Without the axiom of infinity, each number has a successor but there is no set of all the numbers; no infinite set; and no calculus — fishfry

Sure, you are right. Though "the axiom of infinity" is just a name for an axiom that posits the existence of a set with certain properties. But those properties do not include being "infinite" in some basic sense. But thanks for the qualification.

This does not change what I was saying though: like it or not, most of modern physics does use calculus. You can claim that most of modern physics is misguided (for what that would be worth), but you cannot deny the facts.

I never dismissed the possibility. I pointed out -- correctly -- that current theory says that the universe is finite. Your own examples support this. — fishfry

I take back the bit about not denying facts! And this is why I don't usually engage this person.

I can see now that an infinitely large number of planets is not needed for the argument, so thanks for correcting me on that.

I remained unconvinced, though, that an infinite number (can there be more than one?) could be specified; because it would seem that any specifiable number must be finite. This is not to deny that an unspecifiable number might be useful for mathematical operations. In any case I see no reason to believe there are infinitely many planets; but admittedly I am no expert on cosmology. — Janus

I have alluded to some more exotic mathematics in which an infinite number can actually be specified (and yes, more than one) - that goes all the way to Cantor. But that's really beside the point. All these fanciful cosmologies that are bandied around here are backed by nothing more exotic than standard calculus. And while calculus used be called "infinitesimal calculus," it has long since eschewed any explicit references to the infinitely small or the infinitely large. When we say things like "an infinite number," that's just a shorthand that, in a more rigorous formulation, unpacks into the kind of weaselly formulation that I gave you above, where I offer you to play a game: give me any number and I can give you an even bigger (but still finite) number. It turns out that that's all we need to get going.

Which is good, because contemporary physics holds that the universe is finite. — fishfry

Note that fishfry's source for this claim is, apparently, the bizarre little argument that follows it, and not what scientists actually write, which would be something like the following from a NASA site:

We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe. — NASA

Actually, when they say that the near-flatness of the universe "suggests that the Universe is infinite in extent" - that's an oversimplification. A locally flat(tish) universe is compatible with some finite topologies, such as a 3-torus. These guys did some serious number-crunching with WMAP data and came to the conclusion that out of several likely topologies that they considered, a certain compact (finite) topology provided a better fit than the infinite flat topology.

Be that as it may, you would be hard-pressed to find many cosmologists who dismiss the possibility of an infinite universe on such preposterous a priori grounds.

The idea of an infinitely large number is not as unintelligible as you think - don't underestimate the intelligence of mathematicians ;) But we don't even need to invoke infinitely large numbers here. It is enough to suppose that there is no limit to the number of planets: for any number that you may choose, there are (supposedly) more planets than that. That's all we need to assume for Vilenkin's argument.

And the classification of multiverses is given in Tegmark's Parallel Universes.

I think you misunderstood; the point is that there is no actual infinite distance. Even if you traveled away from Earth, for example, forever you would never reach an infinite distance from earth. — Janus

True, but I don't understand how this is relevant to what noAxiom was saying.

For those interested, the argument that, as a generic consequence of inflationary cosmology, there almost certainly exist exact duplicates of Earth (among other interesting things) is given here: Many worlds in one, J. Garriga, A. Vilenkin, Phys.Rev. D64 (2001). (This is still within the parameters of "level-I multiverse.")

Yeah. I have no idea what what a nonteleological account of causation is without making your nature Humean. — Marty

Well, the most popular account of causation nowadays is probably counterfactual dependence, which seems to be as far from teleology as you could get. Causal processes, causal powers - those aren't obviously teleological either. Not that I necessarily subscribe to any of those accounts - just pointing out that a nonteleological account of causation isn't something unheard of - not by a long shot.

In biology, largely for historical reasons, it is common to talk about things in a teleological fashion. This is a residue of the science's history, not a logical necessity, and is a feature not shared by most other sciences. — andrewk

There may be good objective reasons for teleological language in biology, other than it being a holdover from the prescientific era. This is most obvious in behavior science: behavior is, pretty much by definition, goal-directed. But, less obviously, it has been argued that even in other biological contexts we find features that are isomorphic to goal-directedness.

So what's your ideal world? — MountainDwarf

If you are going to imagine a fantastic alternative world that is not "broken," as you say, then why fiddle with all these little details like minimum wages? Why not go for the essence of what you think is broken in this world and eliminate that? That is, imagine a world without suffering?

There, done.

Don't see much food for thought here though.

