Here is a hard question, the second hardest question I can think of: how is knowledge possible? — Astrophel

I hate to say it, but I would not be able to reject an accusation of "whataboutery" if I tried to change the subject to a general philosophical discussion about knowledge. My reaction may be conditioned by my view that much of epistemology has been thoroughly distorted by Cartesian scepticism and the belief that the only certainty is logical certainty; the latter of course, rules out all empirical knowledge out of hand. There is also a danger that if your interlocutor is not convinced by Descartes, your opportunity to persuade them on this specific issue will be lost. Faced with an argument about the existence of God, you try to prove that we don't know anything anyway. No, I don't think so.
Mind you, with a suitable interlocutor, I would be inclined to try to persuade them that the question of God's existence cannot be answered by purely empirical evidence.

What I reject out of hand is that lukewarm admission that there may be some kind of supernatural something behind or underneath of the universe, and that something could be called God - because we can't prove it ain't so. Why should we bother with such a fruitless conjecture? Just not to be called atheist? — Vera Mont

We should wear our badge with pride and not let the opposition use it as a term of abuse.
I it is a mistake to allow supernaturalists to pretend that the question is an empirical one. That is a wedge argument, designed by believers to open the mind of unbelievers. But stick to the issues.
If someone claims to have seen the Virgin Mary, some will propose an explanation such as a hallucination, or down-right lying, and some will propose an explanation such as a vision granted by Heaven. Which is the most likely (plausible)? Even the RCC adopts the former. (This is a version of Hume's argument against miracles.) The RCC is prepared to consider further evidence, and may change its mind, and adopts the latter. Now, either that evidence is of a kind that anyone can accept it, or it is not. What the RCC considers to be evidence is, I understand, evidence that the visionary has caused further miracles, which is clearly circular. No need to fall for blandishments.
If you really need a bolt-hole, you can insist that, where there is insufficient non-circular evidence, the answer is to classify the event as unexplained.
If you get really desperate, you can point out that if a supernatural explanation were to be established (perhaps amongst the paranormal phenomena) on the basis of normal evidence, (not that I can imagine that happening) the explanation would then become a natural explanation.

The fine-grained nature of the world we live it might just be a function of adaptive creative algorithms which feed off of past events, in the simulation. — AmadeusD

I guess that's so. But that would mean that the simulation is a reality of its own, independently of the "real" reality. (As a story has its own logic, even though it is just a story) Still, the algorithms are part of reality - they are not simulated, are they? - they wouldn't really be algorithms if they were simulated. So the simulaton may be different from the real world in all sorts of ways, but it needs to be built from and in the real world.

Much more important than stories about the elements are stories about dead people. — Vera Mont

I don't know about "more important", but I agree that this is something that is addressed in all religions, and it is important to people.

Like screaming children in burning cars. Suffering, that is. That is not a story. — Astrophel

Yes, of course this is also part of the mix. The book of Job comes to mind.

Without intelligent makers, there would be no couches or shoes. — Vera Mont

Of course, and so it is easy to see why creation stories are included in so many mythic cycles.

Before there was worshipping, Gods, and all the trappings of these churchy fetishes (I like to call them), there was a basic problematic built into existence that gave rise to the worshipping and the rest. — Astrophel

there is something empirical behind that swathe of (potential) nonsense. Thunder/rain Gods are one. — AmadeusD

It is not enough, it seems to me, to dismiss the whole business as superstition. We can't pretend that it isn't still important to human beings. It would be reasonable to suppose, wouldn't it, that religion addresses issues that are still important to us? The question of it's historical origin is one way, though it is unlikely that we'll get more than plausibility this far from the events.

I think explanation of cause only gains importance after the concentration of humans in walled cities - after we cut ourselves off from nature and felt we had to master or conquer nature. — Vera Mont

Causal explanation in our sense is a more recent development. It is part of the scientific revolution in the 16th and 17th centuries. But walled cities, agricultural technologies and religion (in our sense) all seem to have arisen at, very roughly, the same time. (Some people talk of an Age of Wisdom.) It makes a lot of sense to see them as interlinked and interdependent. There are many themes built in to religion. It addresses human concerns, but also, as Nietzsche so emphatically pointed out, is involved in the power struggles in the new, complex human societies in the new cities. I think he missed a trick, in fact. Religion gave power to a new version of the shaman - the priest - and supported or enabled much larger human societies. But it also gave a voice to people who are oppressed in those societies.

My best guess is something like: delving into the human psyche reveals that it differs from inanimate objects. That much, I have already stipulated as self-evident. — Vera Mont

It seems more plausible to me to see the sharp distinction between animate and inanimate - and conscious and not conscious - is a product of our times, specifically of - again - the scientific revolution. In natural language, there is no sharp distinction between action in the sense of what human beings do and action in a broader sense. I mean, quite simply, that we talk of, for example the wind blowing the door shut, the lightning striking a tree, the sun drying the washing without batting an eyelid. We all know the difference, but that's because of our intellectual training. Personification of the inanimate in that way is built in to our language.

After all, if one is going to dismiss spirit, it has to be made clear what the term even means apart from the mundane casual (causal?) thinking. — Astrophel

Yes. I do accept that it means something to those who talk about it. My problem is that I don't really understand what that meaning is. Too often, it seems like a way of escaping awkward questions.

Obviously, the lure of magic, wish-fulfillment, personification of natural phenomena and all those impulses that begin with ritual and eventually culminate in huge international institutions like the RCC, is very much a part of that interest. — Vera Mont

RCC = Roman Catholic Church?

But isn't there something "behind" the stories that a person cannot wimp out on even if she tried? — Astrophel

For me, phenomena like personification and our ambivalent (or complicated?) attitude to animals is a clue. The concept of a person can be applied to things that are like people in some ways, but not others and it is particularly tempting for societies that don't have the benefit of modern science. If you think that some sort of super-human being is throwing the furniture around in heaven it is less alarming than not knowing. You can take steps to appease its wrath, which is comforting even if ineffective.
I have a feeling that some conspiracy theories have the same origin.

Perfectly reasonable, IMO. It does seem to exist by definition, rather than anything else (conceptually). — AmadeusD

Yes. The trouble is that believers wouldn't buy that. They think that God is real, so the problem is to discover and describe him/her/it.

I don't quite understand why this would be the case? — AmadeusD

I was thinking what might persuade me to think that a religion was rational. If someone posited God as an axiom, and thought through the consequences for their life and lived accordingly, that would be rational, wouldn't it? Then, if religion was rational, atheism could posit (or just not posit) the axiom but still be rational, if they thought through the consequences and live accordingly. However, if both ended up living the same sort of life, it would follow that the axiom was unnecessary and could be abandoned. That would be a rational approach to religion. Not altogether implausible.
There is a school of theology, known as presuppositionalists, (look up a theologian called Van Til) who do adopt this approach. However, they posit that the Bible is true, which is a whole different ball game. I've never seen a philosophical discussion of this, but that's understandable. If you presuppose that the Bible is true - well, other than as a historical document and evidence for history - there's very little to argue rationally about.

think this the case for a lot of agnostics - they can just leave off the issue entirely by claiming that looking for the evidence is a fools errand. — AmadeusD

"Can't be bothered" as opposed to "Don't know". I'm sure there are people, perhaps many, who are like that. They'll go with the crowd in the end.

it boiled down to just not liking uncertainty. I think this the case for a lot of agnostics - they can just leave off the issue entirely by claiming that looking for the evidence is a fools errand. — AmadeusD

Yes. A lot of philosophers are very bothered by that, as well.

