quantification in the restricted way math does. — Srap Tasmaner

Does it? Do you mean something involving x∈R as alluded to previously? So the drift from

∃x (x∈R, f(x) = 0) — SophistiCat

to

∃x∈R ( f(x) = 0) — SophistiCat

isn't a mere abbreviation, and ∈ a mere binary predicate? (In math?)

(a) what are we talking about? — Srap Tasmaner

What things, or what kinds of thing?

The only thing that all chairs have in common is that we call them all "chairs". — creativesoul

:party:

But then it gets complicated... all and only chairs, or some more than others? We all call, or some more than others?

Bongo's chair.

I might remark, 'Listen to those dogs howling.' If someone else tells me, 'Those aren't dogs; they're coyotes,' they're not telling me I assigned the wrong predicate to an object, they're telling me I picked the wrong sortal. — Srap Tasmaner

I.e., that you assigned the right predicate to the wrong things? Apparently so:

the main error seems to be picking the wrong collection of individuals to consider attributing "howling" to. — Srap Tasmaner

In which case I get:

that what I'm calling "sortals" here might be how we specify the domain for our variables on the fly. — Srap Tasmaner

... As per @jamalrob's comment and probably others.

But "specifying a domain" is flagging up a likely rupture of your individual discourse from the wider "web" :wink:, e.g. your specified domain might be fictional, or (per the OP?) hypothetical, or for other reasons resist identification with any more widely recognised domain. Mending ruptures is difficult, and hence (maybe):

the plain language of that sentence ("I thought the coyotes were dogs") is ludicrous. — Srap Tasmaner

But then, isn't mending or patching together and reconciling domains what science is about? In which case I am surprised if,

What makes me uncomfortable about the predicate calculus — Srap Tasmaner

... is the quantifiers requiring us to make our selections in terms of predicates, define our sorts in terms of attributes. Which it does, so that the selection can be from a maximally inclusive domain. Maybe?

Oh dang. Thought it might misfire, it did and I'm sorry.

Probably I don't even understand "disingenuous". I meant it in an admiring way, thinking you might have skillfully cornered a hard-problem-ist.

I'll stop digging.

Are you just concerned about (not) making metaphysical commitments when we write formulas?
— SophistiCat

Yes. — Pfhorrest

But, the million dollar question is, Does the existential quantifier, ∃, need to make a distinction between fact and fiction?
— TheMadFool

No. — bongo fury

tl;dr: 'Everything is a unicorn' and 'Something is a unicorn' both commit you to there being unicorns. 'Nothing is a unicorn' doesn't. — Srap Tasmaner

Although of course it does commit you to there being non-unicorns :wink:

the wiki page for "ingenue" (from which "disingenuous")

I simply answered the question as given, and do not know what specific part of the hard problem you feel neuroscience cannot answer. — Philosophim

:rofl:

:ok: :up:

So by the time we get to asserting all of modern science every time you ask for the salt, you'll still be fine, because holism, right? — Srap Tasmaner

Obviously you're being sarcastic, but again I have to be grateful for being at least half understood. :smile:

you don't mean the same thing I do by "assert". — Srap Tasmaner

I'd be thrilled if anyone in this thread were prepared to dissolve statements, assertions, beliefs, propositions and truths into one colour — bongo fury

Which is a bit extreme :snicker:

Of course, all manner of things are implied.

But does anyone think that, in saying "A dog is barking", you are asserting the existence of dogs? — Srap Tasmaner

Yes, me, exactly in the sense of,

You're assuming or presupposing there are dogs, and so far as that goes you are committed to the existence of dogs, in Quine's sense. — Srap Tasmaner

(Math doesn't suffer from this weirdness — Srap Tasmaner

How is it weird?

It's not like when you conclude that there is a point within this interval such that ..., you are asserting the existence of points, whatever that would even mean.) — Srap Tasmaner

I think it's exactly like that, and we end up here on TPF discussing what it might mean.

@TheMadFool One thing at a time please.

The "for all", universal quantifier never makes an existential assertion. — TheMadFool

Not so.

why does the particular statement, "some A are B", ∃x(Ax & Bx) have to be translated as "there exists something that is an A and a B"? — TheMadFool

It doesn't. ~(∀x(~(Ax & Bx)))

Hence the square of opposition stuff.

But the configuration of prefixes '~∀x~' figures so prominently in subsequent developments that it is convenient to adopt a condensed notation for it; the customary one is '∃x', which we may read 'there is something that'. — Quine, Mathematical Logic

Meinongian quantifiers — Srap Tasmaner

The substance and conclusion of which appears to be pretty much "nothing to see here". As in, no answer to Quine.

