I don't know about more concise; in practice, for problems like this efficiency is a lot more important. There are more efficient methods of calculating the n'th prime, but that is more of a mathematical problem than a programming one.

If you need to find the n'th prime for a large n, you would first calculate an approximate answer (there is a mathematical method for that), find the number of primes below that number (there are methods for that as well), and then zero in on the exact answer, perhaps using a more efficient primality test than your nested loop. That would most certainly be more lines of code than what you wrote though, and not something you could pull off on an interview, unless you really know this stuff.

Well, there are philosophical issues raised by quantum mechanics itself: its interpretations in general, and more specifically, things like quantum measurement, counterfactual definiteness, locality, etc. There is this popular Feynman quip oft-cited by philosophy-averse physicists: scientists need philosophy of science like birds need ornithologists. But in point of fact quantum physicists often struggle with these interpretational questions, and having philosophical chops goes some way towards not falling on your ass when trying to answer them.

Then there are broader implications of quantum mechanics for the philosophy of science and metaphysics. Here is just one example, a stimulating article that should stand in contrast to the pretentious cooks against whom you rail: Holism and Nonseparability in Physics.

OK, that makes sense.

However, if we suppose that our thoughts have been ordained for us, along with all else, we cannot place any faith in them. They are not in fact OUR thoughts at all. — Tony

This does not follow. You may believe that this is the case, but if so, this is in consequence to your understanding of ownership, personhood, freedom - all tricky metaphysical (or perhaps just psychosocial) notions that do not straightforwardly follow from that assumption.

As I mentioned in the OP, I'm asking for what the answer would be IF the abstractionists' position was to be correct. I figure that it has to be chance, which is entailed by contingency, but I was checking to see if I'd failed to consider or understand something. — Brayarb

What do you mean by chance? Is it any different than contingency?

I can prove that ~p and ~p -> p is a contradiction — Pippen

~p -> p is already a contradiction. Srap was right (and I wasn't paying attention): this second iteration of your argument made little sense. Your first attempt was already logically bulletproof, as you say - it just didn't prove anything interesting, and neither did your second attempt.

If p stands for "something exists", ~p stand for "nothing exists" and ~p -> p for "something follows from nothing" — Pippen

While "p" can stand for any proposition, you are not free to choose the meaning of logical predicates - that is, if you are appealing to logic for your argument. If you accepted the rules of the game, then you cannot assign the meaning to ~p -> p by fiat. That expression states that the denial of the proposition "p" logically entails the proposition "p" - only that and nothing else. (Although entailment can be understood somewhat differently even in logic - semantically, syntactically - that ambiguity won't help you.) The implication of disproving ~p -> p is utterly trivial and has nothing to do with proving ex nihilo, as I already argued.

We can use mathematical and logical terminology metaphorically for creative expression (1 is the loneliest number), but the truth of these sayings does not derive from the use of logical and mathematical terms, it has to stand on its own.

It's the same with 's attempt to prove ex nihilo with arithmetic: he interprets 1 apple + 1 apple =/= 3 apples as saying that an extra apple cannot appear outta nothin'. But, if arithmetic is his tool of choice, then all this says is that if you got an apple and another apple, then together you have two apples (and not three). If then, by some miracle, another apple appears outta nothin', then with the two apples that you already had, you will have three apples all told. That's all that arithmetic gives him. Any other interpretation that he assigns to the symbols will have to be justified independently from the literal meaning of the borrowed terminology.

The moral of the story, ironically, is that in an argument, too, you cannot get something from nothing: if you want to prove a metaphysical principle, you will have to do the hard work of arguing metaphysics, instead of looking for sophistic shortcuts. But first and foremost, you will have to understand what that principle means, and neither you nor Lacrampe have taken that trouble.

"¬p→p" has an obvious countermodel when p is false, which happily you assumed in (1). — Srap Tasmaner

That's what he wants to show, no? that (1) and (2) cannot both be true.

Not that this trivial exercise reveals anything interesting, of course. If p stands for "something exists" and then ~p stands for "nothing exists," all that he shows is that, if nothing exists, then it is not also the case that something exists. Duh.

You cannot begin to cogently discuss a proposition when you cannot even explain what it means. All that symbol manipulation is child's play. You are not even touching the subject.

Well, the chapter from which this is quoted is entitled "The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity," and the thought experiment illustrates said inconsistency. What specifically do you find to be problematic?