I don't care if there are supertasks or not, but I am driven to straighten out the bad thinking around limits (or die trying, is more like it). — fishfry

I'm entirely in favour of the project, but, to be honest, I don't think it is worth dying for.

In math, the notation 1/2 + 1/4 + 1/8 + ... does NOT denote a process or a sequence of discrete steps. — fishfry

I think that's the first time I've encountered anyone on these sites who understands the difference between "discrete" and "discreet". Not patronizing, just saying.

Likewise 1/2 + 1/4 + 1/8 + ... and 1 are two text string expressions for the same abstract object, namely the number we call 1. — fishfry

Now you have me a bit puzzled. In my book, that means that the equation is about the complete series, which seems at odds with the idea that it can't be completed. What does "complete" mean? Or does it mean the sense in which it is "always already" complete? (see below)

Some people regard all possible worlds as equally true. That viewpoint doesn't resonate with me. — fishfry

It might be easier to understand if you thought of them as regarding all possible worlds as equally possible. I could understand that. I hope they don't mean that all possible worlds are equally actual....
But some people tend to think only of one kind of possibility - logical possibility. But there many other sorts - physically possible, legally possible, practically possible, etc. etc. I say that possible means different things in different contexts, but it may be that I should be saying there is cloud of possible worlds for each kind. Or maybe physically possible worlds are a subset of logically possible worlds. It's all very confusing. But I shouldn't get too snooty. There is, apparently, a need to this concept in modal logic, but I don't understand what it is.

You lost me here. I believe I was arguing to Michael that it's at least conceivable that we execute a Zeno walk on the way to the kitchen for a snack; and that therefore, the idea is at least metaphysically possible. That's all I'm saying. — fishfry

Oh maybe I understand ... you're saying that just because the path can be infinitely subdivided, does not mean that I'm actually executing that sequence. I think I disagree. I have to traverse each of the segments to get to the kitchen. — fishfry

Well, in that case, you are also traversing the infinitely many possible points along the way, as well as the convergent series based on "<divide by> 3" and all the other series based on all the other numbers, plus all the regular divisions by feet or metres. Or maybe you could decide that all these ways of dividing up your journey are in your head, not in the world. Think of them as possible segments rather than chunks of matter or space.

But in math, 1/2 + 1/4 + ... is added together all at once. And the sum is exactly 1, right now, right this moment. — fishfry

Yes. Thanks for clarifying that for me. That's what I was trying to express when I started babbling on about "always already" in that post that you couldn't get your head around. The comparison with Loop program captures what I've been wrestling with trying to clarify. All that business about getting (or not getting) to the end... It's important though that it's a physical process which takes time. You can switch it off at the end of 60 seconds, and see how far it got, but it won't have completed anything, will it?

But all I'm saying is that it's at least conceivable; in which case it's not metaphysically impossible. I don't have to argue strongly that it's true; only that it's at least barely conceivable. — fishfry

There's no clear criterion for what is conceivable and what is not, in spite of generations of logicians. It seems pretty clear that some people have a much more generous concept of that than I do. There are famous philosophical issues around that many people seem able to conceive of, but I can't. I don't know what's wrong with me.

Right. Aleph-null bottles of beer on the wall, aleph-null bottles of beer. You take one down, pass it around, aleph-null bottles of beer on the wall ... :-) — fishfry

Make sure you get one of the ones that you can't finish drinking. You would not be popular if you passed round one of the ones that you can't start drinking.

Did my quoting get messed up? Michael keeps saying supertasks are metaphysically impossible, and I want to make sure I understand what he means by that. — fishfry

You won't have bothered with this exchange - his comment, my reply:-

But I would even go so far as to say that supertasks are logically impossible (as shown by the above argument and Thomson's lamp). I simply went for the phrase "metaphysical impossibility" because it's the weaker claim. — Michael

I think it would be better to stick with the strong claim. At least it is more comprehensible. — Ludwig V

The point is simply this: at the point we make a decision, there is a set of determining factors: beliefs, genetic dispositions, environmentally introduced dispositions, one's desires and aversions, the presence or absence of empathy, jealousy, anger, passion, love, and hatred. — Relativist

Surely, there's no problem about one acting in accordance with one's beliefs and desires (and emotions are an aspect of one's desires). That's what freedom means. What would be it be like not to act in accordance with them? So even if you say these are determining factors, they are not factors that threaten free will.

Yes, I realize that sometimes we feel that our emotions have "carried us away", but other times our emotions are exactly what we want to do. The interesting question is to understand which emotions on which occasions threaten our freedom and which don't. In the same way, we sometimes talk of being in the grip of a desire - addiction and habit are the greatest threats with social expectations and manipulation a close second - and sometimes doing what we want to do just is freedom. Again, the interesting question is to distinguish the two. Beliefs also sometimes mislead us - it is better to act on what we know, but hard to be sure which beliefs are knowledge and which not, but that's the interesting issue. No-one wants to act on false beliefs. Everyone wants to act on knowledge. Sweeping generalizations just create fake philosophical problems.

In my opinion.

But I would even go so far as to say that supertasks are logically impossible (as shown by the above argument and Thomson's lamp). I simply went for the phrase "metaphysical impossibility" because it's the weaker claim. — Michael

I think it would be better to stick with the strong claim. At least it is more comprehensible.

Metaphysical impossibilities are things which are necessarily false; e.g. see Kripke's Naming and Necessity in which he argues that "water is H2O" is necessarily true even though not a priori (i.e. logically necessary). — Michael

Yes Kripke does claim that. But he waters down the meaning of "necessarily". For him, it no longer means "in all possible worlds", but "in all possible worlds in which certain conditions hold". But contingent means, or used to mean, "true or false depending on certain conditions". So, on this account "necessarily" means what "contingent" used to mean. Talk about having your cake and eating it!

Where do i get one of these metaphysical beers? — Metaphysician Undercover

At your local metaphysical beer shop, of course. I'm sure Google knows its address and will give you directions. (Shops never stock both metaphysical and mathematical beers at the same time. They fight, you know - very messy!)

I clearly explained though, it isn't "infinite" which is incoherent, it is "infinite divisibility" which is. "Infinite divisibility" is a specific application of the term "infinite" which is incoherent. It is incoherent because the concept of "infinite" is incompatible with, inconsistent with, or contradicts, what is implied by the concept "divisible". Therefore the two together as "infinite divisibility" is self-contradicting. — Metaphysician Undercover

Of course you did. I'm sorry. But in any case you've just accepted that mathematical objects aren't true objects. So what's the problem?

Mathematicians have made "infinite" into a new term, which really has very little resemblance to its metaphysical roots. — Metaphysician Undercover

I would be happy to accept that there are two concepts of infinity here. I think that may be because their concept has its roots in mathematics, whereas the metaphysical concept has roots elsewhere..