If I write "This Dodo is brown" it's logical equivalent is ∃x(Dx & Bx) but we know Dodos are extinct and the logical translation of that is ~∃x(Dx) — TheMadFool

Right... were you unsure whether these would turn out to be compatible or not?

But, the million dollar question is, Does the existential quantifier, ∃, need to make a distinction between fact and fiction? — TheMadFool

No.

The word "exists" has a metaphysical meaning — TheMadFool

Matter of opinion :wink:

Statement 3 makes an existential claim i.e. unlike statement 2, statement 3 asserts that unicorns exist but that's not true — TheMadFool

Fiction generally isn't.

Clearly, ∃x translated as "there exists..." is an issue. — TheMadFool

Why?

Still, that settled by following Quine's clear preference...

Both quantification functions, ∃ and ∀, only specify how many values of the variable they quantify make the statement that follows true, — Pfhorrest

Yes, i.e. they specify how many (actual, existent) things in the domain of discourse the predicate or open sentence is true of. So no call for the "only".

and the statement doesn't necessarily have to be asserting the existence of anything, — Pfhorrest

Do you mean in something like the way talking about numbers (or fictional characters) leaves it open whether they actually exist?

Sure, but that way is to talk as if they do actually exist. So ∃ still specifies that at least one (actual, existent) thing (number or unicorn) satisfies the predicate.

Another possible source of disagreement and quandary is "value of a variable", which equivocates badly between word and object, as "numerical value" equivocates (but shouldn't) between numeral and number.

I was about to continue: "That settled by consulting a dictionary..." but no such luck. So yeah, very likely source.

But there just is no fact of the matter whether a word or picture is pointed at one thing or another. No physical bolt of energy flows from pointer to pointee(s). So the whole social game is one of pretence. — bongo fury

Unless you're a biosemiotician? :chin:

I am opposed to abortion but do not think the state should decide. — NOS4A2

Exactly my position on metaphysics.

To think, to legislate, to act with intelligence, one has to draw a line — unenlightened

Or two lines. If far enough apart they can be as blurred as you please, yet maintain an absolute distinction.

But my question was really about what point the whole sentence was intended to make. — Janus

This one:

A nominalist suspects that the motivation is a mystical fascination with abstractions (e.g. "the cat's being on the mat") and the possibility of grasping them; — bongo fury

... or of combining them with mysterious forces.

Sure, if it works, why not. My interruptions were just a shout out for the more down to earth option.

A calculator understands maths in much the same way as the room in the Chinese Room analogy understands chinese. — Malcolm Lett

Yep.

It has some non-negligible understanding of the maths that it's programmed to work with. — Malcolm Lett

Surely not.

If it had no understanding, then it wouldn't suffice as a calculator. — Malcolm Lett

Why ever not?

The explanatory gap is what a mechanical conception of nature creates. — apokrisis

Couldn't it just be what a wrong conception of consciousness creates?

Hence why biologists and neuroscientists are arriving at semiotics as an alternative conception of nature. — apokrisis

Great, but have they seen the difference between syntax (automatable) and what Searle (somewhere) calls a "proper" semantics: the ability to follow and predict the entirely pretended and conventional connections between words and actual things?

Or are they (or you) mistaking an efficient, automatic, syntactic correspondence (e.g. of proteins with DNA sequences) for the other, far more sophisticated social game?

How exactly does the liar sentence require mucking about with any other kinds of sentence than the declarative, assertoric kind?

The only kind, after all, that we ordinarily expect to divide up into true and false instances?

And why, when we do happen to be focussed on that kind, the sudden skepticism about them so dividing, and the addiction to complicating the issue by introducing beliefs, assertions, propositions, attitudes etc?

A nominalist suspects that the motivation is a mystical fascination with abstractions (e.g. "the cat's being on the mat") and the possibility of grasping them; where one ought to be content to point the predicate "is on the mat" at a cat. (Or the predicate "is on" at a sequence of two appropriate objects.)

I'm going to muddy the waters a bit. — Srap Tasmaner

I'd be thrilled if anyone in this thread were prepared to dissolve statements, assertions, beliefs, propositions and truths into one colour. But belief in the abstractions and the supposed distinctions is no doubt too dyed into the wool.

Bare unspoken sentences that implicitly assert themselves are quite handy for doing logic, of course. — Srap Tasmaner

Arguably, no statement is ever entirely bereft of any illocutionary force, and [such that it?] might be considered a "dud ticket". But we use them quite routinely when doing logic, so I'm not too concerned about that.
— Banno

Great, and when you do logic, aren't you writing (or uttering) tokens, and excluding or contextualising (e.g. attaching "not" tokens to) contradictory ones, from within a system of proliferation of assertive tokens? — bongo fury

We are token-producing agents, in the material world.

