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  1. #341
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by Squatch347
    In the context of a R/S Causet, what is the physical meaning of the order relation that makes this a partially ordered set? The reason these are called "causal sets" is because the order is one of causal influence.

    From our Axioms paper:
    The elements of a causal set are taken to represent spacetime events, while its binary relation is taken to encode causal relations between pairs of events....
    The binary relation < defines an interval finite partial order on C, called the causal order, with the physical interpretation that x < y in C if and only if the event represented by x exerts causal influence on the event represented by y.
    In this way, one can define the causal structure without the explicit presence of a metric. However, when it comes time to express the physical meaning, or even just the geometric meaning in the attempt to associate a metric to the structure, one must conclude as the references cited here do, that ‘p relates
    to q’ means that p connects to q via a suitable causal curve, as defined by the Lorentzian geometry.
    http://www.physics.umd.edu/grt/jacob...ts/brendan.pdf (I cite him not as a definitive definition, but because he is quoting a classic paper I do not have full access too).
    It is conjectured that, when suitable causal sets on a large number of elements are considered, there exist unique lorentzian manifolds (up to small changes in the metric), in which the causal sets appear as uniformly distributed points, with metric-induced causal relations which agree with the partial order relation, and which are approximately flat on the length scales determined by the density of embedded points. These manifolds are free of causality violations and time-orientable, and provide a causal macroscopic interpretation of the partial order relation.
    http://www.researchgate.net/publicat...s_a_causal_set
    The causal set program is one of a number of discrete spacetime approaches to the problem of quantum gravity. It proposes that the microstructure of spacetime is that of a partially ordered set, a causal set, in which the partial order encodes information about the causal structure of spacetime

    http://scitation.aip.org/content/aip...1063/1.2905136
    Okay, but my definition of "Rideout-Sorkin causet" was based on this line (top of p.3) of this R&S paper:

    A causal set (or “causet”) is a locally finite, partially ordered set (or “poset”).

    Given this definition by Rideout-Sorkin, I thought it was reasonable to call a locally finite (here meaning "interval finite") partially ordered set a "Rideout-Sorkin causet".

    Let's assume for a second that this is true. What is the initial condition for this process? It would seem to me that in an infinitely old universe there is no initial condition and therefore this process becomes problematic.
    "Initial conditions" don't necessarily happen at the "beginning" of the process. You might start at some arbitrary point in a doubly-infinite sequence {xz} (where z is an integer), and with the transition rule xz = 2xz-1 + 1 you could reconstruct all "future" (xk, k > z) and "past" (xj, j < z) points.

    I mean it in the same sense we used when initially discussing the difference between a causet labeled by a natural number set and a causet labelled by integers or letters or shapes. The form of the label cannot have an effect on the physical interpretation of the causet. Any order inherent or used in the labeling system must be consistent with the order inherent in the causet. This is the same argument we made back when we were discussing the original "Labeled Causets in Discrete Quantum Gravity" paper.

    Just as covariance dictates that the laws of physics are independent of the coordinate system employed, in the discrete theory, covariance implies that
    order isomorphic causets should be identified. That is, a causet should be independent of labeling.
    Link again for easy reference: http://www.du.edu/nsm/departments/ma...ints/m1410.pdf
    Right, what matters are the order properties of the labeling set, not whether it's, say, English letters or Roman numerals.

    I think my point still stands, though; there are Rideout-Sorkin causets (i.e., locally finite posets) that do not admit a Rideout-Sorkin labeling (a map L from the causet C to the natural numbers N that satisfies c1 < c2 implies f(c1) < f(c2)).

    You are appealing to a different meaning that simply doesn't exist. Your argument has been essentially that I was implying something different by misusing the term, but you can't point out how I implied something incorrect. Nor do your peers seem to have such compunctions:
    In the causal set approach to discrete quantum gravity, a causal set (causet) represents a possible universe at a certain time instant and a possible completed" universe is represented by a path of growing causets [2, 5, 6, 8, 9].
    ibid.

    Is Prof. Gudder misusing terminology when he speaks of growing causets here?
    I assume that Prof. Gudder knows the mathematical meaning of his statements about "growing" causets. I do not make the same assumption for you, Squatch.

    It would perhaps be true if there were a different definition for iterative used by mathematicians, but there isn't. It is a word that means the same thing in project management, computer science and pure mathematics. That is why you find the same definition of the word on Wolfram Mathematics, or in peer reviewed papers. Do you really have no idea what these authors mean when they invoke the term iterative? If no, is that idea substantively different from the one I offered as the definition?
    If you're going to claim that your definition is commonly used in pure mathematics, it is incumbent on you to support your claim. I know at least that the definitions of recursive functions, primitive recursive functions, what is sometimes called countable induction, and transfinite induction use much more precise language even at the undergraduate level. I doubt that the definitions get any easier in graduate and postgraduate literature, but perhaps I'm wrong.

    Because you are using the term in a different manner than is generally accepted. If you wish to communicate effectively, it is a better policy to use terms in a manner that your readers will understand. Crack pot has a specific meaning and it differs from the meaning you meant to imply. However, even the definition you offered does little to alter the objection. No support was offered to indicate that they were doing science in a non-standard or sub-standard way, the term was simply lobbed out as a dismissal.
    It's fine to claim that the examples I gave fail to be iterative; what matters is that you show it.

    Why not do your own research? Why must I be the one to justify myself to you? That is the merit of my objection. Both you and GP have shown that you seem to view yourselves as the academic panel to which I must defend myself and which has the final say on a source's "worthiness." That is not the case here. I made a claim which I defended, if either of you wished to make an objection to that claim then make an argument countering the claim or showing how the source is incorrect.
    I have done years and years of my own research in mathematics, Squatch. How much have you done?

    You are correct, I misspoke. Gregarious children are not casually related across space, they are simply related across space. As I understand it, as you pick a maximal element to be a child you also pick a partial stem to describe its relation to. In this case the child is not causally related the the particular partial stem in question, it exists in spacial relationship to the elements of its parent. This selection also involves (by default) the selection of an anti-chain that contains the causally related elements to the new element (para 3, page 5).
    For the gregarious child, the empty partial stem is chosen for the maximal element (see e.g. the diagram on page 6).

    I think that this is essentially correct. c1 does not come before or after c2 in a temporal sense. If I were to describe c1 in relation to c2 I would use only changes to physical coordinates rather than any temporal coordinates. Do you think that R/S mean something different when they say "spacelike?"
    No, this has been the definition of "spacelike" relation among causet elements that I have been expounding. You have insisted to the contrary that there is a "spacelike" relation aside from the (I assume "temporal") partial order defined on the causet.

    You didn't quote the additional sentence, I just wanted to be clear. Do you also agree with me when I said: "Each of the different ways of adjoining e are children, taken together they are siblings."
    Assuming that "different ways" refer to the different possible posets that can be formed where the "additional" element is maximal, yes.

    Fair enough. But the age of the universe in your example would still be finite right?
    It depends on what you're calling the "age". You proposed that the "age" of the universe is the length of the longest (temporal, if you're insisting that there are different partial orders) chain of elements from the causet representing the universe. For the universe represented by the causet I gave above, there is no longest chain; therefore, the universe has no age.

    You could take a slightly different approach, and say that if there is a chain of length k in C, then C's age is "at least" k. If there is some k such that for all N > k, C's age is not "at least" N, then C has a finite age. If C doesn't have a finite age, then C has an infinite age.

    Under that definition, the universe represented by the causet I gave would have an infinite age.
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  2. #342
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by GoldPhoenix View Post
    Your argument is badly sourced and is thus uncompelling.
    Which is fallacious right? If the actual argument were poor rather than the sources didn't meet your specific requirement, it should be easy to refute. Arguing that it doesn't deserve refutation because you don't like the names of the sources isn't a valid rebuttal.

    Quote Originally Posted by GP
    ...then you relied on --for all intents and purposes-- thoroughly unvetted sources as a back up argument
    Man, super tempted to challenge you to support that statement to give you a taste of your own medicine, but I won't.

    Quote Originally Posted by GP
    Lastly, you seem to have this false notion that getting published in a peer-review science journal is what makes something mainstream
    Which was not my argument. What my argument was was that you were restricting which peer-reviewed journals you were accepting to those that you felt were mainstream. You noted a peer-reviewed article of mine but dismissed the source as not really an acceptable journal.

    Quote Originally Posted by GP
    Now, in your defense, I probably should have thoroughly gone through Shanahan's paper and given a paragraph-by-paragraph critique of exactly how many BS statements, errata, vague assertions, convoluted and unclear reasoning, and just outright false statements that Shanahan was making (on top of the obnoxiously non-standard, convoluted notation, but this isn't an error, it's just irritating). Partly, however, I did not wish to engage in this laborious chore, and I was unconvinced of its effectiveness as a debate tactic.
    If you didn't want to engage in the debate that is fine, there are plenty of debate comments here (ODN) that are full of technical errors that I don't have the time to correct. But don't half engage with a series of long posts about how dumb these sources are. You spent enough time and verbiage on here to have offered a simple proper rebuttal initially and you certainly can't complain that I am just too stubborn to admit I'm wrong when shown the evidence (as I showed when you corrected me earlier).

    Quote Originally Posted by eye4magic View Post
    Does it matter if the source is mainstream or not mainstream?
    I think this is a great point. No, not really. My point was not that the discussion was mainstream, only that it existed.

