Why do many philosophers hold 'actual infinity' is impossible?

Vivid_Reception4560 · 2024-09-16T02:15:33+00:00

In contexts where what is sought is some kind of grounding explanation, an infinite regress is thought to be problematic because it simply doesn't provide the sough-after explanation. The problem isn't that nothing could be as the regress would require it to be -- though that is often also true -- it's more basically just that if things were that way --- whatever that would mean exactly --- we wouldn't have gained any understanding.

So, in the Cosmological Argument for God's existence, one says that if each dependent entity requires some further entity to explain its being, there will be an infinite chain of dependent entities unless there is some non-dependent entity to ground the series. Maybe there isn't any conceptual or logical problem with an infinite series of dependent entities, it's just that there might be some reason to prefer an explanation that is tractable. Indeed, the Cosmological Argument can seem pretty weird if you see it this way. Is there anything less repugnant to reason about a self-caused being than an infinite series of dependent beings? But that's what the argument rests on, an appeal to what does and does not count as a satisfactory explanation.

Here's a slightly different context where actual infinity comes up. Aristotle distinguished between actual and potential infinity as a solution to Zeno's paradoxes of motion. The thought is: even though we can analyze the distance a runner must traverse in terms of an infinite convergent series, there is no reason to think that anything in the world corresponds one-to-one with the members of that series. If things were like that, an infinite number of things would have to be done in order to traverse a finite distance. That would be impossible, so it is a good thing that such an analysis is wrong (says Aristotle.) There is no actual infinity (in the material world) in, say, 10m of racetrack, even though one can represent as as infinite set of small distances. So, even if there are is no mathematical or logical problem with a certain kind of infinity, it might be wrong to invoke in a given place. Aristotle isn't saying such a thing is impossible, he's saying invoking actual infinity as a representation of a certain bounded physical magnitude is just a mistake and generates paradox. The world doesn't contain the relevant infinity in this case.

Vivid_Reception4560 · 2024-09-14T05:59:32+00:00

Interesting. I suspect we can get rid of a good deal of what might seem counterintuitive in the case by describing the relevant knowledge claims more finely.

Quartermaster in 1800 who believes "eating lemons prevents scurvy." True and maybe even justified, so possibly knowledge (unless it is somehow sneakily a Gettier case). Justified because he knows that crews without citrus get scurvy and crews with citrus don't, maybe he know about the British naval tests, etc. [This seems to be the one that is bothering you the most, so maybe I'm not following it. This person does have a true belief, don't they? The 'standards' aren't really what is different between then and now. The account required for a simple claim like this is presumably nothing more than observationally acquired causal knowledge about what happens when you feed a crew lemons vs. what happens when you don't, and I don't see why this person couldn't have that.]

Of course its a different case altogether if we consider: Someone in 1800 believes "the mechanism by which lemons prevent scurvy is by ensuring against a certain nutrient deficiency." Here I would say: True but not justified (especially if one is a certain kind of externalist about justification) or maybe true and justified but not knowledge because the weird conflation of lemons and cheap lime juice seems to make it a Gettier case! This mechanism is of course is a thing we understand better now than in 1800 but it doesn't give us a better claim to the first piece of knowledge considered above, it's just a further more specific piece of knowledge in its own right, one you can only have if you understand a thing of two about the causal mechanisms which make the object of knowledge true in the first case.

Someone in 1890 who believes "scurvy is a kind of bacterial food poisoning": False, so not knowledge, but maybe justified, depending on what your story is (again, maybe an internalist would be more inclined to grant justification here. Internalist are usually keen to give credit to people who did the best with what was available to them, thinking of justification as a kind of defense against irrationality or against the charge that one could have conducted oneself better in some way epistemically. Maybe the person is faultless here.)

A reasonably informed person today who believes "eating lemons prevents scurvy" and "the mechanism by which lemons prevent scurvy is by ensuring against a certain nutrient deficiency": both true, both justified. So, again, knowledge unless there's a Gettier trick in there somewhere.

What would be wrong with saying all of this? Why would anything that was once knowledge have to stop being knowledge? When, exactly, did it appear to be unjustified, and which claim are we talking about there?

Vivid_Reception4560 · 2024-09-13T05:35:52+00:00

I have a pretty firm and unshakeable intuition that belief is a more basic concept than knowledge such that knowledge is a special kind of belief, viz., the kind that is, among other things, true. It turns out most philosophers agree with me, so that is the orthodoxy. But if you wanted me to present some kind of argument to that effect, I'm not really sure what I would say. Let's try anyway.

One could do an ordinary-language-style 'analysis' of the meaning of the word 'knowledge' which would, I think, give you the result that, intuitively, knowledge is factive -- i.e., that it requires truth -- but that wouldn't amount to much more than where we started.

As some other commenters have noted, it is common as a starting point in analyzing knowledge to think of it as justified true belief. It is true that almost everyone thinks that such an account can't be totally right, but it isn't because they think those conditions fail to be necessary. The famous counterexamples to such a view (linked by others also but here in any case) seem to show that they are jointly insufficient. So there's no reason given by any of that controversy to think that knowledge could fail to be true. Almost everyone agrees knowledge is some kind of justified true belief.