This leaves mathematics, and mathematicians in general, as fundamentally incapable of dealing with the metaphysical problems involved with the concept "infinite". — Metaphysician Undercover

So we just have a case of Domains of Magisterial Authority, and no need to fight about it.
Our only remaining issue is whether the problem of Achilles and the tortoise and Thompson's lamp is a mathematical problem or a metaphysical problem. Or maybe it's just a question of understanding two solutions to the same problem. They clearly won't be incompatible.

Again, I do not follow. Metres can be divided. We have centimetres and millimetres. But when we measure, at some point an approximation is made, a rounding off. — Metaphysician Undercover

Quite so. And we know that it is an approximation because we know what more and less accurate or precise measurement is. The exact measure, in the physical world, is the limit that empirical measurements can approach and never reach. That's mathematics and logic.

I don't think that this is relevant. I believe the analysis applies to all objects. But there is a problem with supposed "mathematical objects", and this is that we assume them to be infinitely divisible. And this assumption creates incoherency. This incoherency renders the supposed objects as not true objects. — Metaphysician Undercover

I'll take that. I wouldn't put it the same way, but it's near enough. I think, by the way, that you would have a tough job to convince mathematicians that there is an incoherency in the concept of the infinite. But that's not my problem.
Irrational numbers are built in to the system, so are recurring numbers, and so is infinity. You can't have one without the other. Sad, but true.

Lost in the ether, forever. — fishfry

I expect we'll survive.

I have not said that. I have said that I have no strong opinion about supertasks and am entirely comfortable arguing either side. — fishfry

Thanks for clarifying that. I find it quite hard to remember what everyone's position actually is. It gets lost in all the detail.

One might say that one cannot complete such a series. I'm not sure of my ground here, but I think you will find that everything depends on what is meant by "complete" and it won't mean completing a recitation of all the steps in the series. — Ludwig V

I would be very grateful if you could help me clarify this. When you say:-

When a mathematician says that 1/2 + 1/4 + 1/8 + ... = 1, they don't mean that you can perform this calculation with pencil and paper before lunchtime. They mean that the two expressions on either side of the equal sign denote the same real number. — fishfry

That's not quite as simple as it looks. The left-hand side will never equal the right-hand side as long as I try to make them equal by adding further steps in accordance with the same rule (...1/16, 1/32...). That's what it means to say that 1 is the limit, not the last step. But if I add 1/8 again, the two sides will be equal. Does that count as completing the sequence?

Ok. Possible worlds. I actually took a class where we talked about that, but I have a hard time understanding the concept. There are people who think possible worlds are real. I'm not one of them. And the whole metaphor is lost on me. — fishfry

Whether possible worlds count as real depends entirely on what you mean by "real". For some people, "real" comes down to true. If it is possible that it will rain tomorrow then possible worlds are real because it is true that it will rain tomorrow. For others, a possibility is not actual, so cannot be real.

And even then I reject the claim on its own merits. I could argue (not that I do, but that I could -- hope that's clear) that if time is modeled by the real numbers (agreed, that is a dubious assumption) then I perform a supertask every time I get up to go to the kitchen for a snack. I named my refrigerator Zeno. — fishfry

Quite so. But I think there is a confusion going on here. If you'll allow a temporary and artificial distinction... Roughly, it's the difference between an analysis, which doesn't change or affect its object, and a division or separation which does. That's the difference between measuring a plank of wood as 10 cm long and cutting it into 1cm lengths. The first is an analysis, the second is a division.
There are infinite ways in which I can mark out the plank, and they are all true at the same time and the physical object that is the plank is unaffected by any of them. True, the marks will be physical objects, so there will be limits to what I can do. But the system allows me infinite possibilities, including a convergent series. None of these makes the slightest difference to the plank. So when you visit Zeno for a beer, the fact that there are infinitely many analyses of your journey does not make the slightest difference. It's all in your head.

(Here's a thought. When you drink your beer, you have to drink 1/2 of it and then 1/4 of it and then... Your beer will never be finished. :smile: But then, a similar argument would show that you can't even start drinking it. :sad: )

You could probably help me out by clearly defining metaphysically impossible. — fishfry

It simply isn't clear. "Metaphysics" is a word looking for a meaning. There is some connection with logic, but what differentiates the two is a mystery.

Was this from you to me? That post of Michael disappeared for me as well. — fishfry

I still can't find it. I copied the quoted passage into my message, but not the commentary. Which is a pity.

c) it is metaphysically possible to recite the natural numbers at successively halved intervals of time — Michael

There's another strictly philosophical issue. I know that metaphysics overlaps with logic. I'm still trying to work out whether it is identical with logic.

Supertasks cannot be performed in any possible world. — Michael

suggests to me that it is a question of logic.
Subject to that, I do agree that c is false. I think that those who disagree with you think that they can stipulate by definition some sense in which it is true.

That there really is possible 'evidence' for God which is 'true' regardless of how any particular human sees it? — AmadeusD

Well, I was accepting the widespread belief that the issue is empirical and trying to think through the consequences. I hope I demonstrated that, as at present conducted, the debate will not be resolved, because the two sides talk past each other. On that assumption, agnosticism is the only rational possibility.

I don't rule out the remote possibility that something might turn up that would work as empirical evidence for God. But I can't imagine what that might be. If God did turn up in some way, I would have a great many unanswerable questions to discuss with them.

My actual position is that the concept of God is incoherent, which means that I can neither assert not deny that such a person exists - the concept would have to be coherent for either assertion to be meaningful. So I can't classify myself under any of the four propositions you listed. (I suggested D earlier, but I've changed my mind.)

However, on my understanding of what a religion is - a way of life and a collection of practices and attitudes, if the existence of God is treated as an axiom, it may well be rational. Atheism, then, would be the adoption of the non-existence of God as an axiom, and could well also be rational. (Geometries based on different axioms are all rational - consistent and complete.) Axioms are not adopted on rational grounds, they can only be assessed by their results.

I don't know why we would somehow attribute an ontological free lunch to the concept of God simply to avoid having to resolve the issue. — AmadeusD

I don't quite understand what you mean. What could I do to bring matters to a head?

There is nothing that is divisible infinitely, therefore this ideal needs to be excluded as necessarily an attempt to do the impossible. — Metaphysician Undercover

.... apart from a geometrical straight or curved line. I grant you that that is a concept of an abstract, ideal object. I grant you also that such division does not necessarily affect the unity of the object in any way.

It is a collection of distinct wavelengths, and I believe it is divided by the harmonic principles of the Fourier transform. — Metaphysician Undercover

That is the best representation of colour that physics can manage. But most people do not know about wave-lengths or Fourier transforms. So when I choose a red coat to wear to-day, how do I manage that? The colour that I am aware of is divisible in the sense that there are many colours and shades of colours. These correspond only roughly to the wavelengths of light.

No we don't need infinite divisibility, for the same sort of reason that we need infinite numbers, for the reasons I described. — Metaphysician Undercover

So how can we be sure that anything can be measured in terms of metres, if metres cannot be divided so that they exactly measure the length we are measuring?

I need to think about how to tackle your metaphysics.

