That's not quite right; you're asking about the existence of universals, which you've billed as an explanation for this phenomenon. However, you've said nothing about them other than that they are an explanation; hence, I don't know what they are, and so don't know in what sense they're intended to be an explanation. Hence, the question of their existence is meaningless to me until this can be answered.

Second, it's not clear in what sense you want an explanation for why different things can share properties. If you ask me why two things can be tigers, I could give you a causal, biological explanation; but this is apparently not what you want.

Again, if you're asking a psychological question, it's meaningful. What other question you might be asking, I can't understand. Other people perhaps understand it, but I don't, and so since I'm a native speaker of English, I conclude that it's not sensical, and ignore it. I don't know what else to do, since the question makes no sense to me and you cannot explain it.

the realist can just say that universals have to exist to explain that fact — Marchesk

If nobody knows what a universal is, then it can't explain this fact.

Carnap would say that realists, conceptualists and nominalists are wasting their time trying to answer a question without meaning. But shouldn't Carnap have to account for similarity? — Marchesk

If you can't articulate the question meaningfully, then Carnap (and anyone else) is licensed to ignore it. It's your job to frame a question meaningfully: otherwise, the demand that others answer it doesn't make sense either.

This is a psychological question, and meaningful. But I don't see what it has to do with the existence of universals.

So what makes an individual tiger a member of the tiger group? — Marchesk

If it's a tiger, it's a tiger. What's meant by "being a member of the tiger group" other than being a tiger? Are you asking me what makes it so that if something is a tiger, it's a tiger?

But I really don't know what else you could be asking.

But flygers hasn't been defined. — Marchesk

The parallel was intentional: you said a universal was that which explained some fact. But simply introducing something as that which explains something else makes no sense, because introduced ex nihilo in this way it does no actual explaining, and so I don't know what it is I'm supposed to be arguing about.

I don't understand the English sentence being asked. I know what the individual words mean, and it's grammatical, but I can't interpret it, and don't know what would make it true or false.

I also couldn't understand, for example, if you said "There are tigers. A flyger is that which explains this fact. Are there flygers?" The question simply makes no sense to me.

In the case of universals, I understand that there are things that share properties. I don't know what there is to say beyond this, and the questions about universals don't make any sense to me.

But you've used sentences that I also can't make sense of to do so.

I can try other sentences like, "Do some things have properties in common?" Sure.

But when you ask, "In virtue of what do they have properties in common? Is in in virtue of some other thing existing in nature?" I don't know what that means, because I don't know what it means for two things to have something in common "in virtue of" some third thing (or not).

Can you explain how you can't make sense of it. — Marchesk

I simply don't understand the question. I know what it means for a dragon to exist (or not); I don't know what it means for a universal to exist (or not).

I submit that we can make sense of many ontological questions, such that they can be meaningfully debated. — Marchesk

I'm a positivist at heart, but it seems fine to pick and choose here. Whether consciousness exists seems to me a meaningful question, and the answer is obviously yes. Whether dragons exist likewise, and the answer is very probably no.

But as to the existence of universals, I can't make any sense of the question. When I exercise my powers as an English speaker, I don't know what's being asked. And since I know of no other criterion by which to make a question framed in English sensible, I conclude that it's nonsense.

I don't see what Zeno's paradoxes have to do with commensurability. They have to do with infinite divisibility, which is not the same. The traditional statement of Achilles and the tortoise, for example, is stated only using divisions of two.

Though I must admit that I don't see Zeno's paradoxes as a problems, or a disaster, either – I always took them as didactic exercises. They're so obviously fallacious that it always struck me that anyone could be bothered by them: you give them to a student and they tell you why they're confused. I wouldn't try to redesign mathematics to 'avoid' them, because this falsely presupposes that they are problems.

If the sides are 1, the hypotenuse is radical 2, which is irrational.

If the sides are 2, the hypotenuse is 2 by radical 2, and so still irrational.

What you're asking for is some measure that can be applied to the sides, which is itself rational, and the square root of the doubling of whose square is also rational. It seems like this shouldn't be possible, but I'm not sure.

But they don't involve any incommensurability, right? I'm trying to understand the connection.

Which one of Zeno's paradoxes are you talking about?

Depending on how it's read, it seems to me perfectly unobjectionable given what you've said in this thread. I'm not sure what your issue is.

How do you understand the OP?

I can let Wayfarer speak for himself, but this is what was bolded:

"The physical world cannot be separated from our own efforts to probe it. How could it be otherwise, since we ourselves are embedded in the very world we’re seeking to understand?"