By formal analysis do you mean specifically the positivist approach of defining all theoretical terms through observable properties? I think it would be problematic to define counterfactuals this way. And that makes me think of a problem with this definition of causation:

If c is not the case, then something else is the case, right? What could be the case then? And couldn't some alternate state of affairs result in the same effect? Suppose we see a red ball strike a yellow ball and then the yellow ball rolls into a pocket. We would normally say that the red ball striking the yellow ball (c) caused the latter to roll into a pocket (e). But what would be a counterfactual to that? Suppose that a blue ball struck the yellow ball instead of the red ball, with the same consequences. (c) is not the case, but (e) occurred anyway. Does this mean that (c) was not the cause of (e) after all? It seems that on this definition of causation either there is no multiple realizability of effects or there is no causation - either option is implausible.

I am not sure what you are trying to do here. Are you saying that "c causes e iff..." is a theory and the same sentence with x and y standing for c and e is its Ramsey sentence?

This is getting old.

Is it possible to change the math axioms such that I+I=III is mathematically possible?
I will go with no. Objections? — Samuel Lacrampe

Not possible if the numbers represent an already given concept of "counting numbers" (or similar). The concept then shapes the pattern, gives the requirements for the mathematical formalism.

I understand "nothing can come from nothing" as: it is false that something can follow from nothing. — Pippen

That is no clearer than the original sentence: you just rephrased it and replaced "come from" with "follow from."

I see causality as a special case of inference, so if I can show that such an inference is wrong then it holds even more for causality. — Pippen

We don't know whether causality has anything to so with ex nihilo any more than inference does, because we don't know what ex nihilo means in the first place.

That said, if you think that causality is a special case of logical inference, then you are already on a wrong path.

How do you prove that nothing can come from nothing? — Pippen

Forget proof for a moment, how do you even understand "nothing can come from nothing?"

I think that your attempted proof only serves to illustrate your own confusion. Start with conceptual analysis.

As said, the origin of the "meme" idea is in a Dawkins book, and indeed it is supposed to be analogous to biological evolution, not economics. As to it having "no physical basis whatsoever," that could be debated, but that is a red herring in any case. The important thing is the mechanism. Evolutionary algorithms in computer science, for example, have as much physical basis as memes, but the reason they are called so is because they share essential structural similarities with the process of biological evolution.

"Memetics," however, has been criticized as disanaloguous to evolution, and the whole idea has been condemned by some as pseudo-scientific. Wiki gives some pointers.

Maybe I was not clear. Let me rephrase what I meant in a syllogism:
- The prima facie for all things in the universe is to expect that things don't come from nothing.
- The universe is just the sum of all things in it. (Just like the ocean is just the sum of all water drops in it).
- Therefore, the prima facie for the universe is to expect that things don't come from nothings. — Samuel Lacrampe

No, you were clearer before, and going back to vague expressions like "things don't come from nothing" or "just the sum of all things in it" is not helping.

All things in the universe are part of one causal structure - not necessarily so, but I am willing to accept this as a premise. This is the only sense of "things don't come from nothing" that I understand and am willing to accept. But this premise doesn't scale up to the universe as a whole. The universe is not a part of any structure, assuming the universe is all there is.

Is it possible to change the math axioms such that 1+1=3 is mathematically possible? — Samuel Lacrampe

Not possible if what you are trying to model is intuitive arithmetics. Otherwise, of course, you can redefine any of the symbols and introduce different axioms. We invent mathematics, but we often invent it for particular ends - for ordering and measuring, for instance, for which we have invented numbers. In that sense numbers and arithmetics cannot be much different than what they are, since we know in advance what they are supposed to be like.

Regarding math: I wouldn't disconnect it from reality. Engineers design planes to stay in the air using math. Furthermore, it seems to me that 2+2=4 is a necessary truth, as I cannot imagine it to be otherwise. For my knowledge, could you give an example of an axiom that would change the classic logic? I have heard that claim before but never saw an example of it. — Samuel Lacrampe

As far as pure mathematics and logic are concerned, their plurality is not even controversial. A mathematical or logical system is given by its axioms and definitions, and those can certainly be varied. Indeed, mathematicians have explored numerous mathematics and logics - either for their utility to solving problems, or just for their interesting features and possibilities.

Of course, when we use mathematics to construct empirical models, we have less freedom, since presumably there is only one way in which the world is, and not every model will be equally suitable for describing it. There also are quite definite ways in which we structure our thought and discourse, though here we also confront the question of normativity.

