• Change of thread title
    It's bizarre to me that anyone would see that and interpret it as anything other than an instruction, such as, "If you see a roundabout, then turn around and come back".Sapientia

    Haha. I left my spanner on the bonnet of the lorry!
  • How to determine if a property is objective or subjective?
    Any property that is physical is objective. Why? Because any physical property is measurable (at least in theory), and if measurable, then it is mathematical, and if mathematical, then it is logical, and logic is indubitably an objective property of reality.Samuel Lacrampe

    I hardly know where to start with this chain of bad reasoning.

    Any physical property is objective? I'd give you Bishop Berkeley as a refutation. Or Plato's cave, or Descartes's demon. The fable of the elephant and the nine visually challenged persons. I asked for a single specific example and you have given none. Please give one and we'll take it apart. Name an objective property that can be determined without making a subjective measurement.

    Logic is an objective property or reality? Where was the syllogism five minutes after the big bang? Where is modus ponens among the mosquitos? You've managed to name one of the most subjective things there is. Logic is unquestionably the work of the human mind.

    So please go back to my first question to you. Please name a single specific thing that is objective so that we have something to talk about. Perhaps you'll name something and I'll go, "Oh yeah I see that you're right and I'm wrong." Without a specific example you're just talking vague generalities.

    By way of example -- SPECIFIC example I might add -- we can examine some of the most obvious candidates. Mass. Nope, not objective. Depends on the velocity of the observer. Color. Nope. Depends on the eye/brain system of the observer. Wavelength of light reflected off the object. Nope, depends on the relative velocity toward or away from the the observer. Red shift.

    Etc. That's why I'm challenging you to name a SINGLE SPECIFIC EXAMPLE of a thing you claim is objective, so that in the spirit of rational inquiry we can examine your claim.
  • Change of thread title
    I'm not going to teach you grammar, but I would advise you to teach yourself, since you've demonstrated that you don't know how preferences should be expressed, ...Sapientia

    Interesting point of English usage.

    It's a very common locution among American sportscasters to say something like:

    "If he doesn't fall flat on his face, he scores."

    Now this is a bit of an odd usage in everyday English but it's still legal. If expanded via the pedantic transform (PT), we get:

    "If he hadn't fallen flat on his face, he would have scored."

    A political usage might be: "If Hillary doesn't set up that private email server, she becomes president." Any native speaker of English will understand that as an informal way of saying, "If she hadn't set up the server she'd have become president."

    It was in that vein that I colloquialized

    "In the case that I ever said something you disapprove of, I would prefer that you delete my post in its entirety rather than alter what I wrote."

    to

    "If you don't like what I say, delete me or ban me."

    I confess that to me, your objection seems disingenuous since my meaning is perfectly clear. I truly can't tell why you are continuing to troll me about this. Are you stating that you genuinely did not understand the meaning of what I wrote? Is English your first language? That's a serious question. What I wrote is colloquial English. Not the King's English as they say, but perfectly understandable to any native speaker.

    ps -- I clicked your handle. You're in England. Aha! You are not a native speaker of American English. What I wrote is a very common informal locution on this side of the pond.

    As George Bernard Shaw allegedly said, The United States and Great Britain are two countries separated by a common language."
  • Is Democracy viable in a post-space-age civilization?
    So it's like Great Britain except that the king or queen picks the prime minister? I confess I don't see the benefit but I want to make sure I'm understanding your suggestion. Who gets to be queen of the universe? This is like some cheesy sci-fi from 1950. You will obey!
  • How to determine if a property is objective or subjective?
    OP can you give specific examples of subjective and objective things? Subjective things are easy to give examples of. I'd like to see you or anyone give an example of anything that's provably objective.
  • A Question About World Peace
    People should be more specific about vague goals such as world peace.

    Thought experiment. Remember the Star Trek episode where everyone wears a pain collar to inflict horrible discomfort if they violate the rules. In the end it turns out the society is run by a computer.

    Now that is a totally peaceful society. Any brutal slave regime can achieve peace.

    Wouldn't you prefer a little freedom and disorder? In fact disorder is the very price of freedom. Instead of the American civil war, would you have preferred to let the south keep their slaves? Lots of peace but no freedom.

    World peace without freedom or individual autonomy would be a horrible nightmare.

    Remember that Leibniz said we live in the best of all possible worlds. Be careful with your vague tinkering. You might get what you ask for and regret it immensely.
  • Change of thread title
    If you don't like what I write, then delete what I write or ban me. But don't change my words.