    Quote Originally Posted by CliveStaples View Post
    Okay, but my definition of "Rideout-Sorkin causet" was based on this line (top of p.3) of this R&S paper
    I understand, but that only works if we are to assume they are covering all the aspects rather than (as I believe they are) offering an initial criteria to orient the reader. Their absence of a discussion of exactly what the order relation represents along with the general thrust of the paper seems to indicate that they see this as a causal relationship similar to in the papers I linked. Do you agree that that is probably what is meant in this paper?

    Quote Originally Posted by CS
    "Initial conditions" don't necessarily happen at the "beginning" of the process.
    But we still have the same problem. For any point x the initial condition requires a known value for x-1. But for all values of x-1 we must have a known value of x-2 and so on. Thus it would seem that we cannot have an initial condition because for all initial conditions there is a prerequisite step. This seems to be a variation of the traversing the infinite objection noted above. I think for this idea to get traction it would need to be shown that a process such as this could actually count through an infinite series of steps.

    Quote Originally Posted by CS
    Right, what matters are the order properties of the labeling set, not whether it's, say, English letters or Roman numerals.

    I think my point still stands, though; there are Rideout-Sorkin causets (i.e., locally finite posets) that do not admit a Rideout-Sorkin labeling (a map L from the causet C to the natural numbers N that satisfies c1 < c2 implies f(c1) < f(c2)).
    Agreed, and whether those order properties of the labeling set accurately reflect the order described in the causet right?

    You could perhaps be right on your second point, I'll need to think on it a bit more. In the meantime, there seems to be a more important question, for those R/S Causets that would not admit a R/S labeling to N, are those valid to our universe?

    Quote Originally Posted by CS
    I assume that Prof. Gudder knows the mathematical meaning of his statements about "growing" causets. I do not make the same assumption for you, Squatch.
    Then the appropriate thing (aside from principle of charity) would be to say, "did you mean X?" Not to assume I meant it incorrectly (without explaining why what I implied was incorrect) and state that as if it were a fact. Especially given the lack of direct evidence that I meant something radically different from what Prof. Gudder is saying.

    Quote Originally Posted by CS
    If you're going to claim that your definition is commonly used in pure mathematics, it is incumbent on you to support your claim.
    And I did, way back in post 303. Maybe not from the greatest looking site ever, but it describes the same process as the two links I just offered and is primarily focused on the use of this process in mathematics. If you didn't like the site that is fine, tell me why at the time, again it is the dismissive response without cogent argument that is the problem here. If I used the term iterative incorrectly then point out why or why it is imprecise (IE it could mean X or a very different concept Y), but that doesn't seem to be the case at all, rather I seem to be using the word in the exact same manner as the authors of at least two of our papers here, to describe a repeated process that builds upon itself.

    Quote Originally Posted by CS
    I have done years and years of my own research in mathematics, Squatch. How much have you done?
    Come now Clive, I'm not questioning you (though this is the internet you realize you could be some 50 year old dude in a clown suit for all I know). Regardless though, you experience here is irrelevant to whether or not the claim itself is true. You could be a Nobel Prize winner and be wrong or a crazy homeless dude and be right, now each of those has a vastly different probability of being so, but neither, by their nature is inherently right or wrong. What determines the truth value of the claim is the claim itself, not the relative CVs of the two debaters.

    Quote Originally Posted by CS
    For the gregarious child, the empty partial stem is chosen for the maximal element (see e.g. the diagram on page 6).
    Right, the element is a gregarious child because an empty partial stem is chosen in relation to it. It is not a gregarious child in relation to other elements though that would form its own partial stem, right?

    Quote Originally Posted by CS
    No, this has been the definition of "spacelike" relation among causet elements that I have been expounding. You have insisted to the contrary that there is a "spacelike" relation aside from the (I assume "temporal") partial order defined on the causet.
    I'm saying that the statements offered by the papers presupposes an underlying dimensionality across which the various points are related, though not causally. Statements like "X exists in a spacelike relation to Y" would seem to support that statement as do the quotes I originally offered in support of it in PM as well. Clearly you aren't questioning whether or not there is a spatial dimension in the universe R/S are modeling here and that that dimension is relevant to their theory.

    Quote Originally Posted by CS
    It depends on what you're calling the "age". You proposed that the "age" of the universe is the length of the longest (temporal, if you're insisting that there are different partial orders) chain of elements from the causet representing the universe. For the universe represented by the causet I gave above, there is no longest chain; therefore, the universe has no age.
    My objection to the causet you offered though was that it differs from our observed universe in that we are at a specific N. There is a longest chain for any specific N in that casuest right?

    It also seems to differ from our universe (and perhaps I'm misunderstanding here) in that there should be a possible chain at any point N that connects N to the origin since no point arises acausally. IE in our universe no element arises that has no possible non-empty partial stems (all partial stems for it are empty).
    "Suffering lies not with inequality, but with dependence." -Voltaire
    "Fallacies do not cease to be fallacies because they become fashions.” -G.K. Chesterton
    Also, if you think I've overlooked your post please shoot me a PM, I'm not intentionally ignoring you.


  3. #343
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    Re: WLC's Argument Against an Actual Infinity

    Again, Squatch, I want to emphasize that I respect you, too, but bro, this debate is pretty far from your typical level of argumentation.


    Quote Originally Posted by Squatch347 View Post
    Which is fallacious right? If the actual argument were poor rather than the sources didn't meet your specific requirement, it should be easy to refute. Arguing that it doesn't deserve refutation because you don't like the names of the sources isn't a valid rebuttal.
    ...?


    No, Squatch, that is not a fallacy. Perhaps you should access the "Fallacy Pages" subforum and read my (incomplete) draft of "An Introduction to Logic" or you might consider a refresher on the Nikzor Project. Logic refers to the act of making an inference from premises (regardless of whether the premises are true or false) to reach a conclusion. This is the fundamental difference between the soundness and the validity of an argument. Logical fallacies address invalid argumentation, not unsound argumentation. Unsound argumentation doesn't require careful thought to understand where the error lies.


    Quote Originally Posted by Squatch
    Man, super tempted to challenge you to support that statement to give you a taste of your own medicine, but I won't.
    You made the claim. They're your sources. The only thing I need to do (which I did in this post, in case you've forgotten) is the following:

    1.) State that I have tried to check which of your sources has been published in a peer-review journal.
    2.) I didn't come up with any results for your authors using a search on an online scientific papers database. (This website is HEP Inspires)
    3.) The ball's in your court. It's your support, it's your job to defend that it's valid, especially given that I made an honest effort to see if they were valid.

    Quote Originally Posted by Squatch
    Which was not my argument. What my argument was was that you were restricting which peer-reviewed journals you were accepting to those that you felt were mainstream. You noted a peer-reviewed article of mine but dismissed the source as not really an acceptable journal.
    1.) I originally employed a tactic to deal with the huge number of sources that you had piled up, which was to point out that none of them were physicists (A claim which you've done nothing to correct, not in the response to #250, your post #290, which was honestly such a huge heep of subterfuge and bare assertions that I chose not to respond to it). This is a less compelling argument, which I later correctly diagnosed the problem (See the response to your next quote).

    2.) Squatch, it was an unacceptable journal. At least, if you're referencing Shanahan's work; you didn't really bother to specify which of your copious number of "sources" that you're referencing. To the point, no one put a gun to your head and made you say "I’m not arguing this is metaphysics, but physics and that this is a physics debate occurring between physicists." So if you wanted me to take your philosophical claim seriously, then you have a valid source (a paper from a peer-review philosophy journal). If you want me to take your physics claim seriously, then try peer-review physics journal.

    Quote Originally Posted by Squatch
    If you didn't want to engage in the debate that is fine, there are plenty of debate comments here (ODN) that are full of technical errors that I don't have the time to correct. But don't half engage with a series of long posts about how dumb these sources are. You spent enough time and verbiage on here to have offered a simple proper rebuttal initially and you certainly can't complain that I am just too stubborn to admit I'm wrong when shown the evidence (as I showed when you corrected me earlier).
    Squatch, I explained why I wasn't going to go through every single one of these sources. Please read this:


    If you just grab sources on the internet, and you don't check that they are backed up in a paper that has passed peer-review, this places a tremendous time-commitment on my part. A commitment that, honestly, I'm not willing to partake in because it is not beneficial to me. There's no shortage of pseudo-scientific garbage on the internet (e.g. the long discussion of online crack pots that Nobel Laureate Gerardus 't Hooft gives on his website). Meaning that I was faced with the serious problem that if I did not introduce a stop-gap measure, I had to personally go through your sources to check for their validity. Clive put it best:


    "The work was presented in order to support a claim. The work has elementary mistakes, bad math, and bad physics [GP: Clive is referring to Shanahan's work that we personally discussed at length]. Do you want a technical demonstration of these errors?

    Also, it amounts to a kind of linkwarz if each side can post as many studies as they like as "support" without presenting any mathematics/physics themselves.
    "


    and


    "There's a problem, though, because it takes a good deal of effort to read through and understand errors in bad papers. Good papers are easy to read; their logic is open and clear, their deductions well-reasoned, and their conclusions follow in a logical, reasonable way from previously-established results in the paper. Bad papers can be exceptionally difficult to read, because their logic is often obfuscated, their reasoning often concealed and implicit, their deductions often given without reasoning, and their conclusions often seemingly unrelated or detached from what has gone before.

