I think the answer is:

And every thing is like that. — frank

But Josh is the one who's actually read Husserl. Take it up with him probably.

In a way, the number 5 implies all other numbers, because its meaning is rooted in its place in a sequence. And every thing is like that.

Maybe like this? This is probably what a Babylonian (500 BC) abacus looked like. This is where the number zero entered into the human intellectual scene. It was when a merchant would draw a diagram of a certain abacus result that he or she would need a symbol for the blank spots. Zero was born as a symbol: an attempt to stop that which underway and record it for future reference. Phenomenologically, it's like when we say we were arrested by the beauty of the sky. Stopping, exiting time, inhabiting an inner sanctum.

Our basic experience, the most basic one possible (and this will prove to be crucial), is already theory-laden. — J

Right, if we focus heavily on the ontology of abstract objects, we overlook the accompanying problem: what's the basis of our confidence in the other two categories: mental and concrete? It's all myth building.

Not sure why the question is addressed to me - did I write something about this before? — SophistiCat

No, it's that you're a reliable source for information about physics.

This led to some unfortunate numerology - long since abandoned - that grew ever more convoluted as later, more accurate measurements no longer quite fit that initial 1/137 estimate. — SophistiCat

Oh. So it's not really significant? Good to know. :grin: Thank you!

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

It’s not that the world isn’t involved, it’s just that the world only reaches us through our constructive interactions with it. — Joshs

Right. That's along the lines of what I was saying. Although, that's just a gesture at explaining why math helps us predict events. It's when we take individual cases, like Fibonacci numbers, that we find we haven't explained anything. Yet.

And the structure of the universe isnt the product of imaginative construction? Wittgenstein would say you’re being tricked by your own grammar, that is, by hidden suppositions that project themselves onto the ‘real’ world and then seem to arise from that outside. — Joshs

So you're saying that math can be a community construction without necessarily arising from any activity involving the world. It's that what we call the world conforms to thought a la the Tractatus, so it's no surprise that we find an affinity between our math and the world's shenanigans.

Do you believe that we are also products of analysis? That your individuality arises from reflection on events?

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. — Banno

I was thinking about things like the Fibonacci sequence. It shows up in a lot of places that have nothing to do with human consensus. There's something about the structure of math that matches up to the structure of the universe in some ways.

@SophistiCat Could you explain the thing about the number 1/137 in physics?

Maths as an act of collective intent. — Banno

It would have to be the way collective intent interacts with the world, right?

I agree. I don't think mathematical platonism is supposed to be some big metaphysical statement. It's just reflecting our experience with math: that it's something we seem to discover, that it's not owned by particular people, in other words, it's not mental or physical.

That leaves the door open to trying to explain it anyway we want, kind of like gravity is a thing, but we're still working on how to explain it.

I don't know, I'm not a psychologist. — Michael

Dude. Really?

Why do you think realism is the prevailing view in Phil of math? Why is it found to be a valuable perspective in spite of its drawbacks?

It's weird how accuracy appears to be a property of objects, but it's really coming from us. It's like the way redness is a property of roses, but it doesn't really belong to the rose.

We project out our thoughts onto the world when we say the painting is accurate. We sort of ordain the painting.

Yes, and "true" and "false" are adjectives that we use to describe a sentence. I think Wittgenstein's account of language is more reasonable than any account that suggests that our utterances are somehow associated with mind-independent abstract objects and properties (related somewhat to this, this, and this).

I think that language is behavioral and psychological, not something more as platonism would seem to require. — Michael

I was talking about paintings. How the property of accuracy isn't about the painting so much as about us.

I think we've covered the platonism angle as much as we're going to. I don't disagree with your conclusion, I disagree pervasively with the way you got there, because you just aren't interested in even looking into why propositions still hold a prominent spot in AP and phil of math.

What kind of property is accuracy or truth? Like if we weren't around to say the painting is accurate, it wouldn't have that property. We magically make the painting have a property. Then after we're extinct, the property disappears

It makes you wonder if accuracy is just something people say about the painting.

How can that be if we each were creating our own? — Banno

I don't think you're just hanging around creating the world. The division between you and world arises from reflection on events. Less realism, more mysticism.

...to create the real.
— frank
I'd be happier if you said "...to construct the real". — Banno

What's the difference?

I read as much as I could about David Lewis and needed to go ahead and buy a collection of his papers in order to understand furher, but it was too expensive. Now the fascination has passed. :confused:

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

My two cents worth is that as soon as we stop living and start analyzing, we inevitably end up with gears and springs, wondering how it ever comes back together to create the real.

there's nothing else to discuss. — Michael

Okey dokey. :smile:

The entire argument equivocates, — Michael

I think you're the one who's equivocating. You're trying to jump back and forth between here and wV. When you're here, you admit that vibranium is an idea. When you're in wV, you say it's real. But you're never in wV. You're only here.

Analyze the argument from where you actually are: here and now:

1. wV is a fictional world.
2. everything in wV is fictional.
3. fictional things are ideas
4. fictional vibranium is an idea
5. wV contains fictional vibranium

Conclusion: wV contains an idea. — frank

Remember, wV is just and idea. Everything in it is fictional. Fictional things are ideas. Everything in wV is an idea.

No. — Michael

Which part of the argument is wrong?

(2) is a world without propositions but it's not empty; it's a world with vibranium. — Michael

Let's call this world wV.

1. wV is a fictional world.
2. everything in wV is fictional.
3. fictional things are ideas
4. fictional vibranium is an idea
5. wV contains fictional vibranium

Conclusion: wV contains an idea.

Correct?