Starting from premise (2) (potentiality/actuality) the argument heavily relies on idiosyncratic and antiquated Aristotelian metaphysics, which I feel no obligation to accept, and which in any case is not at all clear in this brief summary (if at all). And this is why this argument has no pull on me. Just my opinion.

Let's take gravity as an example. On a Humean account, gravity is just a shorthand for objects behaving in a similar attractive manner, such that bowling balls and feathers fall at the same rate on Earth, or the planets orbit in the same manner around the sun.

But Einstein notices a connection between acceleration and gravity, and posits the acceleration of objects through curved space as the gravitational force. So now you've moved from a shorthand for particulars to a very general principle. — Marchesk

Why should Humean account (as you describe it) be confined just to Newton's theory of gravity? This contrast between Newton's and Einstein's theories that you keep invoking is quite puzzling. Both are empirical theories that are aimed at explaining certain categories of observations. Relativity has a wider scope of application and, where it can be applied to the same observations as Newtonian physics, it fits some of them better.

Nevertheless, you could paraphrase Einstein's theory in terms of what you call the Humean account just as readily as you did it with Newton's theory: Relativity is just a shorthand for objects [and all of the observables to which the theory applies] just happening to behave [as far as we know] as the theory says they should behave, as a matter of brute fact, without any underlying metaphysical powers of causation constraining or impelling them.

Now, I am curious: how would you distinguish such a "Humean" universe from one that is "enriched" with your favored metaphysics?

Beliefs about ethics aren't 'free floating' somewhere in a purely abstract domain, they concern concrete ethical decisions - if the systems aren't sensitive to variations in ethical decisions then they lose their core content.

More generally, the idea that there are 'purely philosophical problems' is something I don't believe, nor do I believe that 'the love of wisdom', originally founded in ethics, is done justice by the want to entertain abstractions devoid of real problems. — fdrake

Well, I am not sure what a 'purely philosophical problem' would entail for you, but I tend to regard such problems as language problems. And like it or not, a lot of discussion in philosophy comes down to arguments about language - or so it seems to me, from my admittedly superficial amateur perspective. While I admit that working out precise language is akin to fashioning the tools of the trade for an analytical philosopher, I don't much care for such discussion myself - especially when it pretends to be substantive discussion. Still, like good therapy or surgery, a trenchant analysis of philosophical discourse can dissolve pseudo-problems and clear up confusions, and that is a good thing.

But what would constitute substantive discussion of ethics? In addition to laying out and defending the principles for living a good life, I would also include meta-ethics in that category. Although a lot of that discourse would, again, be ultimately about language, it doesn't have to be 'free-floating' if it connects to other ideas and things that matter to us.

Look at Trump. There are plenty of people like him and even admire him. His principles as a manager are (to me at least) repulsive and immoral. — schopenhauer1

One Soviet writer and intellectual who was jailed and later exiled for publishing a book of fiction abroad, once quipped: "My disagreement with the Soviet regime is purely esthetic." The first time I heard this, I thought his remark was flippant and paradoxical. Only later did I come to appreciate its truth and apply it to myself. I suspect that such "esthetic" disagreements run deeper than any articulated principles. We can argue circles around each other about policy and such, but if you are not repulsed by Trump's very demeanor, then I know that there is a moral gap between us that no principles can bridge.

I think you're interpreting my ire towards ethical systems as a kind of quietism towards them - that theory is irrelevant for motivating ethical decisions, considering what we should and shouldn't do. Rather I'm trying to advocate a subordination of ethical systems to ethical decisions. The subordination I'm advocating is that ethical systems should allow a user to think in concrete circumstances about what to do - they should have some heuristic import to applied ethics. If they don't have the ability to give heuristics; using 'heuristic' as 'a method of informing about choices'; then they can no longer have an impact on ethical decisions.

This is related to my claim in the OP, admonishing the idea that people 'pretend that they live their lives by an ethical system they just invented'. This gets the direction of influence wrong; subordinating ethical decisions to theoretical constructs, rather than using theoretical constructs to make ethical decisions. I'm sure that you've also met people who have in their mind a theoretical guarantee that their actions are always right - and these people are assholes. Or, rather, they always get to decide whether what they did was right or wrong, failures in character and lack of relevant experience to a specific context of decision be damned. — fdrake

I read these passages a couple of times, and they still confuse me somewhat. In keeping with my earlier is/ought distinction, I would distinguish descriptive systems and prescriptive systems. These can be the very same systems, but their import is different. A descriptive system is subordinated to ethical judgments in the sense that preexisting judgments inform the construction of the system, and the soundness of the system is tested against ethical problems whose solutions are arrived at independently from the system (such as the trolley thought experiment). Ethical judgments always trump a descriptive system.

