I'm pleased you got the joke. My general opinion of @Wayfarer is that we agree about most things, but that he adds more than is needed; where silence is appropriate he keeps talking. But this is becasue he wants to show us something more, presumable thinking that we (I?) don't already see it. Maybe I don't.

You've read more than I, then, since my knowledge is from the commentaries rather than the original, and mostly as an example of the application of the thinking of Austin and Wittgenstein, as an application of the linguistic approach to wider areas. We do things with words; indeed so overwhelmingly are we embedded in a social structure built with language that like the ubiquitous fish in water we fail to notice our surrounds.

As I understand it, what is unavoidable is our mutual agreement concerning the way the world is, and the language we use to discuss it; and what is irreducible are certain activities we perform, including illocutionary acts and normative assumptions. So "property" unavoidably takes as granted that there is land, that the land can be subdivided into sections, and that we can talk about the land; and it takes as irreducible the idea that I can dispose of this piece of land as I see fit, while you cannot.

While a dumb animal might defend a territory, it does not own it in the way a person owns a piece of land in virtue of deeds and purchases and so on. In this way "property" is dependent on our being embedded in an irreducible social structure that is unavoidable.

Much to the confusion of libertarians everywhere.

Mathematics is presumable also unavoidable and irreducible, in ways that might well be worth setting out.

I'm asking if infinitesimals exist in the sense that would satisfy mathematical platonism. — Michael

And that is the question I answered. I gather I need to be more explicit. You gave the following as yout definition...

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.

There are mathematical objects in the sense that we can quantify over mathematical things such as numbers and triangles. There are even numbers, therefore there are numbers. There are isosceles triangles, therefore there are triangles.

These are not independent of "us and our language", since if we were not here there would be no mathematics. Mathematical entities are however independent of any single individual, but built by a community int he way that a language is built. Hence the "us".

We decide the truth or falsity of statements about planets and electrons by experimentation and inference. We use telescopes and potentiometers. We do not use such devices to decide the truth or falsehood of mathematical entities. We do use inference. The truth of mathematical suppositions is agreed in much the same way that the truth of Ohm's Law or Kepler's Law is agreed. If that is what is meant by "objective", then they are objective. We discover things about mathematical entities, in that we find unexpected results in our construction. This is not the same as discovering that the orbit of a planet is elliptical or that electrons have a specific mass.

I take all of this to be saying that infinitesimals exist, but not in the way set out in your quote.

Well done!

What one believes, desires, feels or cares about will still be there, even if one is honest.

Fine! I have realised the link between Terrence Deacon's absentials and the via negativa. Anyway, as you say, enough for today, thanks all for the comments :pray: — Wayfarer

:wink: My objections just show that you are right.

Yes, indeed - and hereabouts so many of the discussions of existence, essence, and what is real would benefit from simply understanding quantification.

And I don't think the resulting ontological "theory" says that existence is dependent on language — J

Yep. And to this I would add that the relation between what exists and what we do is worth considering. Language is one of the things we do. Didn't Habermas reflect on this in his use of unavoidability and irreducibility? That it is action that has import?

A very shallow analysis — Wayfarer

:grin: If you like. You insist on telling us, at great length, about the ineffable. Fair enough. I'll continue to point out that you haven't, thereby, said anything.

He wasn't there again today. Oh, how I wish he'd go away.

Everything is a conflict between science and religion, for . Here we are talking about Mathematics, and he must introduce god, but not in so many words. Moreover, he sees any objection to this unneeded insertion as further evidence of a supposed scientistic fear of religion.

God explains everything, and so might be introduced into any topic. But of course in explaining everything he explains nothing.

And of course Wayf is entitled to introduce god, just as others are entitled to point out that he is not necessary.