An afterthought. Do I understand rightly that your analysis of wholes and parts applies to physical objects, and not to mathematical ones?

In fact, one could simulate the on/off lamp so that at a certain rate you would see what appears to be a constant light. — jgill

It's a bit more complicated than that. Bulbs like fluorescent ones flicker, but the light really is constant. It's like what is called "motion illusion" or the φ phenomenon. Film and television both rely on it. In a sense, the motion is an illusion, but in another sense, it isn't. The illusion of constant light, paradoxically, is real.

The problem though, is that in the prescribed scenario there is no such thing as "a certain rate". The rate is not constant, but rapidly increasing. The only constant is the rate of increase. That rate of increase is what I say is incomprehensible and incoherent. — Metaphysician Undercover

Yes, but it is not difficult to abandon the (pseudo-physical) lamp for a purely abstract version, which does not have the same problems.

One is to align the infinite sequence "0,1,0,1,0,1...." with the steps in the regress and to ask whether 0 or 1 can be assigned to the last step. An even simpler version is to align the natural numbers with the steps in the regress and ask whether the final step is an odd or an even number.

Those are clearly abstract sequences, and don't have the complications of trying to align the steps of a physical sequence to the steps of the regress. I agree that trying to do that is very problematic and almost certainly incoherent.

This is the trick of the whole thing. It really is about empirical things. These empirical things are space and time, each of these is known through experience. Then we take these empirical things and pretend that they are absolutely abstract, purely ideal, and stipulate ideal principles like infinite divisibility. — Metaphysician Undercover

I don't have a problem with ideal principles. They are very useful. We need infinite divisibility for the same sort of reason that we need infinite numbers. The infinite numbers guarantee that we can count anything. Infinite divisibility guarantees that we can measure anything (that is measurable at all). Limitations on either are physical.

In the case of division though, we may assume that infinite divisibility would allow us to divide anything anyway, but this is really incoherent. That is because division implies, or requires logically, that there is something, an object of some sort, to be divided, and its divisibility will always be dependent on the sort of thing that it is. An object, or thing is a unity of some type, and as such there is always limits to its divisibility, whatever unifies also determines divisibility. — Metaphysician Undercover

I think you are being misled by the temptation to take the divisibility of "medium-sized dry goods" as the paradigm of divisibility. But even that depends on the level of description you are applying, or, if you prefer, the level of analysis you are using.
The weight of a medium sized dry good is infinitely divisible. We couldn't measure its weight or calculate its centre of gravity it if it wasn't.
The colour of something isn't divisible at all. (That's why colour is disregarded in physics and treated as a mental phenomenon, whatever that is.)
You may say that these are not "objects", but that reinforces my impression that you are unduly focused on just one phenomenon in the physical world.

Then, someone creates a scenario, like the lamp or the op, which utilizes this purely ideal feature of infinite divisibility. Now we do not properly separate the purely ideal from the empirical, in our minds, so that "empirical time" interferes, and we say that 60 seconds must pass, it has to because experience tells us that it will. But that is allowing "time" to be an empirical thing. — Metaphysician Undercover

You may be right. I'm afraid that I'm like Augustine. I don't know what time is, though I do know, of course, what time it is right now and what time I woke up.
The great trap with infinity is the temptation to try to get round the endlessness of the sequence by hacking through each step in it.

There's little accounting for what students will do. More interesting is what you do. Assuming you're teaching philosophy and that you have some legitimate pedantic purpose in allowing them to use sources like PSE and TPF, what is your intention/goal in so doing? — tim wood

It isn't a question of allowing them to use PSE or any other site. They will use it or not, as they see fit.

When I was teaching, the most difficult thing was to persuade students to debate philosophy with each other, outside the class-room. I felt then that anything that encouraged them to participate was a good thing. True, they might pick up wrong-headed views, but they are liable to do that all by themselves.

So if I was teaching now, I would encourage them to use these sites and to bring back to class what they found there (within reason). It could be a valuable stimulus to discussion in the class-room or tutorial session. Of course, there would have to be health warnings, but I'm pretty sure the benefits would outweigh the risks. And I would have to insist that the most important thing is to READ THE BOOK.

it's not necessarily that well suited to philosophy. It's more well suited to disciplines that have explicit agreed upon correct answers, and philosophy seems to have remarkably few of those. — flannel jesus

You are too kind. The model for the site is clearly (not "not necessarily") "those disciplines that have explicit agreed upon correct answers". That model is not at all well suited to philosophy, which lives and breathes on disagreements. If the model was strictly followed, it would be an extremely boring place.

There's actually a (somewhat) hidden tension between the model and the democratic structures (modified by the existence of the moderators, who do a reasonably good job) that are also built in to the system. The result is a bit chaotic and inconsistent, and, of course, there is a good deal of using the rules to try to enforce specific philosophical views.

In my opinion, the system of building a reputation by scoring points and collecting badges is much more problematic - and there is a similar system on Reddit, if I remember right. I found that it is quite hard to resist the temptation to score points rather than doing some philosophy.

It's basically, "If someone can disagree with your answer, then it isn't a good answer." To the extent that an answer required thought or creativity or any substantial form of agency, it isn't a good answer. — Leontiskos

You are quite right. But the expectation that answers (and questions) should have some basis in existing philosophy is not altogether unwelcome. But perhaps that's just my personal taste.

There is scope for real philosophical work in the chat rooms, which are not subject to the same restrictions. I found those the most fruitful part of the site.

Don't you think it is ironic that the critique of PSE was posted on Reddit? Talk about pots and kettles. I thought that the response to this question when it was posted on PSE was, overall, quite well balanced and sensible.

PSE echoes Wikipedia, which has similar problems. The place of an expert in the democratic and inclusive times that we live in is difficult and needs constant negotiation.

I have used PSE but found it difficult to negotiate. I find myself using TPF more and more and PSE less and less. I have looked at Reddit, but never signed up - not my cup of tea at all.

There are four words we can use to adequately, discreetly and clearly delineate the four positions of relevance — AmadeusD

I remember that discussion. Thanks for the reminder.

In the context of the assumption that it is an empirical debate, I'm content with C. In favour of it is the idea that existence claims are always empirical. That's more complicated than it appears.

But in any case, the fact (and I do think it is a fact) that the empirical debate cannot be resolved suggests that it is not simply an empirical debate. The heart of the problem is that the debate is not about the evidence, but how the evidence is interpreted. That means that the proposition that God exists is not empirical, but is a principle of interpretation.

Short story, it is an extension of the concept of a person and the associated language-games. The gods of animism are much more like a personification of their various powers than anything else and monotheism is an extension of that.

So that brings into question whether there is a coherent minimalist (or maximalist) concept of God. I think that there is not. D may be more appropriate to that.

But if I think that theism is irrational, I must think that anti-theism is also irrational, which suggest that D may be more appropriate.

Do you agree that the philosopher must uphold, almost, a fiduciary duty towards the public, in terms of living a certain life? — Shawn

The public certainly seem to think that everyone in the public eye is expected to do that. Yet it is not clear to me that the public think that they should uphold the same standards. One might argue that people in the public eye are often role models for others and so have an additional responsibility to conform to a higher standard. But if that's so, everyone is in the eye of some of the public and is likely to be a role model for some people, so everyone has a similar responsibility.