    Citing a bad paper, however, is quite easily done. Treating each paper as reliable unless proven unreliable leads to a large burden on the verifiers. This is the whole point of disallowing linkwarz. If Squatch has an argument about physics, why is he allowed to merely cite papers rather than presenting his (technically-flawless but layman-accessible) arguments himself?"


    tldr: You could have sat there and drawn from a nearly infinite number of "sources", which would have put the onus on me of spending a few hours on each one. Unfortunately, I posted before I realized the central error that you were making. I reposted later and clarified that the error that you're committing is that you aren't giving me a paper that has passed peer-review. I reminded you that this error was very basic, and that if you make a scientific claim, you need to pass scientific rigor. Which you still haven't done, by-the-way --at least, as per post #250, I haven't seen a valid rebuttal to this point.


    Quote Originally Posted by Squatch
    I think this is a great point. No, not really. My point was not that the discussion was mainstream, only that it existed.
    Again, Squatch my initial objection to you in this thread is your misleading language or misinformation about a basic fact of physics --presumably stemming from your lack of understanding of the subject. Some of which, I think, has been clarified to you in this discussion, but let's not re-invent history here. You first brought up Lorentzian Relativity way back in post #161:


    1) The use of the Lorentzian interpretation of Special Relativity. This view on SR has become more prominent in recent years because it allows for absolute simultaneity. Absolute simultaneity is the answer to certain problems within versions of Quantum Mechanics and Special Relativity that would seem to imply violations of causation. These interpretations would seem to indicate that there is a "preferred" reference frame, though they provide no direct evidence for discovering that frame. Additionally, recent development concerning dilation and contraction effects seems to favor this interpretation since the Lorentzian offers an explanation for the reality of these effects, while the Einsteinian interpretation is not. Discussion of these effects can be found here and in Kroess, Peter, “The Physical Status of Time Dilation within the Special Theory of Relativity"


    Now, does this quoted text make it sound like you were initially claiming that LR was anything but mainstream science? I can't believe that you don't know full well what the phrase "has become more prominent" means.
    Last edited by GoldPhoenix; May 28th, 2014 at 02:24 PM.
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  4. #344
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by GoldPhoenix View Post
    "I’m not arguing this is metaphysics, but physics and that this is a physics debate occurring between physicists." So if you wanted me to take your philosophical claim seriously, then you have a valid source (a paper from a peer-review philosophy journal). If you want me to take your physics claim seriously, then try peer-review physics journal.
    I would point out that this thread was posted in the "Philosophical debate forum." Clive could have posted the thread in the technology/science forum where hard/pure physics is debated between physicists, but he posted the argument in the Philosophical Debate forum which reasonably so is subject to philosophical arguments and sources. So perhaps that's part of the issue here: is this philosophical thread's argument a purely 100 percent hard physics argument?
    Last edited by eye4magic; May 28th, 2014 at 03:38 PM.
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  5. #345
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by Squatch347 View Post
    I understand, but that only works if we are to assume they are covering all the aspects rather than (as I believe they are) offering an initial criteria to orient the reader.
    Uh, what? It works because that's what Rideout-Sorkin's definition of a causet is. How does "A Rideout-Sorkin causet is a locally finite poset" depend on Rideout-Sorkin "covering all aspects rather than offering an initial criteria to orient the reader"?

    You might mean something like this: "The Rideout-Sorkin paper doesn't look at locally finite posets in general; rather, they restrict their analysis to locally finite posets that meet certain criteria (e.g., finiteness), and much of the paper's results rely on the causets in question meeting those criteria. So the term 'Rideout-Sorkin causet' should refer not to the general class of causets defined in the paper, but rather the class of causets for which the later results of the paper hold."

    This does not contradict my claim that:
    Not all Rideout-Sorkin causets [here meaning locally finite posets] admit Rideout-Sorkin labelings [here meaning maps L from a causet (C,%) to the natural numbers (N,<) such that c1 % c2 implies L(c1) < L(c2)].

    My original point with making this claim was:
    Hence, if you're going to require that every causet admit a Rideout-Sorkin labeling, you'll need a more restrictive definition of causet than Rideout-Sorkin's.

    That is, if you want the definition of causet to be such that "whenever C is a causet, then C admits a Rideout-Sorkin labeling" holds, then you can't use Rideout-Sorkin's definition of causet.

    Their absence of a discussion of exactly what the order relation represents along with the general thrust of the paper seems to indicate that they see this as a causal relationship similar to in the papers I linked. Do you agree that that is probably what is meant in this paper?
    Oh, I've always thought that the intuitive meaning of the partial order on causets was meant to represent a causal order.

    If I understand your argument properly, you think that:

    (1) If (C,<) is a causet, then < is both a causal order and a temporal ordering.
    (2) There's another partial order <' defined on C that tells you the spatial (i.e., non-causal?) relations among the elements of C

    I'm not sure how you're hooking up "temporal" with "causal" (It seems facially plausible to me that an event E1 can temporally precede an event E2 without E1 being in the causal chain that produced E2). Also, how is <' related to seems to me because I'm not sure how you're defining / constructing <', so it might be that <' is indeed uniquely defined by <]


    But we still have the same problem. For any point x the initial condition requires a known value for x-1. But for all values of x-1 we must have a known value of x-2 and so on. Thus it would seem that we cannot have an initial condition because for all initial conditions there is a prerequisite step. This seems to be a variation of the traversing the infinite objection noted above. I think for this idea to get traction it would need to be shown that a process such as this could actually count through an infinite series of steps.
    You don't necessarily need all the previous conditions, though. If you know x1000, and the rule xz = f(xz-1), then under certain conditions (e.g., f invertible) you can construct x1001 and x999. Under more relaxed conditions, you could 'guess' at x999.

    Now, if xz = f(xz-1, xz-2), then you might not be able to find x1001 or x999.

    Agreed, and whether those order properties of the labeling set accurately reflect the order described in the causet right?
    No, the representation is one-way. All you require is that L: (C,$) -> (N,<) satisfies
    (1) c1 $ c2 L(c1) < L(c2)

    That is, if you know c1 $ c2, then you know L(c1) < L(c2).

    But just because you know L(c1) < L(c2) doesn't mean you can conclude c1 $ c2.

    The requirement is not an if and only if, i.e.
    (2) c1 $ c2 L(c1) < L(c2)

    If (2) were true, and L was a bijection, then C and L(C) would be order-isomorphic, i.e. (L(C), <) is basically just (C,$) with c renamed to L(c) and $ renamed to <.

    But supposing only that (1) holds, then (L(C),<) can have order properties that (C,$) lacks.

    You could perhaps be right on your second point, I'll need to think on it a bit more. In the meantime, there seems to be a more important question, for those R/S Causets that would not admit a R/S labeling to N, are those valid to our universe?
    Maybe, maybe not. My point was that the following argument isn't valid:

    (1) Our universe is modeled by a Rideout-Sorkin causet (C,$). [premise]
    (2) Therefore, (C,$) has a labeling.
    (3) If (C,$) has a labeling, then our universe is past-finite.
    (4) Therefore, our universe is past-finite.

    (2) doesn't follow from (1); if your argument is anything like (1)-(4) (perhaps with additional premises included in (3)'s implication), then you either need to add (2) as a premise or modify (1) so that it implies (2) (e.g., changing the definition of Rideout-Sorkin causet from 'locally finite poset').

    Then the appropriate thing (aside from principle of charity) would be to say, "did you mean X?" Not to assume I meant it incorrectly (without explaining why what I implied was incorrect) and state that as if it were a fact. Especially given the lack of direct evidence that I meant something radically different from what Prof. Gudder is saying.
    All I did was point out that no causet is actually "growing" (in the sense of a causet having its elements changed), but rather the "growth" refers to the image of the causet under various transition maps. If you already knew that, great; you didn't need my explanation. If you didn't know that, great; you did need my explanation. Getting offended is just a waste of time.

    And I did, way back in post 303.
    Squatch, when you say something like this, it's courteous to quote or otherwise reference the language from your source that bears out your claim. Now I have to go through post 303 and try to find which passage I think that you think supports your claim.

    I assume you're referencing this link:

    http://www2.edc.org/makingmath/matht.../iteration.asp

    Maybe not from the greatest looking site ever, but it describes the same process as the two links I just offered and is primarily focused on the use of this process in mathematics. If you didn't like the site that is fine, tell me why at the time, again it is the dismissive response without cogent argument that is the problem here. If I used the term iterative incorrectly then point out why or why it is imprecise (IE it could mean X or a very different concept Y), but that doesn't seem to be the case at all, rather I seem to be using the word in the exact same manner as the authors of at least two of our papers here, to describe a repeated process that builds upon itself.
    The description found here is from a source intended for "middle and high school students" (found in the "About Our Project" section), not postdoc mathematicians. Where's the support for this definition being common in pure mathematics fields?

    The problem with that definition is that it isn't very precise; it's difficult to tell what counts as "iterative" and what doesn't. What counts as a "process" for the sake of that definition? What counts as "input"--are you working with, say, indexed and ordered sets of functions? Functions aren't the only kind of mathematical object that can be said to have input.

    Come now Clive, I'm not questioning you (though this is the internet you realize you could be some 50 year old dude in a clown suit for all I know). Regardless though, you experience here is irrelevant to whether or not the claim itself is true. You could be a Nobel Prize winner and be wrong or a crazy homeless dude and be right, now each of those has a vastly different probability of being so, but neither, by their nature is inherently right or wrong. What determines the truth value of the claim is the claim itself, not the relative CVs of the two debaters.
    You asked:
    Why not do your own research? Why must I be the one to justify myself to you?

    If you don't want to justify your claims, fine. Start a blog.