And this was the 'take-home:'

"What I take this to mean, is that objectivity cannot be absolute. And I think the reason this is controversial is that it undermines realism, which is the (usually instinctive) idea that the Universe simply exists as it always does, and that we humans come into it and go out of it in an instant, relative to the vastness of space and time which science observes. But this undermines that view, because it illustrates the sense in which the observer is inextricably part of the picture. We don't, actually, stand outside of, or apart from, the Universe which we are analysing; so what we're analysing cannot be absolutely objective."

Reworded: Measurement changes the object, insofar as it's being measured, means that we can't ever see something except qua measured, and so... it makes no sense to speak of knowledge otherwise than this. — StreetlightX

Yes, that seems to be the point of the OP, and it is the Kantian conclusion.

'The only things we can measure are those things that we can measure.' — StreetlightX

That's not what I said.

What I said was, "the only thing measurement ever allows us to partake in are those things that are ontologically dependent on it."

That measurement changes the object, insofar as it's being measured, means that we can't ever see something except qua measured, and so can't know what it is independently of that measurement occurring. This is not tautological. Again, look at the jellyfish example.

Ideally this bumping tells you something about the phenomena, — StreetlightX

But there's the rub: what it tells you is only that some bumping took place. In what way would this ever amount to bumping-transcendent facts? This I take it is the worry about being unable to 'exclude ourselves.' We "want" knowledge of things independent of measurement: but by design, that is never what measurement actually gives us.

But this is a false dichotomy through and through. All we ascertain in measurement are our interactions with it, yes, but who gives a fuck about us? Why are we the 'measure or measure', as it were? It's only by elevating measurement itself into a transcendental principle of 'universe-constitution' that you can get the kind of idealist peddling that Wayfrer would like. But that's unwarrented, unscientific hogwash. — StreetlightX

I agree that nothing follows from this about the universe being constituted by measurement; what does follow is that the only thing measurement ever allows us to partake in are those things that are ontologically dependent on it, and hence that the rest of the universe is, or might conceivably be, independent of it, doesn't seem to matter to the actual process of knowledge-seeking. It might be an interesting metaphysical hypothesis (a transcendent one that we could never in principle verify), but that's it.

I don't think I believe the Kantian conclusion here, but I just don't see how what you've said coherently escapes from it. There are two ways to read the OP: one as Deepak Chopra, one as Kant. I think Wayfarer's "real" intention is to be Deepak Chopra, which I agree is silly. But the video he posted with the time stamp seems much more like Kant, and I'm aware of no good argument against this general picture of things.

but who gives a fuck about us? — StreetlightX

We're the ones that have to try to figure it out; hence we 'give a fuck about us,' because we have our limitations to work with in trying to figure it out.

Consider modifying this bold bit to something like: 'what it is to have that property is just to be interacted with in a certain way under certain conditions". Is this a Kantianism? But there are no noumena here: the idea is that all properties are relational in this way: any interaction whatsoever will yield a 'result' appropriate to that interaction. There's only a Kantianism if one tries to substaintialize an 'object' apart from these interactions (like a 'red' without the conditions of 'red': a nonsense). There's nothing special about measurement. If there were no measurement, the universe would still be there, quite independent of it, insofar as measurement is just a subclass of physical interactions, which take place all the time, everywhere. The charge of Kantianism only holds if measurement is not understood to belong to the larger class of physical interactions - that is, if you exceptionalize measurement. But this is just what the QM shows to be false: we are no different to anything else in the universe. — StreetlightX

Would it help if the label "Kantianism" were dropped?

We are still left, on your purported solution, with the inability to ascertain any properties except those that are in relation to the measurer.

That all properties are relational, if they are, doesn't seem to help. When we seek knowledge of things, we don't generally think of ourselves as just reporting how the measured thing affects the measurement apparatus (ultimately, us). But your out seems to be exactly what a hardcore correlationist or idealist would accept: that the only properties we can possibly measure, are those that are artifacts of the measurement.

Whether the universe "is" independent of this is also irrelevant, because those things that "are" independent of the measurement are precisely what the act of measurement locks us out of ascertaining.

if one tries to substaintialize an 'object' apart from these interactions (like a 'red' without the conditions of 'red': a nonsense). — StreetlightX

Or, put another way: what is this, but an admission of what you tried to deny? You warn: do not substantialize the object outside of the interaction of measurement! But that seems to be the point of the OP.

Also, note that you deny the noumenon while affirming it: the universe is, you say, outside of our measuring it, but all we ascertain in measurement are our interactions with it!

By assuming this entails Kantianism. — StreetlightX

I don't follow. Can you explain?

And what is measuring? A: A physical interaction. — StreetlightX

I don't understand. I never denied this, and I don't see why it's relevant.