It might be interesting to check again. I'd just read this:

‘Esse is percipi,’ wrote the empiricist metaphysician George Berkeley around 1710: ‘To be is to be perceived.’ For something to exist or be real, for Berkeley and for many others (Immanuel Kant, for example), was for it to play certain roles in human perception or to correspond to our mental imagery. In a tribute to that style of metaphysics and a parody of it, in 1939 Quine said that ‘to be is to be the value of a variable.’ Now, Quine took himself to be ridiculing the grand pronouncements of metaphysics. But it was hard not to hear that ‘bound variable’ stuff as itself an ontological theory according to which existence is dependent on language: to be was to be picked out by the ‘something’ in sentences like ‘there is something that’s tall and green’ (or, in the language of logic, (∃x)(Fx&Gx), in which the existential quantifier binds the variable ‘x’). — Sartwell, The post-linguistic turn

The theme, one that may be becoming prevalent, is that post modernism has noticed that not just any narrative will do. Global warming does not care what narrative you adopt, and relativism works for oligarchs as well as anarchists. The truth doesn't care what you believe. That's for @Joshs.

I lean toward the quantificational interpretation that allows P to be a "new thing" — J

It's not as if we must choose and stick to only the quantificational interpretation, or alternately we must only ever use the substitutional interpretation. Which we use depends on what we are doing, on the task in hand.

...intersubjective agreement... — J

A misleading phrase, since it implies a background of subjectivity prior to, say, counting; the incoherence of the solipsistic homunculus talking to other homunculi. What is salient is that arithmetic is an interaction between people, and this is so even if one occasionally counts to oneself.

The only form that genuine reasoning can take consists in seeing the validity of the arguments, in virtue of what they say. — Thomas Nagel op cit

A pity then that did not address the argument of my post directly, but instead could only see it as reactionary 'fear of religion'. But yes, it is circular to reason that evolution is needed in order to explain reason. The relevance of that remains obtuse.

We can take Quine's joke seriously: to be is to be the subject of some quantification; and us that to reply to the OP.

Sure, all that, there might be a more accomodating reading of what I said above that can be made compatible with Platonic texts. The difference is that, at least to my eye, the account I gave above indicates how stuff like numbers and property and so on are constructed, by modelling that construction in a higher order logic.

It's not a novel account I believe.

I'm not overly interested in defences of Plato or Thomisim, or even Popper or Searle. Thier value is in what they help us understand.

You can think that, if it suits your narrative.

I've no idea what a Platonic realm might comprise— why would you ask me? Indeed, why ask at all, since the notion of a Platonic realm is fantasy.

these MUST be understood as constructions, hence contingent facts, our own creations, — Wayfarer

Rather, these CAN be understood as constructs. If you feel you need to include, in addition, a god or a platonic realm or whatever, then that's your choice.

How do you apply that to these examples of the Fibonacci sequence? — frank

This is a good question. What the Fibonacci sequence gives us is a way of talking about the things you picture. It doesn't provide an explanation of why the shell follows that sequence. But it's not hard to find one.

All the snail does is to add calcium to the edge of it's shell. Each new shell chamber it grows is built on the previous two shell chambers. If we say the first is size one, then the second is grown on that, and is also size one. The third will be grown on those last two, and so be size two. The fourth is grown on the previous two, and so is size three.... 1,1,2,3,5... and so on.

Think of these as cross-sections of each chamber.

Snails do not have access to a platonic reality. It's not some mystical or divine intervention, but a simple result of a snail adding calcium to the edge of it's shell.


But we have a language that can talk about this growth.



Edt: Here's more than you ever needed to know about mollusc shells:

If the number series is indeed invented, pace Frege, it's easy enough to imagine that early users would then discover that certain numbers -- invented merely for counting purposes -- had the quality of being either odd or even. — J

Yes.