I assume most people (philosophers or not) are flawed and limited beings — Tom Storm

And one would have thought that a certain level of tolerance and even forgiveness might be expected of the public - unless the public never sins.

All we have is a text and the text is a fecund vehicle for alternative interpretations. — Tom Storm

It certainly is. A biography is also subject to interpretation. It is probably a good idea to wait until it is over, but even then a final judgement is difficult to arrive at.

To give an example, take Socrates. His life and philosophy seemed inseparable. — Shawn

It's a good idea to remember always that Plato's account was more hagiography than biography.

Whether Heidegger was a Nazi or not (for me) may well taint our experience of his work, but it says little or nothing about whether the work is any good. — Tom Storm

The interesting question is what basis, if any, there is for Nazism in his philosophy. I don't think there is a determinate answer, but it is worrying.

I don't see why you put Witty on a pedestal. It's well known that he was an awful person. — Heracloitus

I agree. Yet he had friends. I don't think I could have been friends with him, and I don't suppose he would have wanted to be friends with me. I don't care either way, he is an amazing philosopher.

There are questions to be asked about the involvement of both Berkeley and Locke in the slave trade as well. In their case, there is a tricky issue about how far we pay attention to the context that they lived in. I don't suppose anyone is much bothered about whether Plato and Aristotle (or Socrates) owned slaves. Rousseau's life presents other issues.

Something flashing on and off at a constant rate is not comparable, because the description is of a rapidly increasing rate. And the rate increases so rapidly that the prescribed rate becomes incoherent even to the mind, as well as the senses. This is just an example of how easy it is to say something, or even describe a fictional scenario, which appears to make sense, but is actually incoherent. — Metaphysician Undercover

There is no doubt that it is easy to do that. But it seems that people disagree about whether the scenario makes sense or is incoherent and even if they do agree, they still disagree about why.

Jgill talked about how the lamp would "appear", and this implies a sense observation, and empirical judgement. The point I made is that the description describes something far beyond our capacity to sense, so it is incoherent to talk about how this described thing would "appear". — Metaphysician Undercover

I agree that this isn't really about anything empirical, but it sort of seems to be.

OK. You and @fishfry both believe that the supertask is impossible. But you believe that is because it is contradictory and fishfry believes that it is because the last step is not defined. Am I right about that?

I see no contradiction in Thompson's lamp, only a failure to define the terminal state.
— fishfry
See here. — Michael

I followed your link and found this quotation from Benacerraf's Tasks, Super-Tasks, and the Modern Eleatics. I've put the passages of interest in bold and italicized the passage quoted from Thompson for clarity.

Thomson's first argument, concerning the lamp, is short, imaginative, and compelling. It appears to demonstrate that "completing a super-task" is a self-contradictory concept. Let me reproduce it here:

There are certain reading-lamps that have a button in the base. If the lamp is off and you press the button the lamp goes on, and if the lamp is on and you press the button, the lamp goes off. So if the lamp was originally off and you pressed the button an odd number of times, the lamp is on, and if you pressed the button an even number of times the lamp is off. Suppose now that the lamp is off, and I succeed in pressing the button an infinite number of times, perhaps making one jab in one minute, another jab in the next half minute, and so on. ... After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? ... It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off. This is a contradiction.

Pause here. I think Thompson means that

It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on.

contradicts

But the lamp must be either on or off.

That seems to be true.

But the passage continues (Benacerraf's words): -

Rarely are we presented with an argument so neat and convincing. This one has only one flaw. It is invalid. Let us see why. Consider the following two descriptions:
A. Aladdin starts at t0 and performs the super-task in question just as Thomson does. Let t1 be the first instant after he has completed the whole infinite sequence of jabs – the instant about which Thomson asks "Is the lamp on or off?" – and let the lamp be on at t1.
B. Bernard starts at t0 and performs the super-task in question (on another lamp) just as Aladdin does, and let Bernard's lamp be off at t1.
I submit that neither description is self-contradictory, or, more cautiously, that Thomson's argument shows neither description to be self-contradictory (although possibly some other argument might).

That also seems to be true. The three sentences in bold in the first passage are not individually self-contradictory, but the conjunction of the three (the concept of a supertask) could be described as self-contradictory. Nor are Benacerraf's A or B self-contradictory. They could be both true, if a third state that is neither on nor off were possible. Perhaps Benacerraf was assuming that there isn't.

But @fishfry says that the final state is not defined. That would indeed be a third state which is neither on nor off. The idea that this is the case, is supported by the fact that both Thompson and Benacerraf feel the need to consider both alternatives. The point is simple enough - the definition of the infinite set is such that there can be no last step, in virtue of the definition, every step has a successor. So the last step is not defined. You may be thinking that there must be a last step in a convergent series in the series that we've been considering here, it is 1, or 0. But those are limits, not last steps. The series itself by definition cannot reach that limit, so 1 (or 0) cannot be a step in the series. One might say that one cannot complete such a series. I'm not sure of my ground here, but I think you will find that everything depends on what is meant by "complete" and it won't mean completing a recitation of all the steps in the series.

I think I'll leave it there.

PS Since I started writing this, the link to the post that I copied this quotation from seems to have become non-functional. Very odd.

Ok, so we don't know anything for sure, not just the matter of whether there is a God. — Lionino

Well, the first half of that is debatable, but let's save that for another time. You seem to have agreed on an agnostic position.
From observation of philosophical debate it is clear that both (some?) theists and (some?) atheists agree (though I've not seen either side explicitly acknowledge the fact) that the question whether there is a God is empirical. Let's have a closer look at it.

First, it implies that there is a concept of God - in fact several concepts, but let's take the minimalist one. Let's treat it as a hypothesis. Both sides, presumably have an answer to the question what is to count as evidence, either for or against. It comes down to experiences. Theists will cite certain experiences, which are not universal, but are not uncommon, and the various mysteries that exist in the sciences, and possibly the idea of an experiment, in the form of prayer. Atheists will cite the lack of any experiences that specifically prove God exists (and discount all the evidence given by the theist). On top of that, I think that they will not be able to explain what experiences might convince them. Certainly, I can't and I've never seen anyone try.
There has been considerable debate about where the burden of proof lies. Each side makes a case that the burden of proof is with the other side. So no agreement there.

Transcendent experiences may well convince the person who has these experiences, but are of little or no value to the atheist, because they are so subjective. Experimental prayer doesn't stand up to scrutiny by the standards commonly applied in science. A God of the gaps certainly won't convince anyone who isn't already convinced - it comes down to interpretation of the evidence.

Atheists seem to be in a stronger position if the burden of proof lies with the theist. However, proving that unicorns, for example, don't exist is at least very hard. Arguably the only reliable case is a proof that they could not possibly exist - i.e. that the concept of a unicorn is incoherent in some way. The same applies to the concept of God. But that's not going to convince a theist.

I don't see what might happen to resolve this. Suggestions welcome.
For me, both theism and atheism are irrational, even if they are empirical claims. Which leaves agnosticism as the only rational position.