But what is the status of 'us'? — StreetlightX

"Us" would be whoever's measuring.

You're treating 'us' as an exception that is somehow different from 'everything else'; but this is just what is unwarranted. — StreetlightX

How am I doing this?

It misunderstands what it means to be red, which is just to look like that in the presence of light. — StreetlightX

Very well – but if you say all properties of the thing we're interested in are relative to the measurement in this way (what it is to have that property just is to look a certain way under certain conditions), then this collapses into Kantianism. We deal with phenomena, and we learn about things only that they look certain ways to us.

But: 'what does it look like in the absence of a look?' - this is just a badly formed question, leading to false puzzles. — StreetlightX

This is not what I said, though.

? — StreetlightX

The comic is a more intuitive explanation of what I was talking about. I didn't say anything about measurement not being physical, exclusive to humans, etc.

The point is just that many things in the world are unquestionably dependent on measurement, no matter what your view of it is. Those things include the very things we're interested in as data when conducting expriements – say, impressions produced on our sense organs and so on.

Thus, we only ever measure things as they are while being measured. To the extent that what is recorded is an artifact of the measurement, we are not recording what the thing is independent of that measurement. This is a problem because we have no way of 'subtracting' the effect of the measurement except via more measurement.

This becomes especially odd when we consider that, say, even in looking at things, the info we get is from visual stimulus, the entirety of which is dependent on the 'measurement' – no measurement, no visual stimulus. Thus, so the classical problem goes, when we see something we indeed see it (and perhaps not an illusion), but what we see about it is how it hits our eyes, and so learn nothing about what it is as apart from that interaction with our eyes.

↪Snakes Alive Measurement = physical interaction = not exclusive to humans = no Kantianism. — StreetlightX

We seem to be talking past each other. I don't understand what this has to do with my post.

There's no need to try and attempt to 'get outside' because one is 'already inside', if I may put it that way. — StreetlightX

I'm sorry, I don't see how this addresses my post. Can you explain?

Here is an easily digestible illustration of the problem:

StreetlightX — StreetlightX

This is true so far as it goes, but there is a lurking problem: there are parts of the universe that are dependent ontologically on the act of measurement. But then, these are precisely the things that are likely to be involved in what's gleaned from the measurement itself.

In other words, if you take seriously the idea that measurements only reveal things qua measured, and there's no reason to think that it's possible to measure things qua things as they are independent of or prior to measurement, then you immediately end up in Kantianism.

How, then, do we know what effect the measurement has? Presumably, we measure this too...and so on ad infinitum.

The worry therefore is not as trivial as you make it out to be.

In any case, what's wrong with "I don't believe that the keys are in the kitchen, but I can't find them anywhere else, so I will search there anyway"? — Banno

It depends on how you read it. Belief can be neutral – we can be undecided as to p, and so neither believe that p, nor that not p. When undecided, one might of course search the condition on the off-chance.

What does read as a pragmatic contradiction under normal circumstances is "I believe that the keys aren't in the kitchen, and I will search there anyway" – unless of course there is some reason one has to doubt one's own rationality or beliefs, or one is doing so to appease some external obligation or epistemic authority.

The problem is that negations of belief statements can often be read as "negation raising" – that is, we often read (by some process) "I don't believe that p" as "I believe that not p." On such a reading, what you posted is indeed a bit odd.

But either way, I think all this discussion doesn't matter. Yes, you can use belief reports to distinguish truth from merely purported truth (which in fact isn't so). But this is just an epiphenomenon of the fact that belief is taking something to be true, and there's no reason to think that taking something to be true makes it true. We can also use belief to affirm truth, rather than falsity. This simply isn't important.

We ought to be suspicious of the equivalence of (1) and (2), since we can find cases where truth value judgments about them don't coincide.

For example, suppose there are no ravens. Then (2) is true, but the status of (1) is uncertain.

I've read the OP a bunch and I still don't get it.

What is the disaster?

Given the existence of irrationals, isn't the point made here already accepted? The existence of irrationals has been known since ancient times, as you say.

How does the Pythagorean doctrine of commensurability lead to Zeno's paradoxes?

My best gloss is: to believe something is to take it to be true.

The attempts at reduction, in terms of behavior, equation of belief with belief report, belief as distinguishing between truth and falsity, &c. can't be right.

Clearly we can be disingenuous and behave other than we believe. Clearly we can believe something and for this reason act on it – not all beliefs are backward rationalizations of behavior. Clearly a belief report is a linguistic act and a belief isn't. Clearly we can say someone believed something correctly. None of these notions seem to help.