What did you mean by "Nowt (presumably "not"?) so abstract as 'semantic content'"? — Janus

https://en.m.wiktionary.org/wiki/there%27s_nowt_so_queer_as_folk

Janus

Even taking "proposition" as a term of art, it's not at all clear that this is what we ascribe truth to. Some concept of force, and in particular assertoric force, seems to be required. — Srap Tasmaner

Ah, propositions not abstract enough...

So, examples please of sentences (or if you must, propositions) that are truth-apt only when asserted?

There is a distinction between the statement "there is a fire in the next room" and the assertion "there is a fire in the next room.
— Banno

The second is a sentence token having, like a money token, currency and value in a system of interpretation. As such, within that system (of interpretation and production of sentence tokens as assertions), it is licence to produce more tokens, with similar value.

The first, if not an assertion, is outside the system - a dud ticket, a void note, an invalid vote. — bongo fury

Is the first somehow unable to be false?

I haven't said semantic content is "abstract". — Janus

A concrete example, then?

More modestly I would say that a proposition is the semantic content of some sentences or statements. — Janus

False modesty. :wink: Nowt so abstract as "semantic content".

Yes, of course, obviously the meaning of words, what they refer to, is established by convention, by praxis. How else? — Janus

:100: :up:

You're misunderstanding; I am not promoting platonism. — Janus

I don't want to be the Spanish Inquisition, but you did seem to think it absurd that true and false could apply to strings of words; and while this might have been for completely other reasons than the concreteness of words, or belief in beliefs and other mental or otherwise abstract entities (propositions and states of affairs) as the only rightful subjects for such predication, such beliefs do seem rife in this thread, and they seem to me an unnecessary cause of confusion.

The logic behind what I said is simple; the same proposition can be expressed in many different sentences, and when we say a sentence is true the meaning of 'sentence' as 'proposition' is the appropriate one. No platonism required. — Janus

By platonism I mean commitment to abstract entities, and so I would be glad to withdraw the charge (of an excess in this tendency) if it turned out you just meant to recognise a potential fuzzy set of (the "many different") sentences that were rough paraphrases of each other. Have true apply to any and all paraphrases by implication whenever they applied to one. But it seems clear you want to warn me that people round these parts believe in propositions as a separate class of entity. Well that's what I meant by "unnecessary platonism".



Talking of paraphrase, here are some nominalist paraphrases of "this sentence is not true":

• "this sentence fails to point its predicate at the object identified by its subject"
  
  
• "this sentence fails to point its predicate at its subject"
  
  
• "this sentence purports but fails to point its predicate at itself"
  

Where the subject of the sentence is the phrase "this sentence", and the predicate is the remaining word string.

A sentence is just a string of words; how could a string of words be true or false? — Janus

How could a word denote an object? How could a coin have a value? How could a hammer have a purpose? How could a note be a quarter-note?

By convention / a game of pretend.

I think it is more in keeping with what is commonly meant to say that sentences express propositions, and that it is propositions which may be true or false. — Janus

Unnecessary platonism.

the immediate connection between the Liar Paradox and the incompleteness theorems — Kornelius

https://en.wikipedia.org/wiki/Diagonal_lemma?wprov=sfla1

https://thephilosophyforum.com/discussion/comment/342838

by predicating 'not true' of itself, the Liar claims to be a member of the class of sentences that are true or false, and perhaps it is this claim that turns out to be false, making the conjunction of its claims false. — Srap Tasmaner

An inscriptionalist only wants to add to that that turning out to be false can just mean (for this particular claim) being rejected by the system of token-producing agents, who will judge deduction to be an inappropriate treatment for the sentence (i.e. any token of it), and will thus invalidate it in respect of its constituting a licence to print unlimited copies (of itself and other consequent sentences).The speakers will, in other words, put a brake on application of logic to this particular bit of natural language.

:ok: (imv)

Ah, sorry, I get you. Yes, the token is about itself, in such a way as to cause an explosive mess of contradictory tokens in a deductive context.

The token is about the things it is about. The proposition is an unnecessary abstraction?

added a link. Also,

speech act theory, which seems to have continued an anti-abstract trend away from positing of (as entities) propositions to only sentences to only statements on particular occasions. (Yay, tokens! ... utterances, inscriptions.) — bongo fury

Beliefs can be true, propositions can be true, mathematical equations can be true...sentences themselves can't. It's like saying "This horse is true", I don't know what it would even mean? — Isaac

Maybe something analogous to "hammers are for hammering", "this coin is worth two cents", "this note is a middle-C", etc.

I agree that a hammer has a purpose to us in the here and now because we exist. But if thinking beings cease to exist, wouldn't the hammer cease to have a purpose, and be just a collection of atoms, subject only to purely mechanical forces of nature? — Ash Abadear

if you simplify irrelevant details out of a replica you get a map or model, — Pfhorrest

Only on certain conditions: if the replica were already a complete map or model, every detail already relevant in the sense of referring to some detail or aspect of the subject matter, and you just removed some of that already relevant detail; or else, if details not removed were made relevant and significant in that way, even if they hadn't been, before.