On the other hand, ethical judgments are subordinated to a prescriptive system, in the sense that the system dictates the judgments. And this is precisely the case where you have a theoretical guarantee that your actions are right: if you follow a prescriptive system, then actions that are in keeping with the system cannot fail to be the right actions (the only remaining uncertainty is whether the actions really do conform to the system).

In reality, I think, the split between descriptive and prescriptive systems is not so clear-cut. Those people who consciously follow some system of ethics will have chosen the system to follow at some point, and their choice would likely be informed by preexisting ethical judgments. And in practical ethical decisions they would often let intuitive judgments trump whatever principle they are supposed to follow, or they would simply neglect to invoke principles in great many practical situations. We turn to abstract principles in cases of uncertainty, and even then it is often hard to say how much the eventual decision was informed by the "head" and how much by the "heart." Or else we use ethical principles as heuristic shortcuts - so that we don't have to closely examine our conscience for every trivial decision.

If there are no differences - no applicable heuristics that can be 'derived' from the system - then they cannot inform the procedure of ethical decision. Which is supposed to be the core action of these theories. — fdrake

Is it though? This is what I've been questioning. You are, again, implying that the only admissible ethical inquiry is one that can result in practical guidance. I disagree on general principles, and would like to again put this in a broader context of human endeavors. Not everything we do or think about is aimed at immediate practical ends.

The one thing on which I would agree with you is that we should not pretend. We should not pretend that a theoretical difference makes a difference in practical ethical decisions if in reality it doesn't. And we should probably be more mindful of this point when discussing ethics. But I don't think that every discussion of ethics is infected with such pretension.

Let me try and formulate the converse then. 'I don't care about how to live ethically, I only care about what it means to live ethically'. — fdrake

Come now, you know better than that! This is not the converse: what I said was not an either/or proposition.

Indeed, but who is doing that?

And what influence the study of ethics may have depends on the kind of study. Specifically, whether the study concerns the is or the ought. Only the latter provides what you are asking for, i.e. immediate guidance for ethical decisions, but the former can be a subject for ethical inquiry as well.

What's interesting is that, as much as your ire is directed against ethical systems, I can't think of any ethical inquiry other than system-building that can inform one about practical ethical decisions. As I understand it, developing ethical systems is akin to science or engineering, wherein one tries to discover or create overarching structures that bridge the gaps between particular instances of ethical knowledge and thus enable us to find answers where we don't already have them (the counterpart in science would be predicting observations where they are not already available).

If one is skeptical of such enterprise, as I am, then one is left with looking into the is of ethics. I suppose that too can influence one's ethical behavior in some cases, but the influence wouldn't be so direct and obvious.

I think something like this. All ethical inquiry consists in reasoning about what to do. This includes what it means to do something right (is this thing I do ok? is it good?), what justifications are adequate ethical motivation (consequences, duties...), or abstract properties of ethical behaviour (is it rational, emotive...). — fdrake

Well, thinking about what to do would be practicing ethics (of course, not all decisions are ethical decisions, but I am assuming we are talking specifically about the latter here.) The rest would indeed be what constitutes ethical inquiry.

If the way someone thinks about the abstract properties or adequate justifications has no influence on how they live their lives - what might be called practical applications - then the system of abstract properties and demarcation between adequate and inadequate justifications is entirely abstracted from attempts to live a good life. — fdrake

Yes, and?... You imply (and say explicitly in elsewhere) that there is something wrong with that. I am trying to understand why you think so. Why is it wrong to pursue an inquiry into ethics for reasons other than helping yourself make the right choices? For example, out of the love of wisdom (you know, philosophy)?

I am speaking, by the way, as someone who is skeptical of ethical systems. But not of meta-ethics - after all, my skepticism is itself a meta-ethical position. As is perhaps your stance here as well.

Your thesis that no discourse about ethics is admissible unless it is aimed at helping us making ethical decisions in our daily life seems bizarre to me. Can you motivate it? Is there some more general principle of which this is a consequence, or is ethics a special case?

What's your stance on other intellectual endeavors, such as science - must they all have immediate practical consequences? I suppose an alchemist that wants to get rich by transmuting base metals into gold would be OK in your book, but a chemistry professor who has no intention of putting his studies of chemistry into actual practice is a fool and a charlatan. And of course, philosophy of science would be doubly sterile - a pointless inquiry into a pointless study.

Or did I get your completely wrong?