These constraints still leave us with a considerable choice of mathematics and logics of varying utility, but my point is that there is nothing necessary about the constraints themselves (leaving out normativity of logic, as that opens another can of worms).

Very well, but if you expect things in the universe to behave that way, (i.e. apples don't just appear by themselves) then why not expect it for the universe as a whole? The universe is just the sum of its parts. — Samuel Lacrampe

My expectations with regard to apples and other things in the universe are justified in the context of my expectation of the universe's regular, lawful constitution. But what would be the context for the universe as a whole? It doesn't emerge from summing up the parts; all you get are boundary conditions.

"Nothing" is not a term of art with a settled meaning, either in physics or in philosophy (as a whole). Depending on how you want to interpret it, the OP question may not even be coherent. For example, if "nothing" is used merely as a quantifier, then "to get something from absolute nothing" doesn't even make grammatical sense.

Wow. I had no idea some people thought that. Who knew that arguing about math would be so hard. I guess Descartes was over-optimistic when he claimed that math was the one field without any ambiguity. — Samuel Lacrampe

It's worse than you think. Math is fairly unambiguous once you lay down all the rules, but the rules are completely up to you. There is no the logic of numbers: you are free to make up any logic; you are even free to define what numbers are. Math is a pure play of imagination. And that is why you are never going to get any empirical or metaphysical argument out of math alone. We make up mathematical axioms and construct mathematical models, but their application to reality is an extra-mathematical, extra-logical step. Arithmetical operations with zero do not inherently represent anything other than the mechanics of a formal system. If you want to say that they stand for some metaphysical idea, you have to argue metaphysics, not math.

Let me try one last attempt from a different approach: If you believe that the principle 'nothing comes from nothing' is not always true, then does it follow that you would not be surprised, when putting one apple and another apple in an empty bag, to sometimes find three apples later? — Samuel Lacrampe

Of course not. Why would you ever think otherwise? I expect the familiar world to be orderly and to function in certain ways, and the situation that you describe would not be compatible with my expectations. That's not to say that there is something logically wrong with that scenario, but nomologically I would not expect it to happen.

And you have once again locked yourself into this faulty analogy in which nothing is like an empty bag. But if there is a bag, then there already is something, and the only something that we know is our physical world that seems to operate according to certain rules, such as conservation laws.

I believe we are scraping the bottom of the barrel here.

This is just an analogy for what you wish to demonstrate. An analogy can illustrate an argument, but it cannot stand for an argument.

The analogy is not even a good one. A mathematical 0 is not nothing - it is an entity with its arithmetic properties. Your analogy suggests that prior to the universe there was something, some kind of an empty state - a vacuum, a void? And that void was transformed into the universe as we know it. That sounds like some of our religious creation stories, but this would not be consistent with the universe, the totality of all physical being, having a beginning. Because, just like zero is a mathematical entity with properties, that void, that primordial state that was transformed into the universe-as-we-know-it is a state of something, and therefore it should still be considered as belonging to the universe-at-large.

As it happens, the astrophysicist Laurence M. Krauss wrote a popular book provocatively titled A Universe from Nothing, in which he, to the annoyance of some philosophers, draws on that same ex nihilo dictum to outline some actual, though still speculative, cosmological proposals, in one of which the Big Bang universe arises from a kind of primordial void state. Except, as critics were quick to point out, that "nothing" is very much a something, characterized by physical properties (the laws of relativistic quantum mechanics), even though it lacks many of the attributes that we conventionally associate with physicality, such as spacial extension.

The moral is that if you are going to make something out of the "nothing comes from nothing" principle, you cannot take it too literally, on the pain of self-contradiction.

You keep saying that the principle has been reduced to the laws of physics. When in our conversation has it been reduced? — Samuel Lacrampe

Granted, you never did commit to it being a physical principle. But then you never did commit to any systemic explanation. Rather, for some specific examples you found a specific property that fits, be it energy or material or information. Meanwhile, it seems that when we look at any causal process, most of the properties involved do not fit into the scheme of being handed down from the cause in a diminished form, for various reasons. Which is why I remain of the opinion that this principle is an ill-fitting and unhelpful metaphor.

