Theoretical physicist Paul Davies wrote:
But what are these ultimate laws and where do they come from? Such questions are often dismissed as being pointless or even unscientific. As the cosmologist Sean Carroll has written, “There is a chain of explanations concerning things that happen in the universe, which ultimately reaches to the fundamental laws of nature and stops… at the end of the day the laws are what they are… And that’s okay. I’m happy to take the universe just as we find it.”
Assuming that Davies is correct, I find it odd that there is little interest for understanding the laws of nature. There are some interesting questions to be answered, such as: Where do the laws come from? How do they cause things to happen?
Physicist Neil Turok once posed the question:
What is it that makes the electrons continue to follow the laws?
Indeed, what power compels physical objects to follow the laws of nature?
The question I would like to focus on is: what would a naturalistic explanation of the laws of nature look like?
Frankly, I don’t know where to start. What I do know is that a bottom-up explanation runs into a serious problem. A bottom-up explanation, from the level of say bosons, should be expected to give rise to innumerable different ever-changing laws. Different circumstances, different laws.
But this is not what we find. Again, Paul Davies:
Physical processes, however violent or complex, are thought to have absolutely no effect on the laws. There is thus a curious asymmetry: physical processes depend on laws but the laws do not depend on physical processes. Although this statement cannot be proved, it is widely accepted.
If laws do not depend on physical processes, then it follows that laws cannot be explained by physical processes. IOWs there is no bottom-up explanation for the laws of nature.
But what does it mean for naturalism if there is no bottom-up (naturalistic) explanation for the laws of nature? How does the central claim ‘everything is physical’ make sense if there is no physical explanation for the laws of nature? What if it is shown that the laws of nature control the physical but are not reducible to it?
These definitions seem to be deliberately aiming to bring about Russell’s paradox. If this is the only foundations of arithmetic you know, too bad.
None of this explains what you said, “You seem to be claiming that 0 = 1.” Whereas you indeed were saying that 0+0=1 or 2.
Try again or I take that you have no explanation.
See, now you are getting to the point.
To say that “laws cause such-and-such” is an overstatement. Aristotelian legacy does this to people. Aristotle posited a system of four causes whereof at least two are more like correspondences or correlations instead of causes. I personally would say it’s correspondences all the way. Causes correspond to effects and effects to causes. And this regularity is by design. Not by an “intelligent designer” who stepped in to make this correspond to that, but by design or structure of the universe.
So, to me it makes sense to ask for an explanation of natural laws. Or at least to aim at an exhaustive description of them.
No, not at all. They very carefully avoid the Russell paradox.
As usual, you make no sense whatsoever. Better refer me to your source, to your fundamentals of arithmetic in this case. I’m positive that either it’s a source not worth having or you are fundamentally misinterpreting it.
https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
So Neil was wrong. Naive set theory does bring about Russell’s paradox and all the attempted set-theory solutions to the paradox exist precisely because naive set theory brought about the paradox. Neil hasn’t introduced anything that would avoid it.
Most obviously, the paradox would easily be avoided by avoiding philosophically suspect axioms and concepts like “empty sets”. Arithmetic can be defined by its operations instead of getting hung up on what is being operated on as if it were something ontological. To assume that numbers are sets can be a useful analogy to an extent but to assume that something like an empty set can be used to “generate” numbers is already an ontological confusion.
A quote from the review, “…science is able to think a time that cannot be reduced to any givenness, or that preceded givenness itself and, more importantly, whose emergence made givenness possible. One begins to understand the audacity of these claims insofar as they posit a time radically different from that of consciousness, a time that, due to its indifference, would seem to resist the modern tenets of the inseparability of the act of thinking from its content, thus enabling us to conceive the realms of phenomena and of the in-itself each apart from the other.”
For keiths this should qualify as pseudo-profound bullshit. If not, he needs to explain why not.
Nope
Erik,
I’m sure it would, from his perspective. I think it’s intriguing but ultimately wrong-headed. The hard part is figuring out exactly why.
Erik, you’ve crossed the border into Joe G crackpot territory: “All those mathematicians are idiots, but I’ve got it figured out.”
The empty set is a legitimate set just as zero is a legitimate integer.
I’m familiar with postmodernist and poststructuralist doublespeak. Sometimes it’s possible to figure out the meaning and sometimes it’s genuinely insightful, but keiths would not be able to distinguish when it’s pseudo-profound bs and when it’s not.
Yup, Neil was wrong in defending KN’s ontological confusion.
I’m not talking to those mathematicians. They are not posting here.