    Right, the element is a gregarious child because an empty partial stem is chosen in relation to it. It is not a gregarious child in relation to other elements though that would form its own partial stem, right?
    No, the element is not a gregarious child. The causet formed by adding the element and choosing that it relate to none of the elements from the parent is the gregarious child. Remember, the children of a causet are other causets (specifically, the children are all the causets that can be formed by adding a maximal element to the parent).

    Again, look at the diagram on the bottom of page 6:



    In particular:



    I've circled the "new", maximal element in red. This particular causet Cc is a gregarious child of the "parent" causet at the bottom because

    (1) it's a child of the parent, because it's the parent "plus" a "new" element that is maximal
    (2) it's gregarious, because the "new", maximal element isn't related to (i.e., has no line to/from) the elements from the parent causet C.

    The "new", maximal element (circled in red) is not a child at all, let alone a gregarious child. The gregarious child is Cc, not the circled element in Cc.

    I'm saying that the statements offered by the papers presupposes an underlying dimensionality across which the various points are related, though not causally. Statements like "X exists in a spacelike relation to Y" would seem to support that statement as do the quotes I originally offered in support of it in PM as well. Clearly you aren't questioning whether or not there is a spatial dimension in the universe R/S are modeling here and that that dimension is relevant to their theory.
    To my understanding, "X exists in a spacelike relation to Y", where X and Y are elements of a causet (C,$) can be penciled out entirely in terms of $--i.e., neither X $ Y nor Y $ X. If so, the "spacelike" relations are just a property of the causal relation defined on C. I don't know how this relates to "an underlying dimensionality" (whatever that means).

    My objection to the causet you offered though was that it differs from our observed universe in that we are at a specific N. There is a longest chain for any specific N in that casuest right?
    For clarity, I'll define C = (S,$) where S = {0,1,2,...} is the set of all non-negative integers, and $ is defined by 0$1, 2$3$4, 5$6$7$8, etc., where a1$a2$...$ak implies a1 $ a2, a2 $ a3, ..., and ak-1 $ ak as well as the transitive closure (i.e., if ai$aj and aj$ak, then include (ai,ak) in $).

    I'll answer your question first.

    If you pick an N and construct a new causet CN = (SN, $N) such that:

    (1) SN = {0,1, ... ,n}
    (2) $N is defined so that for any x,y in SN, x $N y ⇔ x $ y when x and y are considered as elements of S

    [The fact that CN is a causet follows from C being a causet; the proof that $N is a partial order relies on the partial-order features of $ that get "inherited" by $N.]

    Clearly, since SN is a finite set, CN has a longest chain, and the length of any of its longest chains is finite.


    Just a couple notes of interest:

    I. CN doesn't necessarily have a unique longest chain.

    For example, the chains in C7 are:

    (i) 0 $N 1
    (ii) 2 $N 3 $N 4
    (iii) 5 $N 6 $N 7

    Chains (ii) and (iii) aren't equal, but are both "longest" chains and have equal length.

    II. K < J does not imply Age(CK) < Age(CJ)

    For example, Age(C6) = Age(C5).

    My question is: how do you know that we're at a specific N in our universe? How do you know that our universe isn't represented by (C,$)?

    It also seems to differ from our universe (and perhaps I'm misunderstanding here) in that there should be a possible chain at any point N that connects N to the origin since no point arises acausally. IE in our universe no element arises that has no possible non-empty partial stems (all partial stems for it are empty).
    Using the terminology on page 3 of the RS paper,
    you're saying that if (C,<) is a causet that represents our universe, then
    ∃ m∈C ∀x∈C: m ∈ past(x)

    This implies that m < x for all x∈C, so C has a minimal element.
    Last edited by CliveStaples; May 28th, 2014 at 06:48 PM.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by eye4magic View Post
    I would point out that this thread was posted in the "Philosophical debate forum." Clive could have posted the thread in the technology/science forum where hard/pure physics is debated between physicists, but he posted the argument in the Philosophical Debate forum which reasonably so is subject to philosophical arguments and sources. So perhaps that's part of the issue here: is this philosophical thread's argument a purely 100 percent hard physics argument?
    The way I see it is that "hard physics" and/or mathematics is being used to support a premise in a philosophical argument.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by CliveStaples View Post
    The way I see it is that "hard physics" and/or mathematics is being used to support a premise in a philosophical argument.
    Right, and because it is a philosophical argument that is attempting to use hard physics to support it on a philosophical debate forum, that doesn't mean philosophical arguments and sources can't be used or considered. Why? Because this is the Philosophical Debate forum and the premise is a philosophical argument. Now regardless of this, and as it's already been pointed out, you or GP don't have to accept a philosophical argument or sources for a hard physics argument on a philosophical debate forum, but that's your choice.
    Last edited by eye4magic; May 28th, 2014 at 10:14 PM.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by eye4magic View Post
    Right, and because it is a philosophical argument that is attempting to use hard physics to support it on a philosophical debate forum, that doesn't mean philosophical arguments and sources can't be used or considered. Why? Because this is the Philosophical Debate forum and the premise is a philosophical argument. Now regardless of this, and as it's already been pointed out, you or GP don't have to accept a philosophical argument or sources for a hard physics argument on a philosophical debate forum, but that's your choice.
    The interpretation of physical models is a philosophical question; the role of physics models in our understanding of knowledge is a philosophical question. The argument about whether Lorentzian Relativity is a viable physics model isn't a philosophy question, it's a physics question. As such, an article about the viability of LR as a physical model written by an expert in philosophy and peer-reviewed by philosophers isn't a reliable source, because the question is outside the domain of philosophy.

    For the source to be reliable, the author should be an expert in physics, and the article should be peer-reviewed by physicists. [Although technically to present the model, the author would only need to be an expert in mathematical physics; the viability of the model, however, is a question for physicists.] The author needs to be an expert on the topic that he or she is writing about.

    You can accept arguments offered by sources that are not experts in the fields they are arguing about, but that's your choice.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by GoldPhoenix View Post
    Again, Squatch, I want to emphasize that I respect you, too, but bro, this debate is pretty far from your typical level of argumentation.
    Perhaps a little backhanded, but I also want to emphasize that I think you are a smart dude and good thinker, and I hope we can engage in a more amiable discussion soon.

    Quote Originally Posted by GP
    (A claim which you've done nothing to correct, not in the response to #250, your post #290, which was honestly such a huge heep of subterfuge and bare assertions that I chose not to respond to it).
    I want to highlight this point for two reasons.

    1) It is an interesting read of the debate and I think insightful towards your viewpoint. You realize that your criticism in 250 only dealt with some of the sources offered on the subject. That fact should be illustrative to this entire sub-debate.

    2) The second half of the statement is, I think, a good illustration of exactly what I've been critical of here. You found the substance of my post "unsatisfactory" (an opinion statement by you, certainly not an objective measure) and chose not to respond. You then assumed that because you chose not to deign my point with a response that the burden is still on me.

    Ignoring an argument is not a valid rebuttal GP.

    Quote Originally Posted by GP
    So if you wanted me to take your philosophical claim seriously, then you have a valid source (a paper from a peer-review philosophy journal). If you want me to take your physics claim seriously, then try peer-review physics journal.
    1) You still seem to misunderstand my initial claim, it was simply that this discussion was happening, not that it was the mainstream position, not that it was universally accepted (though the second part of my claim of these two theories being nearly identical in experimental prediction does appear to be mainstream and I think you were begrudgingly willing to accept that), but that it was being discussed as a valid alternative. That doesn't necessarily require a peer reviewed journal paper. More importantly it certainly does not require that the paper come from the specific couple of journals you accept.

    2) The fact that you only looked at about half my sources (which you reference in your last couple of posts) should be telling as to why you probably missed the better sources. The fact that you seem obsessed with Shanahan's paper (which I offered as a background discussion, and was the first paper offered) tells me that you probably saw it, was nonplussed by it and then skipped over most of the rest. This inference seems to fit the language you've offered here. It does not however excuse assuming that I didn't do any research and then accusing me of offering no sources of any substance without having made an argument as to why the sources offered did not have substance.

    Quote Originally Posted by CliveStaples View Post
    Uh, what? It works because that's what Rideout-Sorkin's definition of a causet is. How does "A Rideout-Sorkin causet is a locally finite poset" depend on Rideout-Sorkin "covering all aspects rather than offering an initial criteria to orient the reader"?
    Because you are assuming that definition offered is the complete definition. It would only be a complete definition if you further offered what partial order governs the poset.

    Without us chasing this whole debate down a rabbit hole, let me ask you a simple question. Do R/S Causets rely on a partial order reflecting causation?

    Quote Originally Posted by CS
    (1) If (C,<) is a causet, then < is both a causal order and a temporal ordering.
    (2) There's another partial order <' defined on C that tells you the spatial (i.e., non-causal?) relations among the elements of C
    BLUF (bottom line up front, more detail to follow): All causally related elements (shown by <) are related by (at least) a temporal relationship, though not all temporal relationships require causation. No purely spatial relationships can be causal, however a causal relationship can have a spatial aspect.


    Explanation:


    Concerning 1, I think that the < reflects a partial order that is causal in nature. IE < reflects causation between two elements (nothing more). Concerning 2, I would point out that an element that exists solely in spatial relation to another element (gregarious child) cannot be causally related to it as noted on pgs 5-6 of the Axioms paper and demonstrated in this image:



    But that an element that exists with solely to the future of causet (timid child) can be causally related.

    Now, going back to our definitions of gregarious v timid children we can see that the latter is to the future of the parent (it could conceivably be spatially different from the parent as well, R/S to my knowledge don't really discuss it, but other papers tangentially mention it. Sufficed to say that the important relationship here is that the new element is to the future of all existing elements in the causet).