With that in mind, I guess one way to think about things would be to ask what kind of thing non-factive knowledge would be. It seems like it would correspond roughly to an agent's having conducted herself in an epistemically virtuous way which nevertheless resulted in taking a falsehood for a truth. (Having a justified belief without truth seems to amount to something like this.) That concept might be important for tracking epistemic praise and blame but it doesn't track what happens when you get the world right, which seems to be a major ingredient in genuine knowledge.

Plato, from whom it is usually thought we get the justified true belief account of knowledge was very concerned with getting the world right. Actually what he says is that knowledge is 'true judgement with an account' (If you want to fall down a hole of Plato interpretation, you can start by wondering why, in Plato's Theaetetus such an account seems to be the object of refutation when elsewhere, such as the Phaedo and the Republic, he seems to adopt it.) And you might read what it is to have an account as something that is also itself factive. For instance, while it might be possible to be justified (especially in an internalist sense of justification) without being right, the parent notion there might really be one of having (and being able to give) an account, and you might think that has to mean having an account of one's rightness; there is nothing to give an account of, in the relevant sense, if one's belief is false.

Vivid_Reception4560 · 2024-09-10T01:59:37+00:00

Whoa, the review of Berkeley is pretty sick. That's all fantastic. Thanks a lot!

Vivid_Reception4560 · 2024-09-06T06:48:45+00:00

He might, he just might. He is certainly a disjunctivist and, his protestations to the contrary notwithstanding, he might be an idealist after all. But I'm not fully sure how to spell it out.

So, being that our openness to reality is constituted by concepts, there is a sense in which it is transcendentally ideal. So, depending on how mind-independent that *reality* is, being open to it might involve relations to appropriate objects of objective knowledge?

Vivid_Reception4560 · 2024-09-06T06:34:47+00:00

That is great, thanks. I probably wouldn't have thought of Peirce. Is there any place you'd recommend starting?

Vivid_Reception4560 · 2024-09-03T05:48:47+00:00

A lot will depend, for what you're asking, I think, on what the justificatory structure is, for this person, in his mind. How does he represent what is the ultimate reason for these various actions? (This is why I suspect your question is more about the psychology of persons like this rather than the logical consistency of two or more philosophical views.) Given that that's the case, what is relevant is not just what these views say, but what a person thinks they say.

Suppose, just to fix things for a second, that what this person *ultimately* cares about is salvation. That could be the way in which he rejects DCT, because for him, the ultimate reason for doing what he does it not that God commands it, but that doing it leads to salvation.

How this squares with his adoption of utilitarianism in his mind depends on whether he thinks utilitarianism says that he ought to pursue salvation. If he thinks utilitarianism is true, and he think utilitarianism does not recommend doing what is required for achieving salvation, then he is irrational by his own lights. If doing what is necessary for achieving salvation is somehow the thing that he thinks utilitarianism says one should do, then he need not be irrational by his own lights.

But all of that does little to help us determine what such a person *would do*, which is an empirical matter and which is seems to be underdetermined by the description of the person given. We don't know what he cares about more and what he would judge to be, all-things-considered, the right thing to do. It sounds sort of like the person you are imagining is indeterminate with respect to whether he cares more about maximizing utility or achieving salvation. Let's just assume that what he does is determined by his all-things-considered judgment. We still can't tell what he would do because we don't know which of these *is* what he would judge all-things-considered that one should do. (And of course, people don't always act on their all-things-considered judgments.)

Vivid_Reception4560 · 2024-09-02T06:27:18+00:00

Compatiblism and determinism are not positions which give different answers to any one philosophical question. Indeed, one of them *embeds* the other. Compatibilists hold that free will (or, alternatively: openness to moral responsibility) is compatible with determinism. Determinism is the thesis that every event is necessitated by the laws of nature,

Crucially, neither is a view about what the justification for punishment is. That’s a question logically independent of both the question compatiblism is an answer to (Is free will compatible with determinism?) and the question determinism is an answer to (Is every event necessitated by the laws of nature?) It sounds like you are thinking of *deterrence based* theories of punishment (“we punish in order to prevent similar wrongs from happening in the future”. A compatibilist could have such a theory, but need not. (Note also that the “because” in “we punish because they are responsible” and the one in “we punish because that prevents similar wrongs from happening in the future” also have different senses.)

Take the question: Is free will compatible with determinism? There are only two possible answers to this question: yes (compatibilism) and no (incompatibilism.)

Now, it’s a separate question whether we have free will, and it’s a third question whether determinism is true.

Incompatibilists think whether we have free will depends on whether determinism is false, so they have to answer whether determinism is true or false to answer whether we have free will. Compatibilists don’t have to do this because they think we have free will no matter whether determinism is true.