Sorry about that. I typically select the entire post and hit Quote, and it seems to lose a lot of the attribution. — fishfry

Yes, I find that as well. I work round it by selecting only the quoted text, not including the link that gives the attribution. Then, you can hit "quote" and the system does pick up the attribution. Then, if you separately select the response, it is copied and attributed in the normal way.

The limit is not part of the sequence. so that doesn't run the sequence backward. I am not sure what point you are making about the sequence. The dots merely indicate that the sequence progresses indefinitely. — fishfry

Neither am I, on reflection. I was trying to articulate the point that one can count forward, but not backward, so I don't think anything is at stake.

"If you know what you're doing you're not learning anything." Think I read that somewhere. — fishfry

Yes, I like that. I'm a bit of a contrarian, so I'm tempted to reply that I don't need my surgeon to learn anything while he's cutting me open. Indeed, I would be rather concerned if I thought he was. It applies better to artistic, experimental, open-ended activities - like philosophy and maybe mathematics, at least sometimes.

I'm out of my depth on that. Don't understand what's meant by realism or anti-realism. Simply don't believe that 2 + 2 = 4 has a truth value before some intelligent entity shows up to pass judgment. — fishfry

If you don't understand what realism vs anti-realism means, you have understood correctly - as I see it. Some people would argue that the proposition that "2+2 = 4" does indeed only have a truth-value only when someone passes judgement on it but that 2+2 = 4 independently of anyone doing that i.e. is objectively true. There's a temptation to think that mathematical truth is eternal, i.e. always has been true, always will be true, whatever happens. But that's a mistake. It makes no sense to assign a place in the time series to 2+2 = 4; there is no meaningful way of doing that. (Grammarians recognize a tense that is called the timeless present which is exemplified in propositions like this.)

Ok. Don't think I disagreed with anything you said. — fishfry

I'm glad it made sense.

If one watches the lamp in a dark room, at some point it will appear to be on continuously. — jgill

Quite so. I've been thinking that the rules of the game require one to classify that as a purely physical phenomenon. But I prefer versions of this problem that define a sequence (0,1,0,1,...) and align that with the lamp. Even better, I think, we can count the steps in the convergent series and not that odd and even numbers alternate and ask whether the last count when 60 seconds are up is odd or even. Nothing physical intervenes.

I think that if the lamp is going on and off at an infinite rate, then it's not correct to say that it would be on at any particular time, or off at any particular time, because it is going on and off at a rate faster than our ability to determine a particular time. — Metaphysician Undercover

That's true, but seems to be a purely physical limitation. It raises the question whether that means it is really on or off, or a some sort of in-between state. Fluorescent lights flicker on and off all the time (at least if they are running on AC, and we just say they are on. And it is true that for practical purposes there is no relevant difference between that light and sunlight or candle-light.

Either way, the point is that it's special pleading to argue that it's possible to have recited the natural numbers in ascending order but not possible to have recited them in descending order. It's either both or neither, and it can't be both, therefore it's neither. — Michael

I'm not clear whether you are thinking of reciting as a human action that takes time. In which case, there will come a point in your recitation when you physically have to stop, but have not run out of natural numbers. (If we are talking about a series that is convergent in time, it will take longer to utter the word(s) than the time available.)
To put it another way, to say that the series of natural numbers is countable, doesn't mean that there is anyone (apart, perhaps, from God) who could actually, physically, count them. In my book, it just means that they are defined in such a way that they could be counted and, indeed can be counted, so long as one chooses to count only a part of the series. It doesn't follow from the definition of the natural numbers that anyone could count all of them.

I have to disagree. What you describe is a rate of acceleration which would produce an infinite speed. The rate at which you recite the numbers becomes infinite before 60 seconds passes. And, despite the fact that infinite speed is in some sense unintelligible, it is clearly not at all the same as being stopped. — Metaphysician Undercover

No, it isn't the same as being stopped. Being stopped is an everyday occurrence. Infinite speed, is, as you say, unintelligible. If that's what underpins the supertasks, it makes sense of the narratives - apart from the fact that it doesn't answer the question whether the lamp is on or off.

The rules of this (language-game) still make no sense to me.

It's not so clear to me, many people treat God as if it were something explanatory, sometimes even empirical, in the broad meaning of the term (which includes personal experience). — Manuel

Yes. People may differ, of course. The view I expressed is unlikely to be acceptable to many believers - though there may be some, with philosophical inclinations who could accept it. There are theologians who would be able to recognize a view like mine.

Why did I get a bonus at work? God is gracious. What caused my existence? God. Etc. — Manuel

A nice simple example. But if you look a bit closer, you may think that what is on the surface is not the whole story. When you don't get a bonus, even though you worked just as hard, with the same good results, you don't think maybe it isn't God who gives you the reward, but your employer. You think that God must be angry with you and search for reasons why that might be so. You don't think maybe God is a bit strapped for cash this year so is having to cut back. The idea that it is God who dishes out rewards is protected against refutation. That's important. (I'm sketching here to avoid reams of writing and reading.)

But I do not think that asking for some properties or attributes or facets of God is asking for too much. The more which can be given, the better we can proceed. If it is limited to a Great Being, or a supreme force, then I do not know what this means, or at least, it is very nebulous. — Manuel

Yes, that's a fair demand. Too many "proofs" of God don't explain what that means. (Hence, we find that the God of the philosophers bears little resemblance to the God of the believers, and that's a problem.)

And there's no arguing with axioms, except by their results. In this case, the argument has to be about what life the believer leads — Ludwig V

In many ways, I'm not happy to be dealing with a God about whom there can be no argumentation. Hence belief in God as a matter of faith, not subject to rational comment, is far too comfortable a retreat for believers. That's why I suggested how the argument might go.

So I think we can have arguments about God, even if there may be no chance of getting each other to agree. — Manuel

You are maybe a little too pessimistic. People do sometimes abandon their faith. But it's a complex process that may include rational arguments, but religious belief involves more than that, so they are only one factor.

I think agnosticism is better, with atheism being applied in specific instances. — Manuel

That's a very reasonable position.

"Erm, I can't say either way", even though there is nothing logically contradictory about a green floating donkey tidally locked behind Jupiter in respect to the Earth. — Lionino

On that basis, agnosticism is the only rational response. (It is my preferred response if people ever ask me.) But there are a number of physical impossibilities, not to mention improbabilities, about that the green donkey hypothesis that make it, in my view, unreasonable to be agnostic about it. I assume that you focus on logical possibilities because that's the tradition of our philosophy. But we have to live with physical impossibilities as well, so it seems a bit peculiar to ignore them, if what you want to understand is human beings.
Wittgenstein imagines himself in conversation with a philosopher about the question whether the tree they are sitting under really exists, and then realizes that he has to turn to anyone nearby who's listening and explain "It's all right, we're only doing philosophy". If it's only philosophy how can it matter to actual human beings?