But we can go further than Popper. This, and this, and that, all count as one of something. These, and those, as two. That's an intentional act on our part, which is not only concerned with the things in the world but also concerned with ways of talking about those things. We bring one and two into existence, by and intentional act - it's something we do. Some important aspects of this. First, its we who bring this about, collectively; this is not a private act nor something that is just going on in the mind of one individual. Hence there are right and wrong ways to count. Next, the existence had here is that of being the subject of a quantification, as in "Two is an even number". Notice that this is a second-order quantification: Supose we say that there are two marbles and two flowers. We have not thereby created a third thing within the domain of discourse. We still only have two marbles and two flowers. When we say that two is an even number, we are still talking about marbles and flowers.

Do infinitesimals exist (in the platonistic sense)? — Michael

Infinitesimals exist. They are a higher-order quantification that can itself be quantified. Adding "in the Platonic sense" serves only to confuse what is going on.

This s what I tried to explain here:

Michael's argument talks about the existence of sentences. Hence it make use of quantification in a second-order language - a language about language. In a first-order language we can make an inference by quantifying over a predication - from f(a) to ∃(x)f(x). In second order logic one might perform a similar operation over a group of predicates. If we have ϕ(f(a)), we can infer ∃Pϕ(P) - if f(a) is ϕ, then something (P, in this case) is ϕ. But at issue here is a choice in how this is to be understood. Is it about just the things (a,b,c...) that make up the domain of the logic, or does it bring something new, P, into the ontology? The first is the substitutional interpretation, the second is the quantificational interpretation. This second interpretation has Platonic overtones, since it seems to invoke the existence of a certain sort of abstract "thing". — Banno

A note on logic. Natural languages are free to range over any topic and to say all sorts of strange things. Logic allows us to tie down what we can say with some level of consistency and coherence. The relation between higher-order logics described here sets out a way of talking about concepts without giving them some mystical "platonicistic sense". That's why the logic is useful, as a guide to language use, not as a replacement for natural languages.

Plato's approach was too muddled to be useful. Higher-order logic and intentionality provide a much clearer picture without the mysticism. It explains how such things as numbers can be said to exist when they are clearly not like chairs and rocks. It explains why mathematicians feel like they are 'discovering' things - they are. It gives precision to

I am inclined to argue that maths do not 'exist' in any objective sense. — Tzeentch

Perhaps there's an oddity to do with the way folk think of "mind-dependent", such that they are thinking of individual minds, or their own mind. It might be better to say "minds -dependent".

I explained it quite clearly in my last post here which you opted not to address. — Michael

Indeed, I did not address it, becasue I had done so previously. The repetition is tiresome.

There's something about the structure of math that matches up to the structure of the universe in some ways. — frank

Of course there is.

Yes, because that's what we do. Presumably the sort that don't interact with the world are pure maths, the ones that do, applied.

Maybe this is different, but you have to wonder: does it make sense to talk about something counting as a duck, if you don't know what it means for something to be a duck? — Srap Tasmaner

'Counts as..." doesn't change the words to match the world, but the world to match the words. So "That counts as a duck" makes that thing a duck, an act of intent on the part of the speaker.

Hence, there is not a something that it means to be a duck until the act is performed.

And the answer is: four, because calling a tail a leg doesn't make it a leg. — Srap Tasmaner

...that's not taking the "counts as" act seriously. If the tail counts as a leg, that's five.

This isn't to say that a duck is a social construction, even though counting as a duck is. — fdrake

Yep.

, Popper is unconvincing on the ontology of world 3. Searle begins to answer this with his account of institutional facts and collective intentionality.

Maths as an act of collective intent. Of course there are infinitesimals.

If you like. Much like

Less realism, more mysticism. — frank

I'm not so keen.

But Big Mad H might've been on to something. — fdrake

(p & ~p)⊃q. That's all.

CSIRO accused of ‘pro-reality’ bias following assessment of Dutton’s nuclear ‘plan’

While

Plibersek brags that Labor hasn’t approved any fossil fuel projects for a few hours

Sure. It's just easy to say it with word than with ducks, or rabbits, or some combination.