    That's an instruction.
    Sapientia

    That's a preference. "If you don't like me, ban me." That expresses my preference. If you're deliberately misunderstanding that in order to stir up trouble, knock yourself out. If you have reading comprehension issues I'll try to use simpler grammatical constructions.

    And the moderators of this site are clearly no Einsteins.

    That's an insult.
    Sapientia

    It's a joke. And a commentary on my opinion of their actions in this instance.

    Look I'd love to fight with you but you need much better material.
  • Order from Chaos
    I haven't followed this learned discussion in detail. But it's clear that evolution provided the means for a primate to type the complete works of Shakespeare in only a few billion years. The primate's name was Shakespeare.
  • Can science be 'guided'?
    Run by scientists. LOL. Which scientists? The Lysenkoists? https://en.wikipedia.org/wiki/Lysenkoism
  • Change of thread title
    No. You don't get special treatment, and if that's what you're after, then insulting the moderators is not the best tactic.Sapientia

    I expressed an opinion. I have no idea what you're talking about. I'm always up for a little friendly squabble but I can't understand your point enough to disagree with it.
  • Order from Chaos
    Wosret
    378px-QB_loves_entropy.jpg?20110318181040

    Why doesn't the image thing ever work?

    Clip the URL data after the jpg.

    378px-QB_loves_entropy.jpg
  • Change of thread title
    In my opinion I would rather have a post of mine deleted than changed. If you don't like what I write, delete me or ban me. But don't change my words. The original title was perfectly clear and refers to a quote of Einstein. And the moderators of this site are clearly no Einsteins.
  • Only God could play dice
    You lost me there a bit. The uniform distribution is the line segment y = 1 between x = 0 and x = 1. Yes? I'm trying to translate my math lingo to your probability theory. I'm fuzzy on this. An infinite sequence of coin flips defines a particular real number. Each individual sequence has probability zero, but the probability that SOME sequence gets hit is 1. That's because probabilities are only countably additive, so there's no contradiction. This is everything I know about it.

    When you say "this" is equivalent to an infinite sequence of digits, I'm not sure what "this" is. An arbitrary sequence of digits represents one choice or one element picked "randomly" from the unit interval. That's how I understand this. But I'm not following the point you're making. You get algorithmically random sequences by noting that there are only countably many bitstrings whose bits can be generated by a program. But I didn't get your idea about translating somethign.

    I studied a little measure theory but I don't know any probability theory. So I understand most of these concepts, but not the terminology.
  • Only God could play dice

    I don't know much about probability but I believe you. I'm not really sure what probabalists mean by randomness. Definitely not Kolmogorov et. al. Although Kolmogorov gets credit for the axioms of probability spaces. I'm in an area of my total ignorance so maybe I'll go look at some Wiki pages.

    ... ( a few mimutes later ) ...

    According to https://en.wikipedia.org/wiki/Random_variable,

    a random variable ... is a variable whose possible values are numerical outcomes of a random phenomenon.

    Well! That is no help at all. What do they mean by a random phenomenon? There is no evidence that there is any such thing in the world. One could argue that a coin flip is 50-50 simply because we lack the calculational power to input all the physical variables like force imparted by your thumb, and the temperature and humidity of the air, and every other factor, and determine exactly how the coin will flip. If you don't believe that's true then you must think the laws of physics can not explain the motion of coin.

    So I do not believe this definition is of any help. Certainly not to me. I don't know what a random phenomenon is. I strongly doubt that there are noncomputable real numbers instantiated in the world, since that would be an actual infinity in the world. Or perhaps a couple of centuries from now someone will discover a noncomputable number implemented as a subsystem of our brain ... I'm openminded about the present and the possible future of science.
  • Only God could play dice
    Who here can be satisfied with an "explanation" of.. "Oh it's just random" ..?Jake Tarragon

    Analogy. When our ancient forebears looked up in the sky, they saw a mighty hunter with his bow. That was their science, that was there belief, that's what their coastal elite believed, as it were. The received wisdom of their time.

    From our lofty percth thousands of years in the future. we see it was just a random alignment of certain stars in different galaxies separated vertically from us, ie not in the same plane. It's only as seen from earth that there's even an imaginary hunter there at all.

    Now in two thousand years, we may well look just as foolish. Quarks and gluons may look no more scientific to them than Orion the Hunter does to us.