Numbers can be viewed as sets, but to say that numbers *are* sets is veering towards ontological confusion. To say that numbers are *generated from* sets (even worse, from empty sets) is straightforward ontological confusion.
KN:
KN,
The sentence in bold is incorrect. That set contains only one member, because members of an element don’t count as members of the set.
What you’re forgetting is that each subsequent natural number is defined as the union of itself with the set containing itself:
Erik,
Do you see your mistake? There is nothing “philosophically suspect” about the empty set, just as there’s nothing philosophically suspect about the number zero.
This aligns with my own view very well – to define arithmetic fundamentally as operations. Arithmetic is explained by explaining what addition, subtraction, multiplication and division are, not so much by what numbers are.
So now you’ve suddenly become an expert on what is philosophically suspect and what is not 🙂 For your own good, I will let it pass for now. If you insist further, it becomes your job to explain why it’s not philosophically suspect. I doubt you even know what philosophically suspect means.
Erik,
You’ve gone full crackpot, man. Never go full crackpot.
Fortunately the practices of mathematicians do not bend to the whims of metaphysicians.
When you have a whim, it’s guaranteed you are not doing metaphysics. With scientists it’s a bit trickier.
Mathematicians don’t permit square circles, yet somehow they are permitting empty sets. If you don’t see anything philosophically suspect in this, I can legitimately suspect your philosophy.
Erik,
Crazy-ass mathematicians. Next thing you know, they’ll come up with a number representing nothing.
Oh, wait…
In case you didn’t notice, before a number representing nothing, there was a word representing nothing. Before math, there was grammar. Mathematicians are not doing anything fundamentally new and it’s quite possible to notice in advance when they go astray.
But I am really not talking about mathematicians here. Just about KN and Neil, their ideas about numbers.
But at least he gave us a good laugh.
Neil and I are conveying the consensus view of mathematicians about the relation of mathematics to set theory. I studied set theory and logic in graduate school, and Neil (it must be pointed out) is an actual mathematician. So you are in fact saying to a mathematician that mathematicians are wrong about the conceptual foundations of mathematics.
More generally, I think that it’s up to mathematicians and scientists to construct whatever concepts they find helpful in resolving the problems that they encounter in their fields. I have no more objection to a mathematician’s use of “the empty set” than I do to a physicist’s use of “spin” or a sociologist’s use of “class”.
If a physicist encounters problems in doing physics and introducing a concept of “spin” helps resolve those problems, then philosophers should not make any objection. Likewise with the concepts invented by mathematicians for resolving the problems they encounter in their field.
Actually, I am a mathematician and I am posting here.
This is a rare opportunity for you. Make most of it.
Who says they don’t? We do not restrict ourselves to Euclidean geometry.
I’ll keep that in mind next time you whine about unicorns etc.
Well, we’ve had these two threads:
Perhaps we need a new one:
Sometimes they invent concepts that spill over their own field and wreak havoc. Some are instantly seen as philosophically suspect, unsound such as Krauss’s usage of nothing. Objection to him and his enablers was quite justified. Would you have had no objection to him? Was he inventing a concept to deal with a legitimate problem in his own field or was he spouting abject nonsense?
Erik, what’s the problem with an empty set? Do you also get your knickers in a bunch when people mention empty boxes?
You have forgotten what the issue was. Or possibly you never knew what it was.
He was using a physicist’s concept of “nothing” and assuming that it resolved metaphysical issues. There’s nothing wrong with Krauss using the word “nothing” as he did when doing physics. The problem arose when he assumed that the physicist’s concept of “nothing” was the only one that was interesting and important.
However, in my view, the real problem with Krauss is that he didn’t polite accept the correction when this was pointed out to him by David Albert. Albert was perfectly polite and respectful when he pointed out that “nothing” in Krauss’s sense is not what metaphysicians have meant by that concept — because fluctuating quantum fields are most definitely things, from a metaphysical point of view. Krauss’ response to Albert was condescending (he even claimed that Albert had no background in physics, whereas in fact Albert has a PhD in theoretical physics).
In short, Krauss insisted that he alone knew what a term really meant, and he denied the legitimacy of other uses and contexts.
Which is exactly what you’re doing to Neil.
That wasn’t even a physicist’s concept of nothing. The physicist’s concept was “vacuum state” or the like, not “nothing”.
I was expecting that you knew, having read David Albert even. Expecting too much… You must go read David Albert again,
No. To you. You claimed that numbers are generated from sets, not Neil. Neil didn’t really know what he was getting into when he tried to defend you.