    That does not necessitate that the timid child is causally related to the parent (though it does have a relation to the parent in that it is to the future). See this diagram from the axioms paper:



    Clearly there are elements to the future of describable causets that are not causally related to them. While R/S don't offer an example of a timid child being non-causally related to the parent, I don't see why this couldn't be the case, we just couldn't say that the parent is the past (as defined on pg 3) of the element.

    Quote Originally Posted by CS
    You don't necessarily need all the previous conditions, though. If you know x1000, and the rule xz = f(xz-1), then under certain conditions (e.g., f invertible) you can construct x1001 and x999.
    Which would imply a reverse causation here. IE the universe doesn't "know" what tomorrow is so that it can have today. It requires that the previous condition be existent. This is not a bi-directional equation where you start at any given point and deduce earlier or later moments, it is rather a unidirectional function where prior values are required for current calculation.

    Quote Originally Posted by CS
    No, the representation is one-way. All you require is that L: (C,$) -> (N,<) satisfies[/FONT]
    (1) c1 $ c2 L(c1) < L(c2)

    That is, if you know c1 $ c2, then you know L(c1) < L(c2).


    Agreed, with one caveat. In the case where the resulting order from the label differs from the natural order of the set used (N or Z or whatever) inferences cannot be drawn from the order of the set used to label.

    IE if I use colors to label the causet, {blue
    Quote Originally Posted by CS
    Maybe, maybe not.
    Looking back through our discussions I can't seem to find your proof that there are R/S causets that do not admit an N labeling. I see that you make an attempt a proof that Z cannot be mapped to N as a R/S labeling, but not where you show that some R/S causets do not admit a labeling with N. Could you clarify or remind me where to look?

    Quote Originally Posted by CS
    All I did was point out that no causet is actually "growing"
    Not exactly, you made an accusation of ignorance ("You're using terminology improperly again.") and given the predilection of this thread for points I've made to be summarily dismissed due to the perceived intellectual difference, it was material to the thread to point out that you were incorrect, that I was using the term correctly.

    Quote Originally Posted by CS
    You asked:
    Quote Originally Posted by CS
    Why not do your own research? Why must I be the one to justify myself to you?
    [FONT=verdana]
    If you don't want to justify your claims, fine. Start a blog.
    This statement highlights the critical thinking error made by both you and GP in this thread. You don't seem to realize the difference between "justify myself" and "justify my claim." You understand the two terms as interchangeable when they are not. You accept a point not when it is defended coherently, but when the source linked comes from the pre-approved list of acceptable sources. My argument didn't sway you, you needed me to justify myself as being worth of making an argument.


    Quote Originally Posted by CS
    No, the element is not a gregarious child. The causet formed by adding the element and choosing that it relate to none of the elements from the parent is the gregarious child.
    You missed the point of my response. If a different partial stem (and therefore anti-chain) were selected from the parent during the transition process, it would no longer form a gregarious child, correct?

    Quote Originally Posted by CS
    To my understanding, "X exists in a spacelike relation to Y", where X and Y are elements of a causet (C,$) can be penciled out entirely in terms of $--i.e., neither X $ Y nor Y $ X. If so, the "spacelike" relations are just a property of the causal relation defined on C. I don't know how this relates to "an underlying dimensionality" (whatever that means).
    IE they are not before (x$y) or after (y$x), but exist along some other relation right? Now, given that causets are meant to be physical models of our universe, what do you think the relationship might be if it is not part of the temporal dimension?

    If I were to say a point exists in our universe that is related to another point, but doesn't exist before or after it, what relationship is being evoked there?

    P.S. When I say underlying dimensionality, I'm clearly referring to the physical interpretation of these papers.

    Quote Originally Posted by CS
    Clearly, since SN is a finite set, CN has a longest chain, and the length of any of its longest chains is finite.

    ...

    My question is: how do you know that we're at a specific N in our universe? How do you know that our universe isn't represented by (C,$)?
    I'm reading the first sentence as an agreement that if we are at a specific point, N, then the longest chain would be finite.


    So as for that if (your second quoted sentence). The process of accretion of elements to causets is the passage of time right? We have elements within causets that are not maximal (which exist in the past perhaps) and maximal elements that make up a "now." Given that we are at some step of this process, wouldn't that now be a specific n which we exist at?
    "Suffering lies not with inequality, but with dependence." -Voltaire
    "Fallacies do not cease to be fallacies because they become fashions.” -G.K. Chesterton
    Also, if you think I've overlooked your post please shoot me a PM, I'm not intentionally ignoring you.


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    Re: WLC's Argument Against an Actual Infinity

    How about this, Squatch: How about you give me one source (the source that you think is your best source) that you think supports your claim about Lorentzian Relativity being a valid model, and I'll go through the entire source and explain the problems and strengths of the paper? Would that be fair? (Also, if you could, please tell me what specific points you find compelling)



    (Keep in mind, I'd also like to see something resembling evidence for your second claim that this is "becoming more prominent", but one thing at a time.)

    Quote Originally Posted by Squatch347 View Post
    I want to highlight this point for two reasons.

    1) It is an interesting read of the debate and I think insightful towards your viewpoint. You realize that your criticism in 250 only dealt with some of the sources offered on the subject. That fact should be illustrative to this entire sub-debate.

    2) The second half of the statement is, I think, a good illustration of exactly what I've been critical of here. You found the substance of my post "unsatisfactory" (an opinion statement by you, certainly not an objective measure) and chose not to respond. You then assumed that because you chose not to deign my point with a response that the burden is still on me.

    Ignoring an argument is not a valid rebuttal GP.


    1) You still seem to misunderstand my initial claim, it was simply that this discussion was happening, not that it was the mainstream position, not that it was universally accepted (though the second part of my claim of these two theories being nearly identical in experimental prediction does appear to be mainstream and I think you were begrudgingly willing to accept that), but that it was being discussed as a valid alternative. That doesn't necessarily require a peer reviewed journal paper. More importantly it certainly does not require that the paper come from the specific couple of journals you accept.

    2) The fact that you only looked at about half my sources (which you reference in your last couple of posts) should be telling as to why you probably missed the better sources. The fact that you seem obsessed with Shanahan's paper (which I offered as a background discussion, and was the first paper offered) tells me that you probably saw it, was nonplussed by it and then skipped over most of the rest. This inference seems to fit the language you've offered here. It does not however excuse assuming that I didn't do any research and then accusing me of offering no sources of any substance without having made an argument as to why the sources offered did not have substance.

    1.) An implicit presumption here is that I didn't read through post #290. I did. The problem with post #290 was that it did nothing to address my main problem: You don't have a scientific, peer-review source. The issue that you don't seem to understand is that when you said "I'm saying this is physics", the onus suddenly became for you to either present a full physical model to me and give a defense of it, or you needed to present me a physics paper that has passed physics peer-review. Because that's what it means to say "I'm arguing about physics", Squatch. Most of post #290 was just pushing us further away from this point, rather than facing the issue head on. So yes, I ignored it because it ignored my main issue. If you liked, I could have responded to every line and said either "Yes, but this fails to address why you haven't given me a scientifically peer-reviewed journal article" or "No, I disagree, but either way you've failed to give me a scientifically peer-reviewed journal article.", depending on what you said. I did, however, concede to the points that I thought were valid.


    2.) You're claiming that I was obsessed with Shanahan. Yes, I did focus on his paper in particular because I happened to read his paper first (and the errors were very overt). If what you mean by me being "nonplussed" by Shanahan's work was that I was "confused by how poorly written and thought out" it was, then yes, I was "nonplussed." With that said, I think it's disingenuous of you to say that I placed too much emphasis on him, considering that his article took up a third of your response to me and was clearly a major support for your argument.


    3.) Now, you've claimed that I didn't read "half of the sources." No, Squatch, I read/skimmed through most of your other sources, I think the only one I didn't read up on was Lazlo's paper. Again, it's simply wrong to say otherwise; in post #250 I actually took nearly every single (if not, then every single) author you mentioned, and ran them through HEP Inspires to see their peer-reviewed publications; I found that Giese hadn't gotten any of his papers through peer-review and has a prototypical crack pot website claiming that he can solve dark energy and that the higgs doesn't exist; I pointed out that there's no evidence that Ropolyi actually got a PhD in physics or that there's any existence of a PhD thesis by him, and pointed out that this doesn't even matter because at the end of his paper he says "This isn't physics however, it's purely philosophy" contra your entire argument; I showed you that Spavieri's paper ended up ruling out that version of LR. So the claim that I didn't go through your sources is just odious.


    4.) If I was clearly missing one of your "better" sources, why the hell didn't you redirect me to it? You know, after I repeatedly asked you to give me a source? You could have said "Yeah, GP, fine you don't like those, I disagree, but it doesn't matter because you have neglected paper X. Paper X is an awesome source." and kept the debate going, instead of having a stand still where you refuse to debate me and disingenuously flip-flop between "Your standards are unreasonable" and "I have a source that meets your standard." Why, Squatch, why didn't you do this? What source of yours did I miss? If you had such a source and you felt that I neglected it, then why didn't you direct me to these "better sources" when I asked you for them multiple times?


    5.) As per: "Though the second part of my claim of these two theories being nearly identical in experimental prediction does appear to be mainstream and I think you were begrudgingly willing to accept that", well, the only thing I can say is: "Nope." What I said was that if you were talking about some philosophical interpretation of SR that was equivalent to Lorentz invariance mathematically, then I don't care, I just think it's a bad interpretation, because the Minkowski interpretation is the one that correctly generalizes to Quantum Field Theory and General Relativity which is why physicists abandoned the Lorentzian interpretation a century ago.