First, define what God is, then we can say if we know enough to say, with certainty, that such a thing exists or does not. Maybe we can't reach certainty, in that case we shift to probabilities. — Manuel

That's the logical procedure, and some theists do like to try to follow it. But God isn't an empirical hypothesis. It is how you frame your life. What God means, according to the religions, is how one should (try to) live one's life. (What science means is not just the philosophy of science, but how you do it in practice.) Admittedly, how that works out in practice can be a bit puzzling to outsiders, but that's how the ideas work. (The same is true of science) To put it another way, if you start by defining God, that may turn out not to be a hypothesis, but an axiom. And there's no arguing with axioms, except by their results. In this case, the argument has to be about what life the believer leads.

“If you crush a cockroach, you're a hero. If you crush a beautiful butterfly, you're a villain. Morals have aesthetic criteria.” - Nietzsche — BitconnectCarlos

He's right, of course, in his annoying way. Either there's a justification for that difference or there isn't. If there isn't, then morality is deficient. But I think there is. Cockroaches are annoying and dangerous. Butterflies mostly are not, but they are beautiful - except perhaps when they are caterpillars. (That's awkward, I admit) I don't see anything dubious about not destroying beautiful things that do no harm and something very dubious about not destroying dangerous things that are harmful.

If something is not necessarily right then it could possibly be wrong. Evolution helps us survive, not necessarily thrive or self-actualize. — BitconnectCarlos

Do you not think that the values that we define as necessary for those two are given (majorly) by evolution? — Lionino

Evolution doesn't give a toss whether individuals or a given species survive or not. It doesn't even care much if a species survives. It is a consequence of the genetic variation of individuals within a species and the random effects of that variation on the survival and reproduction of traits amongst those individuals. Morality has nothing to do with it.
Homo sapiens is a social animal. So are many other species. It is curious that we so often see ourselves as individuals and society as an optional extra and a problem. But surely that fact sociality is so common should lead us to conclude that social living enables individuals to survive and reproduce better than competitors. I would agree that this may well have something to do with morality, insofar as morality is about social living. Evolutionary biologists regard this as "kin selection", based on preserving the genome and nothing at all to do with morality, so there is more to be said here.
I do agree that evolution doesn't have much to do with thriving or self-actualizing, as we understand it. Though it does seem very plausible that if morality interfered with the ability to survive at least until reproduction, it would surely die out. (Can you imagine a society in which everyone was celibate? Not for long.) So evolution must influence morality at least in that negative way.
The idea that ethics and morality are not merely about how to live in a society, but also about how to live well as an individual (that is, as an individual in society). Answers to that must be based on ideas about what human beings are and what they can be. But evolution, though it has an impact on everything, does not dictate everything, (though evolutionary biologists seems to forget that), so it is not impossible to choose different ways of living with the constraints of survival and reproduction. If our lives are really limited to survival and reproduction then they are grim indeed. It is better to regard them as the preliminaries to living well but not the whole story. There's more to be said, of course, but I'll leave it there.

I think that (1) is a tautology — Michael

I agree. By "we" do you mean us human beings? You and I? If so, we will necessarily stop, if only when we die.

whereas no evidence has been offered in support of (2). — Michael

Assuming that there are people who believe this, it is reasonable to assume that they can offer what they think is evidence. So it's truth depends on what you mean by "evidence".
By "recite", do you mean some event that occupies a finite amount of time (larger than 0)? In that case, assuming you mean "all the natural numbers", 2 is false, or at least logically impossible.

I hope not, my sources are academic.
— Ludwig V
I have no doubt, and I hope I am sufficiently conveying the humble limits of my knowledge in this area. — fishfry

There's a confusion here. The remark you quoted, which the system attributed to me, is actually @Lionino. I could claim academic sources from what I'm saying, but I read them a long time ago, and if you asked my for attributions, I would have to spend a long time looking them up.

By definition, an infinite sequence is a1,a2,a2,… It only goes forward. Though if the elements are decreasing (as 1, 1/2, 1/4, ...) the points go from right to left. — fishfry

I take your point. So the dots reflect the lack of definition and trying to run it backward finds the dots at the "beginning", so the "beginning" is not defined. But one could define a similar sequence that runs (0, 1/2,1/4.... 1), couldn't one? That would not be the same sequence backwards, of course.

I freely admit to my philosophical ignorance, so I am out of my depth in these matters. — fishfry

But no, that is not about the world. The world is what's real, what's physical. — fishfry

Welcome to my world. Being out of one's depth in it is almost a prerequisite of inhabiting it, so that's not a problem. It would probably unfair to say that people who think they are not out of their depth are always wrong (compare relativity and QM). But it is certainly true that you need to be a bit out of your depth to be doing any serious work. If you have everything sorted out and pinned down, you've lost your grip on the problem. (Wittgenstein again)

Unfortunately "The world is what's real, what's physical" is a metaphysical remark (at least, it is if there are any philosophers around), so you've jumped into the water without, perhaps, intending to. The question is whether numbers, etc. are real things that are not physical; platonist-type theories see numbers as real things that "transcend" the physical world. Don't ask me what "transcend" means - or "thing", "entity", "object". They would probably prefer to tell you what transcendence etc. are. But that's the same question in a different mode. Their mode is metaphysics. Mine is linguistic.

What I was doing, in response to what Lionino was saying, was putting realism and anti-realism together - since they are defined in opposition to each other - and then asking what they disagree about. (There are many varieties of both sides of this coin, so I'm simplifying, and arguably distorting.) In particular, I'm trying to show that "real" is not 'really' in contention, since no-one could deny that numbers are real - what is at stake is different conceptions of reality. And you see how slippery this is because in mathematics, not only are some numbers real and some imaginary, other numbers (like transfinite ones) are neither. Worse still, the imaginary numbers are numbers and exist, so must be real - in the philosophical sense. (At least, you can put me right if I'm wrong here.)

What "real" means depends on the context in which you are using it. Some philosophers want to use "real" in a context-free sense. But that generates huge complications and confusion. Better to stick to contexts. (The same applies to "exists") That's why I try to avoid metaphysics and metaphysicians will classify me as a linguistic philosopher - and that is indeed where I learned philosophy.

Let me ask you a different question. Before chess was invented, did all the games of the grandmasters exist "out there" in Platonic space? Did the collected games of Bobby Fischer exist before he played them? After all, each game could be encoded as a number, and the Platonists believe numbers exist independently of minds. I find that difficult to believe, that all the symbolic works of humanity exi(s)ted before they were created. — fishfry

All right. Those are good questions. They lead one in a certain direction. I am very sympathetic, so it would be better to let a platonist answer them directly. But I don't think that platonism needs to rule out the possibility that humans might be able to create some things, such as fictional stories - (although Plato was very scornful about such things on moral grounds, though he made liberal use of them himself.) - and games.
But in this field, it is as well to understand your opponent's (colleague, hopefully, in a joint attempt to discover truth) position. So consider. Games like chess are unlike games like football. Once they are defined, all the possible games are defined (so long as you limit the number of moves). So you could argue that the Sicilian defence, for example, was not created, but discovered. That's the germ of platonism.
In the end, I think, one has to see these arguments, not as simple question of truth and falsity, but of how you think about things. The answers, then, are quite likely to be pragmatic or even moral.

Humans create. That's what we do. Humans are, if you like, the very mechanism by which the universe figures out if 2 + 2 = 4. — fishfry

Yes, that's fine. There is an approach that sees humans (and perhaps some animals) as the means by which the universe becomes self-conscious. I think that's going a bit too far, but I can see the attraction.
My enemy in this field is dogmatism.