Ontological confusion is a philosophical problem, not a mathematical one. Given the current example, it can be elucidating to philosophy of mathematics.
Well, the whole idea that all the mater and energy of the universe can emerge from quantum fluctuations (in “empty” space?) is still mind blowing. Can you imagine what it would be like to travel back in time and tell Aristotle or Aquinas about it?
ETA: but yeah. Krauss can be an a-hole. I remember that debate with William Lane Craig where he was plain obnoxious
dazz:
Erik:
No, Erik, you have forgotten what the issue was. You wrote:
That’s just dumb.
Origenes is confused about physics and concludes that naturalism is false. You are confused about mathematics and conclude that empty sets are “philosophically suspect”.
The problems lie not with naturalism or set theory, but with your incompetence.
Dunning-Kruger rides again!
Erik,
Just for fun, tell us why the concept of the empty set is “philosophically suspect”.
Since it’s Erik’s initial claim that the concept of the empty set is ontologically suspect, the burden is on him to explain why he says that. Without that explanation, there’s nothing for the rest of us to respond to.
The talks about actuality / potentiality in the other thread made me wonder if Erik also finds the concept of infinity in mathematics suspect
I already explained, but maybe it was so fast it went over everybody’s head. So I’m typing slower now.
Square circles are suspect, right? Similarly, empty sets are suspect. They involve definitional self-contradiction (supposing that a set is a collection of things) and this makes them suspect.
I’m not saying that they are useless concepts. Square circles are very useful as a warning example of how not to think. And empty sets have a similar use, unless somebody unpacks the concept so that it doesn’t involve a definitional self-contradiction. Set theory doesn’t unpack the concept as required. Instead, set theory posits empty sets as an axiomatic starting point. A dogmatic kind of thing. That’s philosophically suspect, possibly unsound, no matter how imaginarily useful for mathematicians. Caution must be exercised when you deal with philosophically suspect stuff. Otherwise you might end up like Krauss.
KN was not cautious. The statement that natural numbers are generated from sets necessarily involves highly suspect metaphysical assumptions about the nature of numbers and of sets, such as: What does it mean to generate numbers? What does it mean to generate from sets? Is this the only way how to obtain numbers or are there more ways? If more, then why not mention those other ways? Are numbers the only things generated from sets? If there’s more, then why not mention what else can be generated from sets? Etc. KN has general disdain for metaphysics anyway, so nothing too surprising there.
No. Finite and infinite are opposites. Opposites, contrasts, definitions and distinctions are the stuff of metaphysics, the way to figure out anything and everything.
So in reality what you have a problem with is the concept of zero (empty set = collection of zero “things”)
So you don’t think the metaphysics of infinite series, for instance, are problematic?
That would make more sense than finding the empty set suspect. But apparently, Erik does not have a problem with infinity (see his reply to you).
So are something and nothing, yet you seem to have a problem with zero / nothing
Well, according to him the issue is some definitional self-contradiction. If there’s any such contradiction he should be able to provide an argument in propositional form exposing it, I guess
I have no problem with them. Problems arise when people don’t know what zero and nothing are. People such as Krauss and set theory radicalists. And more problems follow when they don’t care to find out.
I did. In parentheses in my previous post. Maybe that was too fast for you again.
I won’t be holding my breath waiting for Erik to do that.
He seems to be unacquainted with mathematical thinking. Mathematicians have no difficulties with
the empty sum
the empty product
the empty union (of sets)
the empty intersection.
On the other hand, “the empty quotient” does not make sense. That’s because division is a strictly binary operation. But addition, multiplication, union, intersection are not strictly binary. You can add any bunch of numbers. And you can multiply any bunch of numbers. Here “bunch” is being used as a colloquial (non-technical) term. And if you can add any bunch of numbers, you should be able to look at the limiting case where there aren’t any numbers at all being added. That’s what gives you the empty sum.
Can you lay out a syllogism for us exposing the contradiction?
You are unacquainted with what is philosophically suspect. KN knows, I’m sure, but he has so little respect for his own field that he simply doesn’t care.
Looks like you have no idea what a definition is.
Do you affirm the three classical laws of thought?
You said there was a definitional self-contradiction. Is this “contradiction” the kind of contradiction that classical logic deals with in one of it’s axioms? If it is, I think it’s reasonable to ask for a syllogism, me thinks
You thinks wrong. For a definitional self-contradiction you don’t need a syllogism. You only need to recall the laws of thought, specifically the law of non-contradiction in this case. Unless you don’t affirm it (Krauss doesn’t), in which case all attempts to explain things to you are doomed.