    However, I asked you if this was the version of LR that you believed in. You said it was not, that Einstein's theory is wrong, and that your theory is a different model of relativistic effects, and not a different interpretation of SR. In order for me to agree with you that LR predicts virtually identical results to SR, I would actually need to see a coherent model presented with equations and their interpretation, which would actually be capable of making predictions. I have no such thing, so I can't agree to that proposition. And that brings us back to the fact that you haven't presented me with a paper that's made it through peer-review and has presented a clear, delineated model of LR that is not SR but looks like SR. Well, I mean other than the one which did make it through peer-review and was immediately falsified, of course.
    Last edited by GoldPhoenix; May 29th, 2014 at 04:12 PM.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by Squatch347 View Post
    Because you are assuming that definition offered is the complete definition. It would only be a complete definition if you further offered what partial order governs the poset.
    No, no, no. You think that the definition for causet has to specify what the partial order is--i.e., what elements of C x C are in the partial order?

    Rideout-Sorkin call "locally finite posets" causets. As long as you know that (S,<) is a locally finite poset, then Rideout-Sorkin would call (S,<) a causet.

    Without us chasing this whole debate down a rabbit hole, let me ask you a simple question. Do R/S Causets rely on a partial order reflecting causation?
    I don't know what "reflecting causation" means in this regard. R/S causets are locally finite posets; an R/S causet is a set S along with a partial order < on S such that the intervals defined by < on S are all finite. In that sense, R/S causets rely on S having a partial order--a particular kind of partial order, one for which the resulting intervals are all finite.

    BLUF (bottom line up front, more detail to follow): All causally related elements (shown by <) are related by (at least) a temporal relationship, though not all temporal relationships require causation. No purely spatial relationships can be causal, however a causal relationship can have a spatial aspect.
    Okay.
    Explanation:

    Concerning 1, I think that the < reflects a partial order that is causal in nature. IE < reflects causation between two elements (nothing more). Concerning 2, I would point out that an element that exists solely in spatial relation to another element (gregarious child) cannot be causally related to it as noted on pgs 5-6 of the Axioms paper and demonstrated in this image:



    But that an element that exists with solely to the future of causet (timid child) can be causally related.
    Which of the lines in the third image denote spatial relations, which denote temporal relations, and which denote causal relations?

    I can imagine a few relations you could define WRT time and space; since you haven't specified what the relations you're talking about are, or how they relate to the required partial order (hereinafter "<")--what I believe you consider the "causal" relation--I suppose I'll just take a few guesses.

    You could say that two points p1=(x1, y1) and p2=(x2,y2) [where the x coordinate is on the space axis, and the y coordinate is on the time axis] are related:

    (1) spatially if x1 > x2 or x1 < x2; write p1Sp2
    (2) temporally if y1 > y2 or y1 < y2; write p1Tp2
    (3) spatially only if p1 is related spatially but not temporally to p2; i.e. p1Sp2 but ~(p1Tp2)
    (4) temporally only if p1 is related temporally but not spatially to p2;

    From the images you've provided (I was going to say "From your images", but cstamford always threw a hissy fit about that stuff so I'll be more precise), it seems that there are points p1 and p2 that are causally related (i.e., there is a line between them) but where p1 is both spatially and temporally related to p2.

    Now, going back to our definitions of gregarious v timid children we can see that the latter is to the future of the parent (it could conceivably be spatially different from the parent as well, R/S to my knowledge don't really discuss it, but other papers tangentially mention it. Sufficed to say that the important relationship here is that the new element is to the future of all existing elements in the causet).
    Gregarious and timid children are defined in terms of the partial order of the causet. There's really no need to talk about these "spatial" and "temporal" relations you're bringing up, because all of the relevant relations are captured by the partial order.

    That does not necessitate that the timid child is causally related to the parent (though it does have a relation to the parent in that it is to the future). See this diagram from the axioms paper:



    Clearly there are elements to the future of describable causets that are not causally related to them. While R/S don't offer an example of a timid child being non-causally related to the parent, I don't see why this couldn't be the case, we just couldn't say that the parent is the past (as defined on pg 3) of the element.
    I'll take some more guesses at what your terms mean.

    First, assume the definitions for temporal and spatial relations I gave above. Then a point p1=(x1,y1) is to the future of a set C if, for all p2 = (x2,y2) in C, y1 > y2.

    Are you saying that you can pick a set of points S such that there is a point p satisfying:

    (1) p is to the future of S [by the above definition]
    (2) p is spacelike to all elements of S (i.e., for all y in S, neither y < p nor p < y)

    That seems true.

    Also: Again, in R/S the children are causets, not an element of a causet. A gregarious child is a causet; a timid child is a causet. I don't know what it means for a child causet to be "causally" or "non-causally" related to its parent--perhaps that the new, maximal element is not causally related to elements from the parent? But then the "non-causal" children are just the (single) gregarious child.

    Which would imply a reverse causation here. IE the universe doesn't "know" what tomorrow is so that it can have today. It requires that the previous condition be existent. This is not a bi-directional equation where you start at any given point and deduce earlier or later moments, it is rather a unidirectional function where prior values are required for current calculation.
    How would it imply that there is reverse causation? x1000 is still "caused by" (i.e., is the transition-image of) x999.

    Agreed, with one caveat. In the case where the resulting order from the label differs from the natural order of the set used (N or Z or whatever) inferences cannot be drawn from the order of the set used to label.
    "Natural" has a specialized meaning in mathematics, so I'd advise using a different word.

    The "caveat" you give here is just a restatement of the argument that you're responding to.

    IE if I use colors to label the causet, {blue


    This seems like an incomplete thought.

    Looking back through our discussions I can't seem to find your proof that there are R/S causets that do not admit an N labeling. I see that you make an attempt a proof that Z cannot be mapped to N as a R/S labeling, but not where you show that some R/S causets do not admit a labeling with N. Could you clarify or remind me where to look?
    First, if (C,$) is a causet, then what I've described as an R/S labeling on (C,$) is a map L:(C,$) -> (N,<) such that x$y implies L(x) < L(y). I'm not sure what "a labeling with N" means, unless you're referring to (what I've defined as) R/S labelings.

    Second, I think you've simply misunderstood the proof.

    (1) (Z,<) is an R/S causet
    (2) There is no R/S labeling on (Z,<)
    (3) Therefore, there exists an R/S causet for which there is no R/S labeling

    (1)-(3) is valid, obviously; if (1) and (2) are true, then (3) necessarily follows.

    (1) holds because Z is a locally finite poset under the standard order <.
    (2) holds via the proof by contradiction I gave.

    Not exactly, you made an accusation of ignorance ("You're using terminology improperly again.") and given the predilection of this thread for points I've made to be summarily dismissed due to the perceived intellectual difference, it was material to the thread to point out that you were incorrect, that I was using the term correctly.
    I apologize, then. I overstepped; I shouldn't have said you were using the terminology improperly.

    This statement highlights the critical thinking error made by both you and GP in this thread. You don't seem to realize the difference between "justify myself" and "justify my claim." You understand the two terms as interchangeable when they are not. You accept a point not when it is defended coherently, but when the source linked comes from the pre-approved list of acceptable sources. My argument didn't sway you, you needed me to justify myself as being worth of making an argument.
    Honestly, Squatch, I don't even think you have an argument at this point--at least, one that isn't circular.

    Frankly, I'm no longer trying to persuade you that your conclusion isn't likely to be true or isn't more probable than its negation; you just argued in endless circles.

    At this point, I'm merely trying to help you give a precise, non-circular argument for your conclusion.

    You missed the point of my response. If a different partial stem (and therefore anti-chain) were selected from the parent during the transition process, it would no longer form a gregarious child, correct?
    I hope you didn't miss the point of mine. You said:

    It is not a gregarious child in relation to other elements

    Elements are related to other elements; gregarious children are causets, not elements of causets. I'll repost the diagram I posted earlier, so that you may review it at your leisure:






    Also, I think you're confused about what partial stems and anti-chains are.

    An antichain in (C,<) is a set A such that:
    (AC1) A⊆C
    (AC2) ∀x∈A ∀y∈A: ~(x y

    A partial stem in (C,<) is a set P such that:

    (PS1) P C
    (PS2) n :|P| = n
    (PS3) xP: past(x) P



    Theorem:
    If P is a partial stem of (C,<) that contains at least one non-minimal element, then P is not an antichain.


    Proof:

    Let P be a partial stem containing at least one non-minimal element x.
    If x were minimal, then for all y in C, ~(y Since x is not minimal, there exists a y in C such that y Thus (AC2) is contradicted.
    Therefore P is not an antichain.

    Corollary: The only partial stems that are antichains are:

    (1) The empty partial stem, i.e. P =

    (2) A partial stem containing only minimal elements.

    From "a different partial stem (and therefore antichain)", I infer that you are assuming every partial stem different from the empty partial stem is an antichain. By the above corollary, this is, in general, false: in general, there are non-empty partial stems that are not anti-chains.


    The "process" of creating a child from a given causet (C,<) defines a unique partial stem (under certain finiteness conditions), as follows.