If there is a cause to the existence of the universe, then there is a 'process' from the cause to the effect. If not, then not. I suppose this brings us back to the original disagreement on the 'Nothing comes from nothing' principle. Do you really believe this principle to be false? If so, then we should focus on this fundamental point before anything else. — Samuel Lacrampe

Rather than saying that I deny the "nothing comes from nothing" principle, I would say that I find it unclear and unhelpful. The principle that I would be comfortable with is the principle of causal closure that I outlined above. I wouldn't say that causal closure is necessarily the case, but it is something I am comfortable accepting as a working assumption, seeing that it fits well with experience and that without it any empirical conclusion would be on shaky ground.

However, the causal closure principle characterizes the physical world and its states or events in relation to each other. Any cause in this context would necessarily be of this world. Which is why it would be incoherent to talk about the cause of the universe. If you have something else in mind, some other rending of the "nothing comes from nothing" principle, then you would have to explain it and motivate its acceptance.

Returning to the 'process' that is responsible for the shape of the universe, perhaps I was too dogmatic in arguing that it is necessarily non-physical. I can imagine a cosmological model in which the universe has a beginning in time, and in which some of its attributes are randomly selected at T=0. If this model of the beginning is continuous with the model of the evolution of the universe, then it could be viable. But it would need to be argued for, it's not something we should all assume as a default.

The thought experiments refute your claim that the principle 'no effect can be greater than the sum of its causes' fails in the example of water boiling. As such, the principle still stands. I have apparently failed to convince you of it, but it has yet to be refuted. I can provide more supporting examples upon request.

I am not sure if you are saying yes or no. Either the law of conservation of mass and energy applies in the case of the big bang, or it does not. If it does, then the big bang necessarily possessed all the mass and energy found in the universe today. If not, then not. While the laws of physics may change, logic does not. — Samuel Lacrampe

You can always rescue a vague premise by retreating to less controversial, though usually less interesting positions, and this is what you've done by reducing what sounded like a universal and far-reaching metaphysical principle to some particular references to popular physics. I think we have explored this avenue as far as it would go.

If I were to give my most generous summary, it would be something like the principle of causal closure: The universe evolved from its earlier states according to some constant (though not necessarily deterministic) laws. Any earlier state of the universe had the potential to evolve into its present state, with no outside influx or interference, nothing other than its instantaneous state and the timeless laws. And we can trace this process to the earliest times that are open to empirical investigation, beyond which we can only speculate. That early post-Big Bang universe, that undifferentiated "particle soup," was already energized with potential to bring about the present world, complete with stars, planets, cellphones and Donald Trump.

But this potential cannot be located in any one attribute, such as energy (which, as I tried to explain, is difficult to apply beyond local interactions, to the universe as a whole). Already from classical thermodynamics we know that no amount of energy is sufficient to bring about change: there also has to be a disequilibrium. And even then the change is not guaranteed to result in anything interesting (from our subjective, biocentric point of view): as you must have read somewhere, if, for instance, fundamental constants were different, we could have ended up with a universe full of nothing but black holes, or a universe with no complex chemistry.

Which brings me to your fine-tuning argument:

You are correct that the argument is founded on these assumptions, but they also seem rather common sensical. As such, they are the prima facie and the onus of proof is on the other side. — Samuel Lacrampe

No, what may be regarded as "commonsensical" is the original statement: that the (putative) initial configuration of the universe was extremely improbable. That seems like a very common idea. I cannot tell now whether it ever seemed commonsensical to me, because I have since given it a closer look and went beyond common sense - which is what a philosopher is supposed to do, you know. And when I deconstructed the implicit assumptions, they turned out to be quite arbitrary and contrived. I do not accept the burden of disproving them, because I cannot see any reason to hold them true in the first place.

Regarding assumption 2: We don't need to know what is outside of the universe. We can just use logic: either the process is random or it is not. If random, then it results in the existence of our configuration to be highly improbable, therefore making the 'random' hypothesis highly improbable in return. If not, then the process is deterministic or designed, which in turn points to a designer. — Samuel Lacrampe

You are assuming that there was a process, which is the assumption that I challenge. If we are talking about the physical universe as all there is that is physical, then there could not be any physical process that brought it about. To assume a process is to beg the question, because such process could only be supernatural (and yet somehow having physical effects).

If not, then the process is deterministic or designed, which in turn points to a designer. — Samuel Lacrampe

You are kidding, right?

That's an interesting point. Here are thought experiments to show that the claims are not arbitrary — Samuel Lacrampe

I don't know what you think you are getting out of this line. Your initial premise has been reduced to well-known conservation laws (i.e. if you care to generalize from the examples that have been considered so far; otherwise you don't even have that). I don't think it gets you anything interesting.