In other words, you are still confusing the referential function of a map or model (or description or representation) with replication. Which is what "the map is not the territory" (but equally well also your excellent example of the voice-coded bit-map) should remind us are separate.

The most naive view of representation might perhaps be put something like this: "A represents B if and only if A appreciably resembles B", or "A represents B to the extent that A resembles B". Vestiges of this view, with assorted refinements, persist in most writing on representation. Yet more error could hardly be compressed into so short a formula.

Some of the faults are obvious enough. An object resembles itself to the maximum degree but rarely represents itself; resemblance, unlike representation, is reflexive. Again, unlike representation, resemblance is symmetric: B is as much like A as A is like B, but while a painting may represent the Duke of Wellington, the Duke doesn't represent the painting. Furthermore, in many cases neither one of a pair of very like objects represents the other: none of the automobiles off an assembly line is a picture of any of the rest; and a man is not normally a representation of another man, even his twin brother. Plainly, resemblance in any degree is no sufficient condition for representation. — Nelson Goodman: Languages of Art, p3

and if you add sufficient detail to a map or model you get a replica. — Pfhorrest

Only if you insist on (and have some way of) making the enhancement of referential function of the map coincide with an increase in the degree of physical resemblance. But obviously this is not how scientific models are typically enhanced.

Whatever you can do in real life but can’t do with the map, it’s because there’s some detail that’s been left out of the map. So a map that did include absolutely every detail would just be a replica of the territory it is a map of. — Pfhorrest

Only if you assume maps are meant to be replicas. "The map is not the territory" reminds us that this is far from being the case, and that they (maps) function rather as descriptions: which is to say, symbolically, like sentences (in the relevant respects).

You seem to be trying to convince yourself that,

Whatever you can do in real life but can’t do with a description, it’s because there’s some detail that’s been left out of the description. So a description that did include absolutely every detail would just be a replica of the territory it is a description of.

You may even have succeeded, I don't know.

So a “map” of reality that includes every detail down to the most fundamental physical level would be a replica of reality. And it would thus include humans like us in it, who would function just like we do, and experience that “map” as their reality. — Pfhorrest

No, unless the map (or description or theory or representation) were your fantasy of a map (etc.) as an imperfect replica.

There is thus no reason to think that maps and territories are ontologically — Pfhorrest

It goes on like this. :roll:

I am explicitly endorsing the equivalence of physical reality and a mathematical object, — Pfhorrest

So am I.

[*] an abstract mathematical structure in the sense of model theory. Potentially instantiated: in which case, a piece of the world; but otherwise only fiction [/possibility etc.]. — bongo fury

But I'm not confusing the object (whether actual or only fictional/possible) with a representation/description/map of it... which I think you are doing. (No idea why.)

so pointing to that as an absurdity is unpersuasive. — Pfhorrest

I was pointing to what I hoped were clear enough cases of said distinction.

All maps, models, etc, are effectively descriptions, — Pfhorrest

Good...

even if they are not descriptions in human-readable verbal languages — Pfhorrest

Sure ...

A visual map can be encoded in binary on a computer, and a human could read off those ones and zeros, even if they didn’t understand what they were reading. All the information in the picture would be retained in the sound of the human voice. — Pfhorrest

So this seems to me an excellent example of the obvious differences to be found between an object (whatever it was, a still life?) and its representation or description (the vocalised bit map). The map is certainly not the territory.

If that picture were to be perfectly detailed down to the subatomic level, it would have to be animated — Pfhorrest

If you mean represent temporally successive states, gradients etc. then, sure. If you mean represent them by a temporal succession of symbols, then surely not? Why? (I know the bit map is vocalised as a succession, but thus far that aspect was irrelevant to what it described, and could continue to be so, I would have assumed.)

or at least include temporal information in it like momentum, and all of the structural details that give a complete picture of its function, — Pfhorrest

Sure, why not. We're on a flight of fancy as regards the level of precision achieved by the description, but that's ok. Bolt on another hard drive (or immortal chanter) to store the whole bit-map.

and contain within it all the exact information that the physical thing the “picture” it is of does. — Pfhorrest

(Interesting syntax... reminds me of "no head injury is too trivial to be ignored" ;) )

Do you mean, "the physical thing that the picture is (a picture) of: the thing it depicts; the bowl of fruit?

Ok, the picture/bit-map/description must be as complex as the physics of a bowl of fruit; but was this paragraph meant to show how the bit-map must become a replica of the bowl of fruit? That's what I'm not getting.