It seems that you haven't made much progress in developing your argument, so let me try to prod you along, starting with premise 2: There is objective morality.

You have gestured towards an argument with your references to moral evils, such as the Holocaust. This is a common road to take for those advocating "objective morality," and it generally takes the form of an ad hominem. Now, don't cringe: ad hominem is not necessarily something bad and fallacious; it can be an effective strategy in an argument. In this context it means just this: Suppose you have a contested thesis, such as your premise (2). You then show by way of an argument that rejecting this thesis inevitably leads to accepting some proposition that most people would be loath to accept (e.g. "Perpetrating the Holocaust was not wrong.") Now your opponents face a dilemma: either they concede and accept your thesis or they bite the bullet and accept the unpalatable consequences of rejecting that thesis.

So let's take me for example. I am strongly convinced that the Holocaust was an evil. (And I also think that any person ought to have this attitude, not just me.) At the same time, let's say that I do not believe in "objective morality" (if nothing else then because I don't have a very clear idea of what it is.) But I am not laying any other cards on the table: I am not claiming a commitment to any particular system of morality, nor for that matter any other metaphysical system.

So how am I wrong? Based on what I said above, am I committing myself to some untenable position? Or perhaps I really do believe in (what you take to be) "objective morality" without realizing it?

as said in (2) - without further measurements and observations, there is a 50% chance that any of the two possibilities is true. — Henri

This is really exasperating. Three times I challenged you defend your premise - and you respond by repeating it, almost word-for-word, still without providing any reasoning.

You can point to some reasoning that justifies premise (2). I don't know how I can make this point any clearer than I have already done.

I am talking specifically about premise (2), and no, it is not "confirmed" by anything, as far as I can see. If I missed some reasoning, please point it out for me.

Problem with yours and other poster's (fdrake) answer is that you stop at premise (2), as it seems. — Henri

Well, if there is a problem with a premise, there is no point in going further until that problem is addressed. As it is, your premise comes out of the blue with no justification whatsoever, so there is no reason to accept it.

I didn't vote. The options of "too strict" and "not strict enough" are too broad to be meaningful. Besides, since posts are deleted and edited stealthily, it is difficult to see how much moderation is actually taking place. I've seen some examples of questionable and petty moderation decisions, but for all I know those may have been exceptions.

Anyway, I've made my more specific complaint elsewhere.

That still doesn't make sense, but no matter. I see that people are largely satisfied with the forum as it is, and that shit-posting will continue unchecked.

A man and a dog walk into a bar.
Barman: Sorry, dogs aren't allowed.
Man: But it's not an ordinary dog, it is a talking dog!
Barman: Oh yeah?
Man: Let me show you (to the dog): What's the outside of a tree?
Dog: Bark!
Barman: Yeah, I see where this is going...
Man: Wait, here's another: What's on top of a house?
Dog: Roof!
Barman: OK, you've had your fun...
Man: Why don't you try?
Barman: Fine. Who is the greatest 20th century composer?
Dog: Orff!
Barman: Get out of here, both of you, and don't come back!
The man and the dog turn to leave. At the door the dog turns around and says: You think it's Shostakovich?

I don't disagree in general, but we should acknowledge that we share much of what we call human nature with other animals. — T Clark

Come now, you won't say that nothing distinguishes our cognitive faculties from those of other species, or that there is a smooth transition? But sure, we ought to have a lot in common with other animals, and psychology should not be an exception. I would be careful about the theory of the "primitive brain" overlayed by higher functions though - I understand that contemporary science paints a more complicated and nuanced picture. It's "almost" as if there was no general architectural plan at work, and things rather developed in a messy ad hoc fashion.

1. Beethoven's String Quartet in A minor Opus 132, especially "Molto Adagio; Andante", the 3rd movement.
2. Beethoven's Piano Sonata Op 109 and Op 111
3. Schubert's String Quintet D.956, especially the 2nd movement, the adagio. Oh, and Schubert 's Piano Sonata D 960 in b-flat major. — Beebert

Oh god... musical orgasm!

You must love the opening movement of Beethoven's 5th piano concerto, am I right?

Carmina Burana by Carl Orff — Bitter Crank

I have a terrible memory for names, but there's this silly old joke that helps me remember Orff's. Do you know the one?

4. Bach - Cello Suite #1 Prelude - There's a singular beauty to Bach's lone cello exploring this musical territory on its own. It is the awakening of the human voice without, of course, an actual human voice. — Brian

Bach is the (unrequited :P) love of my life, and the solo cello and violin works are at the top of my list. I never tire of hearing them and replaying them in my head.