Are you saying that the laws of thermodynamics don't apply to the early post-Big Bang universe? I thought they were called laws because they applied to all cases (in physics). — Samuel Lacrampe

No, I am saying that it's more complicated than you suppose and can't be adequately summed up by a simple aphorism. In General Relativity energy of a macroscopic volume isn't even well-defined. Thermodynamics still works - but locally. It's when you try to integrate over volume that you run into trouble.

Laws, by the way, are formulated within a particular theoretical framework, which usually has some limited scope of application. Classical laws of thermodynamics, strictly speaking, work in classical non-relativistic physics. They do generalize to quantum mechanics and relativity, but with some caveats and complications. For example, in Relativity energy (or rather that entity to which energy generalizes) of a finite volume very annoyingly becomes tangled up with the choice of coordinates - a big red flag for anything that is supposed to be a genuine physical quantity and not just a modeling artefact. That's not to say that conservation laws are dead, but the picture becomes a good deal more complicated.

First, to be clear, by 'configuration' I meant the narrow range of settings (such as the gravitational constant G) that allow for life to be possible. I am assuming this statement to be true, as I am no expert on the necessary ingredients for life. Let's just buy into it for now.

Now if I understand correctly, [the probability of an outcome] = [the number of desired outcomes] / [all possible outcomes]. In this case, the number of desired outcomes, that is, the configuration with all settings that allow for life to be possible, is close to 1 (assuming a really narrow range of settings). And the number of all possible outcomes is the number of combination of all possible settings. It appears to me that this number is infinite, if each setting has logically an infinite possibility of values. This results in a very low probability of our configuration to occur. Thoughts? — Samuel Lacrampe

Your reasoning depends on the following assumptions:

1. Physical laws are a priori fixed, with the exception of a few free parameters (fundamental constants) that can vary within finite limits.
2. The actual values of those constants are set via some stochastic process that is somehow prior to or outside of the universe, i.e. it is not itself physical (because we count anything physical as part of the physical universe), even though it functions like a physical process and has a physical outcome.
3. The probability distribution in that stochastic process is more-or-less uniform, so that we can assume that a narrow range of values has a small probability.

These assumptions seem to be completely unjustified, and, in the case of (2), perhaps even incoherent. Why should an atheist be committed to them?

An alternative to (2)-(3) could be not a non-physical universe-generating stochastic process but ignorance: we don't know why the values of fundamental constants are what they are; we have no reason to a priori favor one assignment of values over another; therefore, we assign ignorance priors: a uniform distribution of epistemic probability. But ignorance is not a theory but a state of knowledge. All that this formulation says is: "We don't know why the universe is the way it is; we have no rational warrant to propose a theory; for all we know, it could be different."

I'm with you on that one: The undeniable order in the universe strongly points to an order-giver.

I think an objector might say that "while improbable, this current configuration of the universe could have happened at random, and maybe countless of different random configurations failed before that one happened". Now maybe this hypothesis is not possible if, as you say, there can be no 'before' prior to the big bang. I just don't know much about this. — Samuel Lacrampe

This objector would not say this. What does it mean to say that this [organization of the universe] is improbable? Probability is meaningful either in the context of a statistics built up from multiple observations, or in the context of a stochastic model (which in turn is based on observations). Neither of these contexts exist in the case of the universe. One could speculate that some random mechanism is responsible for the particular shape of the universe that we see (and some speculative cosmologies suggest something of the sort), but an atheist need not be committed to this view. And, as you say, this hypothesis does require for there to be something prior to or outside of the known (post-Big Bang) universe - but the option of a pre-Big Bang history is still open (hence the speculative cosmologies that I mentioned).

So there is no basis for saying that this configuration of the universe is improbable, any more than any other configuration. And in any event, nothing points to a magic order-giver.

I wonder still if the definitions are not essentially saying the same thing in different ways. Aren't natural sciences dealing only with things that are empirical; and all that is empirical is material? — Samuel Lacrampe

Yes, I like this approach as well. I think the key to naturalism/materialism/physicalism is not a commitment to a particular ontology, but a commitment to empiricist epistemology.

Sorry to have dropped out from the conversation. But frankly, your argument, which started from some puzzling and provocative premises, has unfolded into something rather vague, slippery and tepid.