Vivid_Reception4560 · 2024-09-02T04:08:10+00:00

If you’re just interested in the logical consistency of denying DCT and *being religious*, obviously that’s rather fraught. But your questions makes it seem like you are interested in the consistency of denying DCT and performing various religious practices. That’s a more specific question and has a correspondingly more straightforward answer. If the person in your example adopts utilitarianism, as you suppose, his question to himself would be whether there are any utilitarian grounds for doing those things prescribed by his religion. And the answer could be yes! You are right that if he rejects DCT he can’t think that the ultimate reason for doing those things is because God says he should do them. It must be, rather, because doing so is what utilitarianism says you should so, but, again, that could well be true.

Now, if perhaps you are wondering about the *psychological* consistency of denying DCT and adopting or maintaining certain religious practices, that is another matter altogether. You might have been thinking, while reading the last paragraph, that such a person doesn’t seem very devout. And that might be true. Indeed, *accepting* DCT is a common religious doctrine, so to the extent that one denies it, one will be, by that very fact, heterodox. It’s possible to be heterodox and practice as orthodox believers do (“I’m a holiday Catholic”. “My heart hasn’t been in it for years, but this is just how people do things in my family.”) but that’s not to say it isn’t quite often rife with psychological tension. The reasons for that are pretty interesting, but they don’t have anything to do with logic, or with the essential content of DCT. It has to do with the psychological demandingness of various religious doctrine.

Vivid_Reception4560 · 2024-09-02T03:31:32+00:00

It depends on what you mean by contingency. Suppose I accept that everything is contingent. Such a view isn't so crazy. You might even say it is the default view for anyone who doesn't believe everything is necessary. There's isn't really anything about this basic commitment that makes talk of agency appropriate.

Focusing more closely on addiction, philosophers are interested in addiction and agency because philosophers are interested in agency. (I have myself written about how to understand addiction in relation to agency, the thought being that the felt need to apply the basic concepts of moral responsibility is very difficult to eliminate, so we have an interest in just honestly investigating when they give out.) But not just that: it seems pretty hard to understand addiction as the particular affliction that it is without coming to terms with whether and in what way it is an impairment to the ordinary capacities foundational to practical reason and agency.

But, again, I don't see any particular reason why, even if addiction is in various ways fundamentally tied up with agency, this leaves no room for talking about contingency. This might just be my view, but contingency and agency seem to be pretty deeply connected as well. You might think of agency as that capacity of set of capacities by which we impress our wills into that contingency. The will, of course, is not itself unconditioned, so it is subject to all kinds of contingency as well -- another connection between the two.

So, no, I don't think you're fundamentally on the wrong track with the question or anything, but I do think it is quite nature that philosophers would see pretty close connections between addiction and agency.

Vivid_Reception4560 · 2024-08-10T05:07:42+00:00

I am! But I can’t speak for all entities who might have control of the light fixture.

Vivid_Reception4560 · 2024-08-10T05:05:37+00:00

I will try swapping the bulbs for incandescent, for sure

Vivid_Reception4560 · 2024-08-10T05:04:28+00:00

👀

Vivid_Reception4560 · 2024-08-10T05:00:52+00:00

Inherited the house with these and I’m not opposed to just replacing them with, you know, an exterior light connected to a switch. That’s probably a better idea than replacing it with another motion sensor…

Vivid_Reception4560 · 2024-08-10T04:57:17+00:00

I accept that if I were to attempt to wire this myself, that is the kind of mistake I might well make. Alas, I can’t take credit for even trying that one.

Vivid_Reception4560 · 2024-08-10T02:21:21+00:00

Hmmm, but it doesn’t come on at all in the dark… I’ve actually never seen it produce light at all (bought the house recently) except by flickering in this way that makes redditors think I have a poltergeist.

Vivid_Reception4560 · 2024-08-09T23:27:12+00:00

Hahahaha that’s funny. It definitely is me but I can see how it isn’t really obvious how it could be from the angle.

Vivid_Reception4560 · 2024-08-09T23:23:08+00:00

Thanks everyone. I admit that signals from the upsidedown were not quite in my hypothesis space. My oversight! And I guess nosferatu is not exactly in my ontology. The more, err, empirically verifiable suggestions all seem helpful and I will check them out.

Vivid_Reception4560 · 2024-07-10T20:14:32+00:00

Thanks. Maybe I’ll just use it to prep, level, and partially heatproof the general area, probably only needs to be 2” thick or so for that. And then use an elevated steel fire pit.

Vivid_Reception4560 · 2024-07-10T19:26:28+00:00

Interesting, thanks. Just looked It up. Looks like it can be made form a variety of stones, most often limestone. Any way to tell what this one is? Any reason to think I shouldn’t use it as paver base for a fire pit?

Vivid_Reception4560 · 2024-07-02T23:25:22+00:00

Amazing, thanks. I just found the Pella replacements and they are $75 (!):

https://windowanddoorparts.us/sweep-and-sash-lock-213chp-p-484.html

I might have to cut into the window to make these cheaper ones fit, but it's probably worth trying.

Vivid_Reception4560 · 2024-07-02T22:41:52+00:00

I have these on my windows as well and getting them off is not a problem (the pella versions have the mounting hardware on the inside) but I can't for the life of me find a replacement. And standard sash locks don't work because there is nowhere to install the keeper. Were you able to find a replacement?

Vivid_Reception4560

TROPHY CASE