Sorry, I can't say anything "philosophical" here - I am a complete savage when it comes to art.

Right, I understand and agree. But the nature vs. nurture debate is not really about whether people have any mental traits and predispositions in common with each other and at variance with other animals - the debate usually concerns the degree to which our predispositions are innate, how flexible they are, how important their role is, etc.

The level of absurd posts in the philosophy of science is an example of where this gap is clear that causes me to avoid it. — TimeLine

Yeah, that's basically my concern. @Bitter Crank made light of the way I had put it elsewhere, but I don't think that my stance is ridiculous. If people start to avoid a forum, that's a problem.

A more interesting question would be, 'what are you trying to do on the site?' — unenlightened

To communicate with people like yourself, on subjects more-or-less philosophical.

I'm out to make the world substantially better — unenlightened

Yikes! I take back my words :P

I think for something to count as human nature it has to be something innate while simultaneously pointing to or articulating what is fundamentally distinctive about us (so DNA is completely useless). — bloodninja

I wonder why you think that "DNA completely useless," but let's set aside DNA for a moment. DNA is a specific biological mechanism of inheritance and expression of traits. All we really need to know is that there are inherited traits that humans express at variance with other animals, that set us apart as a distinctive species. Is that all that you are saying? That's rather obvious, and I can't imagine anyone denying it.

Examples of this innate human nature are Plato's tripartite theory of the human soul, Aristotle's claim that man is the rational animal, Chomsky's ideas about language, perhaps Nietzsche's the will to power, etc. — bloodninja

If I understand you correctly, you are referring to general features of human psychology ("psyche," "spirit," "soul," etc.). And to say that people have "human nature" is just to say that there are such generalizable characteristics that are shared by all, or almost all people. Is that about right? That too seems pretty uncontroversial, as long as you don't get into specifics. Does anyone really deny that?

The difference between possessing an innate nature and not is that if the former is true then we can ground our moral claims and give them strong normative force. If the latter is true, and there is no innate human nature, then it appears that we have nothing to ground our moral claims in so they have weak normative force; we would be a social construction just like the socially constructed moral claims. Morality would be completely meaningless and arbitrary. To the question why be good? there would be no sufficient answer. I hope this clears things up — bloodninja

No, sorry. Here you are just restating your original thesis: that HN (whatever that is) is a necessary precondition for genuine morality. If HN is as I understood you to mean, then HN is such an obvious and uncontroversial fact, so bound up with our background knowledge about the world and ourselves, that it is hard to even separate it out, so that we could evaluate its specific relationship with morality. You may as well say that for there to be human morality there have to be humans.

Your ideal solution is not going to happen, and, lacking that, your method would lead to more of the kind of thing that you're complaining about. We need to be pragmatic about this — Sapientia

I don't understand what you mean. What is my "ideal solution" and my "method," respectively (you imply that these are two distinct things)?

It was not my intention to debate crackpots. Quite the opposite, in fact.

The problem with that is that all discussions appear on the main page, irrespective of category (unless you manually turn them off here). So moving bad discussions into a "Rubbish" category wouldn't really make much difference for most people. — Michael

That can be seen as giving more options to people. Those who prefer a more curated experience could either browse specific subforums or filter out what they don't want to see on the front page. On the other hand, casual visitors may be turned off by what they see.

Philosophy of science deals with the nature of theory, of evidence, of confirmation, the nature of induction, of confidence and certainty. It is a branch of the theory of knowledge. — Srap Tasmaner

I understand that that's where your interests lie, but I wouldn't be so restrictive. Science informs metaphysics, and conversely, metaphysical underpinnings can be seen in scientific theories and scientific debates. There are also what may be seen as strictly scientific issues that nonetheless can benefit from the attention of philosophers, simply because philosophers have dealt with such issues before (e.g. observer selection issues in cosmology).

I agree with myself :) What made you think I wouldn't? I still think that one or two subforums where "non-standard" posts could be moved would be preferable to deletion. I dislike heavy-handed moderation, but I have come to believe that some kind of curation is necessary for a forum like this.

By "dying" I mostly mean degrading. There is a large and thriving community in Youtube comments, for what that is worth. Yes, messages are still being posted, but the intellectual life seems to be seeping out little by little.

It seems to be the case that the majority of people on here don't think there is a "human nature" as such. — bloodninja

Really? What do you mean by "human nature," anyway? What would be the difference between possessing and not possessing "human nature?"

It may just mean that this forum, and web forums like this, are dying. Perhaps they really are past due, like the BBS or Usenet of old (anyone still remember those?)