    (1) Pick an element x that is not in C; this forms the set Cchild = C U {x}
    (2) Form a partial order <child on Cchild, as follows:

    (2a) ∀a,b C: a < b a <child b
    (2b) Choose the elements in C that will be related to x, i.e. those y∈C such that y <child x. Call this set Rx. Since x has to be maximal, there must be no y in C such that x <child y.
    (2c) If you choose y <child x, then to ensure that <child is transitive, you need z <child x z past(y), since z <child y [since z,y
    C and z < y, along with (2a)] and y <child x. This amounts to choosing the partial stem Py = {y} U past(y)
    (2d) A finite union of partial stems is a partial stem; therefore, if C is finite, then Ptotal = UyRx Py is a partial stem.
    (2e) past(x) [WRT (Cchild,<child)] = Ptotal


    The unique partial stem defined by (Cchild,<child) is past(x).

    Its uniqueness is apparent, since if past(x) [WRT(C1,<1)] = past(x) [WRT(C2,<2)], where (Ci,<i) are children of (C,<) (so Ci = C U {xi}), then for all c in C, c <1 x1
    c <2 x2 [since c \in past(x1)
    c \in past(x2)].

    In light of this, the map f:(C1,<1) -> (C2,<2) where f(c) = c for all c \in c, and f(x1) = f(x2) is an obvious order isomorphism.

    Thus (C1,<1) and (C2,<2) are the same child (since children are distinguished by their order properties).


    So picking which elements from the parent get "hooked up" to x is equivalent to choosing partial stems in the parent, C, when the parent is finite (and in general whenever (Cchild, <child) is such that past(x) is finite).





    Conversely, given a partial stem P in (C,<) you can construct a child (Cchild, (1) ∀a,b C: a < b a <child b
    (2) Set past(x) := P (i.e.,
    ∀p ∈P: p <child x)

    Then <child is a partial order on Cchild (although by the irreflexive convention ~(x < x); the partial order here is to <child as is to <).

    Proof: Let a,b,c Cchild.

    <child antisymmetric:

    Suppose a <child b and b<child a.

    Case 1: a = b. Then anitsymmetry holds.
    Case 2: a != b. Then a
    C or b C.
    WLOG, suppose a
    C.
    Then if b = x, x
    Therefore b!=x, so bC. Thus a < b and b < c; since < is a partial order, the result follows.



    <
    child transitive:

    Suppose a <child b and b <child c. Then c = x or c != x.
    Case 1: c = x. Then b
    past(x). Since past(x) is a partial stem, it contains its own past; in particular, it contains past(b). But a past(b), so a past(x) and thus a
    <child x.
    Case 2: c != x. If b = x, then x is not maximal, so b != x. Similarly, if a = x, then x is not maximal, so a != x. Then a,b,c C, so a < b and b < c; since < is a partial order, a < c, and thus a <child c.

    Since <child is a partial order on Cchild, and each interval in (Cchild,
    <child) contains at most one more element than an interval in (C,>), then since (C,<) is locally finite, (Cchild,<child) is locally finite. Thus (Cchild,<child) is an R/S causet; since it has been formed by adjoining a maximal element x to C, and it contains <, it is a child of (C,<).




    In general, past(x) =
    (Cchild,<child) a gregarious child of (C,<).


    Proof: This follows straight from the definition of gregarious child.
    (<=) If (Cchild, <child) is a child of (C,<), then Cchild = C U {x}, where x is some element not in C that is maximal in (Cchild, <child).
    If (Cchild,<child) is a gregarious child of (C,<), then its maximal element x is spacelike to all other elements; i.e., for all y
    C, ~(x <child y or y <child x).
    Let z != x be an element in past(x); then z <child x. Since z != x, z
    C. But then x is not spacelike to z, an element of C, and thus (Cchild,<child) is not gregarious.

    (=>) Suppose past(x) =
    , where x is a maximal element in (Cchild,<child) such that Cchild = C U {x}.
    Suppose x were not spacelike to some element y \in C. Since y \in C, y != x.
    Then y <child x or x <child y.
    If y <child x, then y \in past(x). Thus past(x) != \empty. contradiction.
    If x <child y, then x is not maximal. Contradiction.
    Therefore, ~(y <child x or x <child y).
    Thus (Cchild, <child) is a gregarious child of (C,<).


    The only way you get a gregarious child, if you're constructing children using the above processes, is to choose the empty partial stem in (C,<).

    IE they are not before (x$y) or after (y$x), but exist along some other relation right? Now, given that causets are meant to be physical models of our universe, what do you think the relationship might be if it is not part of the temporal dimension?
    I don't know what "exist along some other relation" means. Sure, you could trivially come up with some other relation % (a partial order, if need be) such that x%y, or y%x, if you wanted to.

    Do causets determine these other relations? My understanding is that causets determine causal relations (i.e., (C,<) determines <-relations); any non-causal (i.e., non-<) relations are left undetermined or unspecified.

    Is my understanding wrong? What additional, non-< relations are you proposing for (C,<)? Are those non-< relations derived from < somehow? Are they uniquely defined for (C,<)?

    If I were to say a point exists in our universe that is related to another point, but doesn't exist before or after it, what relationship is being evoked there?
    I don't know. Perhaps it's browner than the other point? Perhaps it's raining at that point?

    P.S. When I say underlying dimensionality, I'm clearly referring to the physical interpretation of these papers.
    Okay, but the dimension of what? A spacetime regime? You're talking about a mathematical dimension, right?

    I'm reading the first sentence as an agreement that if we are at a specific point, N, then the longest chain would be finite.
    Well, that depends on what you mean by "we are at a specific point, N". The length of the longest chain in (C,<) doesn't depend on "where you're at"; the length of the longest chain in (C,<) depends only on the definition of C and <.

    So as for that if (your second quoted sentence). The process of accretion of elements to causets is the passage of time right? We have elements within causets that are not maximal (which exist in the past perhaps) and maximal elements that make up a "now." Given that we are at some step of this process, wouldn't that now be a specific n which we exist at?
    Well, we're looking at causal relationships; causally maximal elements shouldn't be assumed to be contemporaneous with each other.

    As I understand it, the process that "we're a part of" is a transition from causet to causet. If we view causets as representing a universe at a particular state, then the current state of our universe is represented by a causet; perhaps that causet is (S,$). "Future" states of our universe will be the image of, say, (S,$) under some suitable transformation mapping.

    The "now" might be (S,$), as opposed to (SN,$N).
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by CliveStaples View Post
    You can accept arguments offered by sources that are not experts in the fields they are arguing about, but that's your choice.
    Whether philosophical sources and experts or hard physics sources and experts, what's relevant to bear in mind is that those choices are within the context of a philosophical debate posted on a philosophical debate forum.
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    Re: WLC's Argument Against an Actual Infinity

    Whether philosophical sources and experts or hard physics sources and experts, what's relevant to bear in mind is that those choices are within the context of a philosophical debate posted on a philosophical debate forum.
    Sure, but if a physics claim is part of that philosophical debate, then physics sources should be used to support it.

    If we're having a debate about politics, and I make an economics claim (say, about the empirical effect of minimum wage increases/decreases), then my support should be in the form of an economics source. Political sources would, of course, abound on both sides of the issue; but what politicians or political agents have to say bears far less meaningfully on my claim than what economists have to say.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by CLIVE
    Sure, but if a physics claim is part of that philosophical debate, then physics sources should be used to support it.
    I would think that a physics philosophy source, if it was considered valid by qualified peers such as a journal, should be sufficient.

    I mean, i could hardly offer a valid philosophical critique of the morality of the civil war without getting the facts at least close, and a highly qualified philosophy person would not accept invalid facts as sound philosophy.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by MindTrap028 View Post
    I would think that a physics philosophy source, if it was considered valid by qualified peers such as a journal, should be sufficient.
    If it passes peer review by physicists, it's a physics source. It might also be a philosophy source--say, if it were peer-reviewed by philosophers--but it would have to be at least a physics source to support a physics claim.

    I mean, i could hardly offer a valid philosophical critique of the morality of the civil war without getting the facts at least close, and a highly qualified philosophy person would not accept invalid facts as sound philosophy.
    It depends on what the philosopher was trying to assess.

    If your argument is something like:

    (1) X,Y,Z are factual statements true about the Civil War [premise]
    (2) If X,Y,Z are true about the Civil War, then Philosophical Result about the Civil War follows [premise]
    (3) Therefore, Philosophical Result about the Civil War. [conclusion]

    A philosopher might only be interested in (2)--that is, whether good philosophy was done in the arguments for (2). To that end, the philosopher might not care at all about whether (1) or (3) are true.

    Conversely, if the philosopher is interested in (3) (say, if the discussion is about the philosophical aspects of the Civil War), then the philosopher would probably find your argument unpersuasive, since (1) fails to hold and therefore the argument is unsound.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by eye4magic View Post
    Whether philosophical sources and experts or hard physics sources and experts, what's relevant to bear in mind is that those choices are within the context of a philosophical debate posted on a philosophical debate forum.
    Quote Originally Posted by MindTrap028 View Post
    I would think that a physics philosophy source, if it was considered valid by qualified peers such as a journal, should be sufficient.

    I mean, i could hardly offer a valid philosophical critique of the morality of the civil war without getting the facts at least close, and a highly qualified philosophy person would not accept invalid facts as sound philosophy.
    Sorry, guys, but the answer to this is simply: "No. That's wrong."


    Peer-review is field specific. For instance, philosophical peer-review checks for the validity of philosophical inquiry rather than judiciously checking the facts of the matter (This is because philosophers aren't experts on facts of the matter, but on are experts on philosphical inquiry). However, the expectation is that if they're making an argument premised by historical facts, then they are going to have to cite a historian. Philosophers are not allowed to simply say "The following about history is true." based on them having a PhD in philosophy. Philosophical peer-review expects them to have a source (from a valid source, so that means cite a paper by a relavent expert, e.g. historian).