Here is one illustration that shows why I find your argumentation unconvincing:

The energy from the fire (property 1) causes an energy increase in the water (property 1). Then the energy increase in the water (property 1), combined with the potential of water molecules to boil at 100C (property 2), causes the water to boil (property 2 actualized). — Samuel Lacrampe

So the move here is to point to a transient property, such as "boiling," and say that it always existed in potentia, and needed only a suitable cause to be actualized. This clever get-out-of-jail clause can paper over any difficulty with properties that appear to be new in effects. But why not use the same move on every property? Well, then it would be hard to link back to the original idea, that of invariant property transfer from cause to effect. For that you have appealed to energy, matter and other more-or-less conserved quantities, chosen ad hoc for each particular case.

- The first cause possesses all properties from all effects, and to an equal or greater degree.
- If all that exists is material (matter and energy), then all properties from all effects are material things.
∴ The first cause possessed all the matter and energy that currently exists in the world, to an equal or greater degree. — Samuel Lacrampe

The key here is that you take a physicalist view of the world as a common ground with your presumably physicalist audience, and try to extract from it an evocative metaphor. This is a dubious endeavor at best, because the metaphor will never be adequate to the actual meat of the physical theories from which it is extracted. And if you try to use it to reach conclusions with physical, empirical implications, you will most likely run into trouble, as you did in this case.

Indeed, it is inaccurate to say that the early post-Big Bang universe (the closest thing we have to the "first cause") "possessed all the ... energy that currently exists in the world, to an equal or greater degree." The issue with energy at macro-scale becomes complicated when you get to General Relativity and non-flat, expanding spacetime. In some interpretations it seems that energy is conserved only in local interactions, but not globally. With careful analysis you can recover a globally conserved quantity, but it is no longer just energy, and it is "conserved" only in a special sense that requires a lot of exposition to explain (like I said, it is complicated). It would be hard to translate all this into a simple metaphor.

I don't understand your position. Are you denying that there is energy transfer from the fire to the water? If yes, then what is the causal relationship between the two, if any? If no, then what is wrong with my premise? That energy is the common property between the cause and the effect. — Samuel Lacrampe

We agree on the facts, but the facts do not support your case. The energy transferred from fire to water is neither the energy of the cause (fire) nor the effect (boiling water). It is also distinct from the property of temperature, which the cause and the effect do not share, and the property of boiling, which only the effect possesses. Nothing here fits your premise of property conservation between cause and effect. Something is conserved, but it is not what you need for the premise to be true. The cause does not have all the properties of the effect: it does not have the energy of the effect, it does not have the temperature of the effect, it does not have the property of boiling.

Perhaps the problem here is that 'cause', 'effect' and 'property' have not been defined and thus it is not clear what it means for the cause to have all the properties of the effect. As I already mentioned, talk about causality is usually pretty loose. We say that fire underneath the pot causes the water in the pot to boil. Is fire the cause and boiling water the effect? Or should we rather be talking about events? Processes?

And then there are properties. The simplest definition of a property is anything that can be predicated of the thing in question. Thus "has the temperature of 100C" and "is boiling" are both properties of boiling water at normal conditions. But on this definition "does not have the temperature of 100C" and "is not boiling" can also be properties of something. It is clear then that for the cause to have all the properties of the effect, cause and effect will have to be identical. (Suppose that the cause has a property P not possessed by an effect. Then the effect has the property not-P, which the cause cannot possess. Thus the cause does not have all the properties of the effect.)

The fire emits the energy received by the water to boil, and the "boiling" effect is just the combination of the energy (caused by the fire) and the potential of water molecules to boil (not caused by the fire). And we know the energy received cannot be more than the energy emitted, due to the first law of thermodynamics.

"For that matter, the fire that brings the water to a boil does not have the property of being at 100C." — SophistiCat

Indeed. The fire has a property of being greater than 100C, which agrees with my point that the cause(s) may be greater or equal to the effect. — Samuel Lacrampe

Recall your own explanation:

'Greater' here means that the effect cannot possess a property that was not present in its cause(s). — Samuel Lacrampe

The fire underneath the boiling pot has neither the energy nor the temperature of the boiling water. It also does not possess the property of boiling. So while what you say here is correct, it does not mesh with your premise. Do not pass Go, do not collect $200. Go back to your premise and make it conform to these facts, on which we both agree.