    Maybe it's all random. It's certainly possible. And humans -- consciousness -- is the subjective experience that tells stories about it.
  • Only God could play dice
    Randomness isn't an absence of any pattern. Most things which can be considered as random have patterns. The basic example is a fair coin, flipping it gives you 50% chance of heads and 50% chance of tails. So it's a random outcome, but the generating process for the random outcomes has properties that can be analysed and accounted for - in principle anyway.fdrake

    Some can, some can't. Letting 1 stand for heads and 0 for tails, a sequence such as 1010101010... can be generated by the deterministic process "start with 1 and alternate 1's and 0's". So this string isn't very random.

    A string such as 11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101110000000110111000001110011010001... seems random, but it's not. If you put a decimal point after the first two 1's, this is the binary expansion of pi. So the recipe, "Write pi in binary and drop the decimal point" deterministically generates this string.

    On the other hand, many (most in fact) bitstrings (or infinite sequences of coin flips) do NOT have recipes or processes that generate them. The proof is that there are only countably many Turing machines but uncountably many real numbers; and we can turn any bitstring into a real number by putting a decimal point in front of it.

    A bitstring can be said to be random if there is no Turing machine, or program, or recipe, or as you put it, "generating process" that cranks out its bits. If you threw a dart at the real number line, the probability is 1 that you would hit a random real; namely, a real number whose digits can not be generated by a finitely-expressible recipe.

    There's a lot more to this idea. This is the Kolmogorov/Chaitin idea of randomness. A string is random if it can't be compressed to a simpler string. For example "print pi in binary and drop the decimal point" is a simple string that generates the seemingly random bitstring I showed earlier. Although the bits may well satisfy all the known statistical tests for randomness, the string is not random. In this case it's called pseudo-random. It looks random but it's not.

    Note: I hope it's clear that there are short simple algorithms that crank out the digits of pi. That's why the decimal digits of pi aren't random. And since there's a deterministic algorithm to convert decimal to binary, the bitstring isn't random either]

    https://en.wikipedia.org/wiki/Kolmogorov_complexity
  • Rømer and the speed of light 1676
    what would determine the difference between the time the admiral detects the ship, and the time in which the lower officer does the same in turn? It is in fact a very simple operation: if the difference is equal to the time it takes the ship to get in visual range of the naked eye, then we can say that the telescope is showing the location of the ship in real time. If, on the other hand, the difference between the detection times is negligible, then we can say that the telescope allows us to see objects not there where they are, but where they were when their light started its travel towards us.Hachem

    I can not believe that this is the correct explanation. If a photon is capable of reaching the outer lens of a telescope; it is certainly capable of going a few more inches or feet and reaching a retina.

    In fact the admiral with the telescope and the underling with his naked eyes must necessarily see exactly the same set of objects. The telescope simply magnifies an image so that it can be processed in detail by the eye/brain system; whereas the naked eye image can't be resolved in sufficient detail.

    In other words the underling is looking for a tiny little spec that takes up only a tiny little spec's worth of retinal cells. The telescope makes it so that tiny little spec's worth of photons is spread out over a larger area of the retina.

    It can't have anything to do with the fact that the telescope is a couple of feet long hence getting the photons first, if that's what you're saying.

    A similar thing happens with photography. If I stand in one spot and take a picture with a wide-angle lens then a telephoto lens, the telephoto is simply cropping the field of view. If you had enough resolution you could shoot exactly the same shot with a wide angle lens and then crop it in the computer.

    I'm no expert on telescopes or optics so if I'm missing something let me know. As I understand it, it's just about making a given set of photons take up a larger portion of the retina via telescopic magnification.
  • My guess is that what's different now is how people react
    American culture is deeply neurotic at the moment. Terrified of its own shadow. The usual suspect is political correctness. But I think there's another reason. Americans have been at war in the Middle East since 9/11 and it's not going well. We've become a torture regime. We are still in Afghanistan and Iraq and several other countries too. We've spent trillions. But it's all with the "volunteer" army. The left gets busy with social causes, Use the right pronouns or we'll shame you and take away your livelihood.

    They do that so they don't have to think about what their nation is doing abroad.

    I always had that complaint about liberals. Toss them a bone on gay rights and they'll look the other way on torture. And now that the Supreme Court finally (and correctly IMO) put the issue to bed by legalizing gay marriage, the left needs to screech about pronouns and transgender rights. They need smaller and smaller causes as the foreign policy gets worse and worse.