    A problem arises for the philosophers of science. A lot of them are well-read on the history of science and on a few scientific theories, but it's easy to cite a scientific paper. It's a bit harder to actually know what is the best source. You have to know what's going on in the entire field, and unless you're actually a scientist, it is easy to cherry pick a single scientific paper (usually at the beginning of a scientific discipline, where the full theory, experiments, and understanding weren't present; amplify this by a factor of ten if they use words like "relativity" or "quantum mechanics" or "field theory" where understanding these topics is actually quite laborious and probably requires at least a BA in physics). Scrupled philosophers of science (Like the giants in the field, such as David Hume, Karl Popper, Thomas Kuhn, Willard Quine, Imre Lakatos, Paul Feyerabend, etc) never do this, they take the entire scientific process into account and focus especially on the science after the foundations of the theory has firmed. Of course, scrupled philosophers of science often content themselves with digging up the tacit assumptions of scientists or raising questions about how the scientific method works, rather than claiming that all scientists in the past 92 years have done science wrong. That's an audacious claim that you won't find many credible philosophers of science stating (not even by Paul Feyerabend).


    However, this is precisely the error made by Shanahan and it's one that can pass philosophical peer-review because in order for philosophers to catch the mistake, they would need to have knowledge outside of their expertise. Shanahan exclusively cites the early period of quantum mechanics as evidence for his claims (Before non-relativistic quantum mechanics was understood!). He acts as though the subject that he's discussing --relativistic quantum mechanics, i.e. Quantum Field Theory-- isn't well understood already, as though the list of possible theories hasn't been thoroughly explored, as though they haven't been experimentally tested, and as though the unique candiate hasn't been confirmed many times over. These questions aren't up for grabs anymore. They weren't even up for grabs by the 1940's. These theories are open to interpretation, but he has to accept the actual facts of the matter, which he doesn't and that relegates his ideas to be "crackpot." The questions he's (clumsily) posing were already posed almost 100 years --however, they were not merely posed, they were also answered by the efforts of Paul Dirac, Enrico Fermi, Markus Fierz, Wolfgang Pauli, Werner Heisenberg, Vladimir Fock, Eugene Wigner, and Julian Schwinger in the early 1930's to the mid-1940's, only a decade or two after de Broglie's paper, and they collectively gave birth to Quantum Field Theory (the subject that I study). This is the price you pay when you ignore that last 90 years of physics research. It turns out, they might have thought about your question already.



    This is why when you want to make a scientific claim, your immediate impulse shouldn't be to go to a philosopher, but a scientist who actively researchers in the field in question.
    Last edited by GoldPhoenix; May 30th, 2014 at 01:36 PM.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by GP
    Peer-review is field specific. For instance, philosophical peer-review checks for the validity of philosophical inquiry rather than judiciously checking the facts of the matter (This is because philosophers aren't experts on facts of the matter, but on are experts on philosphical inquiry).
    That would be true if the reviewer is ONLY a philosopher. It doesn't account for people who have varied fields of expertise.
    I highly doubt that one trained in philosophy and a given field, will ignore obvious fact errors in evaluating a philosophy paper.

    Your basically making a blanket claim that doesn't necessarily apply and as I understand it is specifically false in the case of sources in this thread.

    You have to make the positive claim that those that were reviewing the paper were not qualified Or you have to maintain that valid philosophy can be done with incorrect facts AND that is a common practice.

    Are either of those what you are saying? As I'm not sure you have attacked the reviewers of the sources in this thread.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by MindTrap028 View Post
    That would be true if the reviewer is ONLY a philosopher. It doesn't account for people who have varied fields of expertise.
    Requiring that a person peer-reviewing philosophy claims be an expert in philosophy does not require that the reviewer be an expert in only philosophy; requiring that a reviewer be a physicist (i.e., an expert in physics) does not require that the reviewer be an expert only in physics.

    A medical doctor needn't be an expert in archaeology; nevertheless, there are probably medical doctors who are experts in archaeology. But medical doctors insofar as they act as medical doctors, or qua medical doctors, are not experts in archaeology.


    I highly doubt that one trained in philosophy and a given field, will ignore obvious fact errors in evaluating a philosophy paper.
    Unless, of course, the fact error lies in a field outside the philosopher's expertise.

    Your basically making a blanket claim that doesn't necessarily apply and as I understand it is specifically false in the case of sources in this thread.
    How many, and which, sources were even authored by an expert in physics, let alone peer-reviewed by experts in physics?
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by CliveStaples View Post
    Sure, but if a physics claim is part of that philosophical debate, then physics sources should be used to support it.
    And Squatch did use some physics sources along with a philosophical source. Was it really that unreasonable for him to include a philosophical source along with his physics sources? I don't think it was unreasonable. Why? Because this entire debate is within the context of a philosophical premise posted on a philosophical forum. However, more relevant to the hard physics argument, Squatch made the point that his philosophical source may indeed not be correct in supporting his position, but he was presenting it nevertheless on his list of support that he posted on Post 228 not as his only support, but as one of several positions that are out there and being discussed.

    If this entire debate was a purely physics debate with a hard physics premise in the science forum, and only one philosophical source was provided to support a physics claim, then I would say that this would be unreasonable and worth challenging. But that’s not the circumstance in this thread. One philosophical source among a list of other physics sources was used to support a physics position on a philosophical premise on a philosophical debate forum. This is not unreasonable gentleman.

    If we're having a debate about politics, and I make an economics claim (say, about the empirical effect of minimum wage increases/decreases), then my support should be in the form of an economics source. Political sources would, of course, abound on both sides of the issue; but what politicians or political agents have to say bears far less meaningfully on my claim than what economists have to say.
    In your example I would add that a political scientist's view and argument would not be unreasonable to consider in such a debate. Whether such an position would be accurate or not is a different issue. To review and consider the argument of a political scientist about an economic claim would not be unreasonable.

    Bear in mind that critical thinking does not require us to accept an argument while we consider/review it.
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    Re: WLC's Argument Against an Actual Infinity

    Quote Originally Posted by eye4magic View Post
    And Squatch did use some physics sources along with a philosophical source.
    Support or retract. We wouldn't be having this conversation (And month of bloviation & 50 posts spread out over 4 pages of debate) if Squatch actually had peer-review physics sources.

    Quote Originally Posted by eye
    Was it really that unreasonable for him to include a philosophical source along with his physics sources? I don't think it was unreasonable. Why? Because this entire debate is within the context of a philosophical premise posted on a philosophical forum.
    This may surprised you, but I firmly agree. Unfortunately, that was not what happened. The only paper that I could verify (Meaning: I made an honest effort to vouch for Squatch's sources, if I couldn't find another paper, the onus is on him to correct me that I missed one) that has passed physics peer-review was a paper on a specific model of Lorentzian relativity that was later confirmed to be false. Squatch has conceded this to me. However, every other source that I could find either did not make it through physics peer-review, were published in philosophy journals, or were relegated to websites with no academic affiliation whatsoever.

    However, if Squatch had given me philosophy papers and science papers, then I would say that adding a little bit of back drop would be fine.


    Quote Originally Posted by eye
    However, more relevant to the hard physics argument, Squatch made the point that his philosophical source may indeed not be correct in supporting his position, but he was presenting it nevertheless on his list of support that he posted on Post 228 not as his only support, but as one of several positions that are out there and being discussed.
    Once again, I agree with you 100%, but the problem is again with your premise. These would have been fine examples of philosophers discussing theses issues, and I would have conceded, on the spot, to Squatch that I was wrong and that this was a (however small) debate amongst philosophers.


    But here's the problem: I never said that philosophers weren't having this discussion, and I never objected to Squatch saying that they were. And I didn't object to Squatch saying this because he never said it. What I objected to was what Squatch actually said:




    So when he chose to support it with examples of philosophers debating over LR... Well, I don't think it should be very difficult to intuit where my objection lies.

    ---------- Post added at 08:39 PM ---------- Previous post was at 08:24 PM ----------

    Quote Originally Posted by MindTrap028 View Post
    That would be true if the reviewer is ONLY a philosopher. It doesn't account for people who have varied fields of expertise.
    I highly doubt that one trained in philosophy and a given field, will ignore obvious fact errors in evaluating a philosophy paper.

    Your basically making a blanket claim that doesn't necessarily apply and as I understand it is specifically false in the case of sources in this thread.

    You have to make the positive claim that those that were reviewing the paper were not qualified Or you have to maintain that valid philosophy can be done with incorrect facts AND that is a common practice.

    Are either of those what you are saying? As I'm not sure you have attacked the reviewers of the sources in this thread.
    If your point is to object that there could exist a scientist and philosopher, then, indeed, I agree. We need look no further than Thomas Kuhn. However, my point is not that "All philosophers are not scientists.", rather that "Not all philosophers are scientists." (This is a quantifier scope fallacy for someone to confuse those; I don't think either of us have done that, this comment is just for reference).

    The implication of my statement is that "being a philosopher" is not sufficient to let them be an expert on science, but it doesn't forbid them from being an expert on science. But they would need to receive training and preferably degrees in both science and philosophy for this to happen. Now, as you have commented, the philosophers on this thread have not been scientists, and I'm here to talk about what Squatch is claiming that scientists are saying.
    "Those who can make you believe absurdities, can make you commit atrocities." --Voltaire

 

 
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