Do you understand the difference between these two fictions?

1. A world in which magic exists but Santa is a fiction
2. A world in which magic exists and Santa is real

Something can be real within a fiction without being real within the real world. — Michael

My question is about the ontology of the world where magic exists and Santa is real. That whole thing is just a set of ideas, right?

A world with planets and stars but no people is not an empty world; it's a world with planets and stars. — Michael

Real planets and stars? Or fictional ones?

By the way, I was going to buy one of David Lewis' books one time, but it was three figures, so I decided to wait until the price comes down. We should go in on a purchase.

we're talking about a fictional world in which there is actual, real, physical gold but no people. — Michael

How can you have actual, real, physical gold in a fictional world? That's like if I dream of a cat, I have an actual, real, physical cat in my dream. How can that be?

It's a fictional world in which planets and stars exist but people and propositions don't, just as the Lord of the Rings universe is a fictional world in which orcs exists but computers don't.

Like Banno you're equivocating. The fact that we use language and propositions to talk about a fictional world does not entail that there are languages and propositions in this fictional world. — Michael

You keep misunderstanding me. I'm not on a mission to blow up your viewpoint. I'm just exploring the ideas associated with it. You brought up possible worlds and the in/at distinction. Then you said possible worlds can be sets of physical objects in spacetime. Do you want to back out of that now? Because Frodo definitely isn't a physical object in spacetime. He's just an idea. Do you want to continue talking about possible worlds or just drop that notion?

That depends on whether or not there is an (infinite) multiverse. If there is then there is likely some universe in which there is gold but no people playing chess or using language (and so no propositions). If there isn't then World X is just a fiction. — Michael

If World X is just a fiction, then it wouldn't be a set of physical objects in spacetime, would it?

No, a world can be a set of physical objects situated in spacetime. — Michael

So what's the ontology of World X? Is it in another dimension?

If "there are no propositions" is true at World X then there are no propositions in World X. — Michael

Doesn't that mean World X is empty? A world is basically a set of propositions.

Okey dokey. :cool:

Firstly, "having ontological commitment to mathematical entities" does not entail platonism. Immanent realists and conceptualists also have ontological commitment to mathematical entities. — Michael

I wouldn't say accepting mathematical entities entails platonism. I would say that platonism best reflects the way we generally think about things like the set of natural numbers N.

An immanent realist is stuck saying that N is a property of something in the world. I don't think anybody knows what exactly that object is, which has N as a property, but the immanent realist is asserting its existence anyway. Immanent realism is more of a gesture toward avoiding platonism rather than a full bodied alternative.

The conceptualist is saying that numbers are mental objects, which means their only existence is in specific acts of thinking about numbers. Do I really need to explain why nobody believes this?

Instead of those, look at the SEP article on philosophy of math. It shows the alternatives to platonism are logicism, intuitionism, formalism, and predicativism.

Do you want to go through those?

You don't need to believe in mind-independent abstract objects to believe in mind-independent physical objects, and you don't need to believe in mind-independent abstract objects to believe that these mind-independent physical objects move and interact with one another. — Michael

Yes. Neither of these sentences has anything to do with Quine's argument, which has shaped the prevailing view in phil of math and phil of science. Just check it out, that's all I'm saying.

The indispensability argument is about mathematical realism. I just wanted you to look at what Quine was saying, which is that if you deny platonism of any kind, you're rejecting science in general. You can do that, I was just encouraging you to be aware that you're doing that.

There's no mystical connection between utterances and mind-independent, non-spatial, non-temportal abstract objects; there's just actual language-use and the resulting psychological and behavioural responses. — Michael

Yeah, Quine is the inscrutability of reference guy, in the neighborhood of behaviorism.

I think I’m looking into it only as deeply as it needs to be. Platonism is a result of being bewitched by language, misinterpreting the grammar as entailing something it doesn’t. — Michael

You're basically saying Quine was an idiot.

I don't think you're bothering to look very deeply into this. I was just saying you should look into the consequences so you don't end up contradicting yourself.

An immanent realist about propositions would have to believe that propositions exist only in particular things, and presumably the only particular things within which a proposition can exist is an utterance. — Michael

A proposition is the meaning of an uttered sentence. So this would be saying that the meaning of 2 is a prime number resides in the pixels on the screen. That doesn't make any sense to me, but if you like it, just pay attention to the consequences. For instance, what does it mean if you and I agree that 2 is a prime number? What is it that we're both agreeing to? Pixels?

Hence it seems that with respect to propositions we must be platonists (mind-independent propositions), — Michael

Right. Just look at Quine's indispensability argument in the SEP article I cited. Just be aware of what you're giving up if you reject mathematical realism.

With respect to propositions, I think immanent realism collapses into conceptualism — Michael

I'm not sure how. Note the SEP article you cited says of this kind of conceptualism: "As we will see below, this view has serious problems and not very many people endorse it."

I reject platonism. I'm undecided on nominalism and conceptualism, but the things I am saying are consistent with both. — Michael

That's cool. This is the indispensability argument from Quine:

"According to this line of argument, reference to (or quantification over) mathematical entities such as sets, numbers, functions and such is indispensable to our best scientific theories, and so we ought to be committed to the existence of these mathematical entities. To do otherwise is to be guilty of what Putnam has called “intellectual dishonesty” (Putnam 1979b, p. 347)." here

Propositions are also indispensable to folk theories about agreement. Soames lays this out in his book on truth. I think you'd find the argument intriguing.

However you handle abstract objects, you need to look at the consequences of your approach to avoid contradiction.

You just let the meaning of the sentence be its truth conditions (per Davidson).