Remove God and life can lose its sanctity quickly. — BitconnectCarlos

That right? All the time the majority of the people believed in God, none of them killed any other? — Vera Mont

The truth is, you are both right.
What religions don't often face up to is that brotherly love and sanctity are actually applied only to believers. When it comes to unbelievers, all too often it's a different story. (Unbelievers includes those of a different sect.)
It's difficult to state this accurately. Not all religious people all the time regard unbelievers beyond the pale of sanctity, but it frequently goes that way.
But I don't think history shows religious people any worse than irreligious or atheistic people. (Though the majority of people through the majority of history have been religious, so the comparison is a bit flaky.)

Maybe you are misunderstanding what "abstract" means in those quotations. It doesn't mean something that we conceive in our minds, but a real object that exists independently of any conscious being, but that is outside space and time. — Lionino

But one of the minimal characteristics of mathematical realism is that things such as "2+2=4" are true and they are true even if we are all dead — in other words, it is about the world. — Lionino

If both of these are true, then we need to be very careful about what we mean by "the world". There is an application that takes "the world" to exist in space and time. Note, however, that the space-time world continues to exist even if we are all dead, even if we never existed at all. If "the world" includes everything that exists, then it can, of course, include things that exist "outside" of space and time - provided that we understand how anything can exist "outside" space, which seems to indicate a location, but does not.

Is not existing at any particular location in space the same as existing outside space? Where does platonism or Darwinism exist? or football or judo? Or the possibility of rain where I live tomorrow? Or the English language? Or the recipe for doughnuts?

Sorry - rhetorical questions. I realize that you are reporting the things that platonists might say.

Reality is what's really going on in the world. Not sure why you regard that as problematic.
A bat has a particular view of the world, as does an ant, as does a sea slug. None of them, and that includes us, know what ultimate reality is. Not sure what your objection or concern is with this idea. — fishfry

I agree with "a bat has.... what ultimate reality is" But then, I wonder what the status of "what's really going on in the world". Is that ultimate reality? From what you say, the answer is not clear. My concern is that both "ultimate reality" and "what's really going on in the world" are not defined in a way that reminds me of the way that the last step in a converging series is not defined - and cannot be defined. Yet, the sun is really shining at the moment and there really is a war in Ukraine - in short, we all (including bats and ants and slugs) live in the same world and interact in it.

Physics is inaccurate, but what if it's wildly inaccurate, as inaccurate as an ant's view of the world relative to the real world? — fishfry

But how can you say that an ant's view of the world is inaccurate? I think I can grasp what you are getting at when you say that physics is inaccurate. It reflects the fact that physics is an on-going enterprise. "What if it's wildly inaccurate.." is a style of question that I'm very sceptical of. It reminds me of "what if everything's a simulation?" I classify it as a speculation and not capable of a meaningful answer.

As I understand it, Tegmark believes the world is a mathematical structure, like a group o a topological space. — fishfry

One might interpret that belief as a dramatic way of putting the point that we can find a mathematical structure that applies to the world. If he doesn't mean that, I want to know what he means by "is".

I have the worst habit lately of only responding to my mentions and not reading the rest of these threads. — fishfry

A very sensible policy. It is easy to drive oneself crazy by trying to respond to everything. But sometimes I can't resist intervening in discussions that haven't mentioned me. It doesn't always work, in the sense of developing into something interesting, but some times it does.

I ended up spending all my time explaining the ordinals and that detracted from my resolution of the lamp. — fishfry

That's my fault. Sorry. I did benefit very much.

But the limit isn't defined in the lamp problem. — fishfry

Yes, I understand that now. I was talking about the limit of the convergent series. The series "0,1,..." has no inherent limit. If it ever is limited, it is by some event "outside" the series. That's badly put. I just mean that I can stop following the instruction for any reason that seems good to me or even none at all. The series as defined is infinite.

I'd say that the standard mathematical rules for dealing with infinity are perfectly clear, and do apply. — fishfry

I didn't mean to suggest that wasn't the case. Thinking of the series backwards is a vague handwavy imagining. That's all. I intended to contrast that with a series that can be defined forwards or backwards. It's odd, that's all.

Yes, sure, a fixed body of knowledge evolves. But that body of knowledge is added to every day by every math journal and university colloquium. — fishfry

Both sentences are true - the first sentence does not imply anything platonic, in my view. I think the difference between us is a question of emphasis rather than an actual disagreement.

I believe I lost track of what this paragraph referred to, sorry. — fishfry

Yes, that was a step too far, and it is very speculative, more a musing than a thought. I should not have pursued it. Let's just let it go.

I read your post. It is really helpful. I don't know enough to respond meaningfully, but I have a feeling I shall find my way back to it from time to time.

It did provoke the heretical speculation that it is an assumption that just one of these accounts applies to the whole of mathematics. Perhaps mathematics is not just one language-game, but a family of them.

For me, numbers exist more like Superman exists or an equation exists rather than how my hand exists. — Lionino

Yes, for me, that is the most helpful approach. Different kinds of object - different modes of existence. If you haven't come across it before, you might find this reference useful.

Fictionalism is an approach to theoretical matters in a given area which treats the claims in that area as being in some sense analogous to fictional claims: claims we do not literally accept at face value, but which we nevertheless think serve some useful function. — Stanford Encyclopedia - Modal Fictions

The only downside I can think of is that it might lead to us conceding that God exists just because so many people believe that he/it does. But then, the same would apply to Zeus, Apollo, Thor, Loki, Horus, Ptah etc. So no-one could draw the conclusion that one is a believer in any of them.

Because I think people should not claim X when whether X is far from being settled by specialists. Not exactly the same but close to how you put it: — Lionino

Yes. That annoys me as well. Though there has to be a little wriggle room, doesn't there? Philosophers, in particular, would be very constricted if such a rule were strictly enforced. Though I do agree that some philosophers would do well to be much more cautious than they are. For example, it is clearly wrong to treat the latest speculations from speculative cosmology as established fact.

Zeno was definitely using techniques beyond the state of the art at the time. — noAxioms

Yes. And as you say, they were beyond the state of the art at the time, so what he was doing needs to be rather carefully described (unless you are going to propose time travel.) It is very difficult to handle anticipations of later developments in historical texts. Some people have seen anticipations of Einstein in Berkeley. In a sense, they may be there. But I think that's merely a similarity rather than an anticipation. I don't know how to represent this case properly.

There are people today that say that there are no real infinities, whatever that means. — noAxioms

Yes, and I think that @Lionino may have been protesting at such ways of talking. If one is not a platonist, the way to say what you want to say is to conceptualise "real" in a non-platonic way. To outright deny that infinities exist is just attention-seeking. Though perhaps philosophers are not exempt from such a very human temptations.

A list is not a parent, so I disagree with the '=' you put there. I'm sure there is a correct symbol to express that any member of that list satisfies the definition of parent. — noAxioms

I've noticed a variety of extensions of the use of "=" lately, so I'm sorry if I misused it. I'm glad you recognized what I was trying to say.