I wonder if the universe were infinite, then wouldn't what is actually possible have to become actual at some point? — Cavacava

Depends on what kind of possibility you have in mind. Nomological possibility combined with infinite probabilistic resources results in all possibilities being "almost surely" realized. But a planet made of cheese, for example, is not any more likely with an infinite universe than with a finite one, even though such a thing is conceivable.

- If something can exist, then it can be conceived of, because we can conceive all logical possibilities.
- If something can be conceived of, then it must exist. (as defended by Hume)
∴ If something can exist, then it must exist. — Samuel Lacrampe

Already had a go at this, and I would like to add that I also have a problem with both these premises.

The first premise is, at best, a rather optimistic statement about our cognitive faculties. But, even if it happens to be true, I wouldn't take it as a metaphysical first principle: the world has no obligation to be comprehensible to the human intellect. And if you take it definitionally (possibility is conceivability) then you are trivializing your conclusion.

The second premise is obviously false and doesn't follow even from the simplistic "blank state" account of cognition that you attribute to Hume.

I think this is logically provable: Once again, let's start with the self-evident principle that 'nothing can come from nothing'. — Samuel Lacrampe

No, let's not. I keep telling you that I don't regard the PSR, in any of its forms, as a necessary truth, something that any possible world must conform to. You just go from one form of it to another, firmly convinced that I must subscribe to at least one such principle. I am telling you that I do not. That's not to say that I believe that things happen for no reason. I just don't think that they are obligated to happen for a reason by some a priori principle. (And, as points out, you can push the principle to absurdity if you apply it to the world as a whole or to the putative first event, but I don't think you are doing this, yet.)

I tried to prove this here. Where do you see a flaw in the reasoning? — Samuel Lacrampe

Unfortunately, you can't link to specific posts this way. I think I have read all that you wrote concerning the principle of conservation of properties (as I call it) in this thread, but I don't see where you have given a sound argument for it. You just say, in effect, that it follows from some principle of sufficient reason, but I honestly cannot see how.

And it is such an odd principle! You might find one or two examples that work, more-or-less (considering that causation talk is generally pretty loose and there is no universally accepted account of causation). But isn't it obvious that in general there is no such conservation of properties? Indeed, it often isn't even clear just what might be conserved and in what way. But if you want clear counterexamples, phase transitions work particularly well. A boiling pot, for instance: neither the fire under the pot nor the water prior to the onset of boiling have the property of boiling. For that matter, the fire that brings the water to a boil does not have the property of being at 100C.

Ah, I see now, I didn't realize that the passage quoted here wasn't the entire poem. Thanks for the links, . I just finished chewing my way through a couple of annotated Shakespeare plays; when I recover a bit, I might work that annotated Keats.

This interpretation still goes against the grain of the poem: here enchantment is a mortally dangerous deception, not something quaint and charming and romantically wistful.

The tender-person'd Lamia

Can someone explain this titular metaphor to me? My Google scholarship and Graves' Greek Myths tell me this about Lamia: that she could pluck out and replace her eyes at will (ewww!), that later, mad with grief over her slain children, she became a monster who snatched and devoured the children of others, and that she may also have sucked out the blood of young men while they slept. Nice. Is that really who Keats had in mind?

Logically, either a thing has a cause or else it is an eternal being which has always existed, because everything that begins to exist requires a cause for its existence. — Samuel Lacrampe

"Everything that begins to exist requires a cause for its existence" is just a variation on the Principle of Sufficient Reason, which I don't think we are obligated to accept as a dogma.

But that was just an aside. Even if we provisionally accept the PSR, it still doesn't logically follow that a cause must have all the properties of its effects (whatever that might even mean). The most that PSR entails in this case is that there must be a cause for any property, which is a plausible (though not necessary) principle if by that we mean that the property is either entailed or made more probable by a prior state of the world combined with dynamical laws. But conservation of properties does not follow from this.

Wow, what a mess! You really need to be careful with quantifiers and modal operators.

'Greater' here means that the effect cannot possess a property that was not present in its cause(s). This follows from the self-evident principle that 'nothing can come from nothing', or 'nothing can bring itself into existence'. Therefore, whatever property the effect has (be it physical or not) must come from its cause(s). — Samuel Lacrampe

Your premise is that everything has a cause. It is very much debatable that this is a self-evident truth or that we have no choice but adopt this a metaphysical axiom. In any case, your conclusion (that the cause must possess all properties of its effects) obviously does not follow.

Indeed, it is hard to even think of a single example, while counterexamples are easy to come up with (especially since "cause" and "effect" are such vague concepts).