretical one which we all engage with.

Well that paper is very similar to the debate we're having.

I suppose it's also why people have invited you to reconsider the kind of things that can count as direct realism!

Well we're kinda screwed if we can't agree what we're disagreeing about.

And then, of course, there are direct realists who view experience/perception as the actualization of a capacity that persons (or animals) have to grasp the affordances of their world. Brains merely are organs that enable such capacities. — Pierre-Normand

Yes, that's a species of externalism isn't it?

Edit: removing some laziness in the question. There's the adage that externalism means "meaning ain't just in the head", ecological perception like Gibson sees signs and capacities for acting in nature. Environmental objects themselves are seen as sites of perceptual interaction, which imbues interactions with them with a dynamic/semantic content.

And this would be wrong. — Lionino

Eh, a perception is still an event in the world. Like your body adjusting under a load is proprioception.

I think that's one of the central axes this debate is happening on. Direct realists in thread seem to see experience/perception as a relationship between the brain and the world that takes place in the world. @Michael seems to see experience/perception as a relationship between the brain and the world that takes place in the brain.

Edit: so we've got externalism+directness+action vs internalism+indirectness+representation.

No. Experience exists within the brain (either reducible to its activity or as some supervenient phenomenon), whereas proximal stimuli exist outside the brain. So neither proximal stimuli nor distal objects are constituents of experience. — Michael

I think I understand. So for you, this process goes like:

distal object -> proximal stimulus -> interpretation -> mental phenomenon

and/or

distal object -> proximal stimulus -> interpretation -> experience

and for you, "interpretation" and "mental phenomenon", as steps of the process, are what perception is?

Mental phenomena; colours (inc. brightness), shapes, orientation. — Michael

Proximal stimuli?