But folk will use that to go all Hegelian.

I suppose we could quibble about the boundary between philosophy, psychology and neurology. — fdrake

Roughly, philosophy does the conceptual stuff and psychology does the empirical stuff. Whether we "learn that the practice of counting as", as you ask, seems to me to be an issue for empirical investigation.

I think they're species of counting as. — fdrake

i didn't see that in your example. Sure, the paper can count as different things, bitt hat' not different types of counting as...

Counting as... has a world-to-word direction of fit; the world is changed so that the crate becomes a calf raise platform. (I had to look that up. Though at first it had something to do with animal husbandry.)

That reversal of the direction of fit is what embeds mind into the world. It's what gets mistaken for implying idealism. @Wayfarer does this in many of his posts. @Michael thinks it invokes platonism. But it seems to me a relatively trivial thing.

Repeating the same error does not correct it.

Tania Mihailuk joins exodus from One Nation, leaving Pauline Hanson’s party without representation in NSW

How sad.

I noticed that. Arguably the remnants of the Australian Country Party suffer from a poor combination of honesty and ignorance. And poor judgement.

Even to learn that the practice of "counting as"? — fdrake

I take that as a psychological or neurological question. Arguably neural nets are built in order to continue in some pattern - to "predict" is how it is usually phrase.

My calculator is a phone. Puzzling.

But taking on your example, if one were to treat a calculator - not the phone sort - as a phone, there would quickly be certain problems. Lack of reception, for a start.

So aren't pretending and imagining different to "counting as..."? When we count as, we "carry on" in the same way. We say this paper counts as money, and use it for transactions in an ongoing fashion. But pretend money or imaginary money - say a toy dollar note or a dream of a lottery win - can't do this.



One of the astonishing things I've learned on this forum is that there are folk who didn't learn to "Carry on..." in the requisite sense. Or perhaps they do carry on, but deny that they can.

Construction requires something to construct from.

Not just any consistent narrative will do. One needs to check that the narrative works.


So sometimes the story surprises us, we come across new things. How could that we if it were only our own creation? And we agree on most of the narrative. How can that be if we each were creating our own? And sometimes we are wrong, but how could we be wrong about something that was no more than our own creation?

Novelty, agreement and error - the trinity of realism. :wink:

It's a cliché, but "counts as" expresses a hinge, where language and the world meet - "fdrake" counts as a reference to fdrake. It's what we do, a habit, and needs no further explanation.

...to create the real. — frank

I'd be happier if you said "...to construct the real".

We could explore natural disasters, like the closing of King Island Dairy.

No more Lighthouse Blue Brie!

Take a look at table 2 in Renewable electricity policy for Australia. P.7.

Australia is a bit larger than Germany, (about 20 times the area), with correspondingly much longer grids, plural, and with different parts of those grids in very different locations. Modelling apparently suggests that "base load" can be ignored over such a scale, especially if the network is made more efficient and interconnected.

Foremost is perhaps the problem of local wiring being too thin to take the load form rooftop solar during sunny days. It will become prone to overheating and failure.

This is an issue to whcih we might return in a year or two, when the experiment has run it's course.

I do think "where the types come from in nature and norm" is a very different question than "under what conditions are sentences true", and a slightly different question from "where does the correlation between nature types and norm types come in". — fdrake

My two bits. Saying things that are true is something we habitually do. Doing otherwise is the exception.

Calling some particular act "eating" is a "counts as..." exercise. Putting it in your mouth, chewing and swallowing counts as eating. I read the PI Wittgenstein as saying that this is just what we do, and that philosophical investigation stops there. We might ask "Why do we call it eating", but this becomes a question for physiologists and etymology.

We should also keep in mind expressions such as 'I'll eat my hat" and "eating humble pie".

Contra Levi-strauss, it's all cooked, by the words we use. We can't step outside language, nor outside our culture into "nature".

"Counts as..." underpins language.