    And the right doesn't much care, they love the wars. The few anti-war conservatives get marginalized, like Pat Buchanan, or absorbed by the swamp, like Trump.

    So we focus on pronouns and statues and virtue signaling.

    Only a coincidence I'm writing this on 9/11, it would be true any day of the year. But today is sixteen years into this collective insanity. We "honor the heroes" and refuse to ask questions about where our government has taken us since that day. Where we've allowed our government to take us.

    So we focus obsessively on things that don't matter. To avoid the things that do.
  • Can this be formulated as a paradox?
    Not all people can achieve salvation. Most people who can reach salvation require suffering (in order to reach salvation). Altruistic conduct removes suffering. Thus, altruistic conduct is not (always) helpful. Altruistic is only helpful for those who cannot achieve salvation. Yet how can one know that one “helps” via altruism is not being impeded on their “path” to salvation? Is this an epistemic paradox?jancanc

    Sounds like psychopath logic. You attack some innocent person, subject them to horrible pain and suffering, and tell them, "It's for your own good. This is the only way you'll achieve Nirvana. You'll thank me later."

    I'm not buying it.

    There is a very commonly believed form of this nonsensical mode of thought called the broken windows theory. In this theory, a broken window stimulates economic activity because you have to call the glazier to replace the window. He can use the money to buy shoes, and the shoemaker uses the money to buy bread, etc. In this way, a broken window is a huge economic stimulus to the neighborhood.

    The fallacy is that the owner of the window is out the cost of replacing the window. Absent the broken window, the owner could use that money to do something actually productive, and still have his window.

    You'll hear this a lot in the coming days, as moron reporters tell you that hurricanes Harvey and Irma are an economic stimulus because of the construction boom to follow. That's nonsense. Absent the hurricanes, the money could be used to build new things without having to destroy the old things.

    Else why not nuke New York City to stimulate the economy? You see how wrong that is.
  • Technology can be disturbing
    Is it the wood shack, reading by candlelight (you could read in the daytime, ya know), or dying at 30 that you find unsatisfactory?Bitter Crank

    I like flat screen tv's and the Internet and modern medicine and products in stores. I can't imagine functioning a hundred years ago.
  • Technology can be disturbing
    People say tech has a downside. Sure. But I like tv and high speed internet and automobiles and a huge variety of products on the store shelves enabled by the computer networks that run global commerce. I for one do not want to live in a wood shack reading by candlelight and dying at 30.

    How about medical technology? How much of that are people willing to give up?
  • Taxation is theft.
    I agree with szardosszemagad we pay our taxes voluntarily. Income tax is based in what is called an honour system, you voluntarily declare your income and pay the tax which is due. Of course if you lie, then that's fraud and you will be punished.Metaphysician Undercover


    Isn't that a rather strange interpretation of "voluntary?"
  • In defence of the Great Chain of Being
    Wait, harlots are male? What are their characteristics? How did that usage evolve to the modern meaning of harlot being an obsolete name for a lady of ill repute?
  • In defence of the Great Chain of Being
    Ok I'll play the game.

    Baby Hitler and your cute little cat are in a burning house. You can only save one.

    I'll make this sharper. The adult Hitler is inside and he's fully evil already.

    Your system says you should save Hitler because he's human. I say, save your cat who loves you.

    In this case an animal may be placed above a human in ontological value.

    Some takeaways:

    * Ontological value is subjective. Hiter's mom would save Hitler.

    * There may be some overlap in your levels. A cute kitty outranks an evil human.

    ps -- What are angels? Are you arguing from a purely Christian perspective? Metaphysically I know what a God is, but I'm not sure about angels. Like if we're a simulation, would God be the project manager and angels the grunt coders? How does all this work exactly?
  • Evidence of Consciousness Surviving the Body
    I will present the argument after we clarify these foundational issues, at least provide some clarification.Sam26

    After that shaggy dog story you didn't even say what you're posting about?

    An inauspicious start.
  • Floyd Mayweather vs Conor McGregor
    @Baden, This is good stuff. I'll look into Debord some more. Thanks for the pointer.
  • Floyd Mayweather vs Conor McGregor
    There's a lot of philosophy in this event. It's the philosophy of hype. Of "events." This is not a boxing match in its normal sense. Mayweather retired undefeated, but that was two years ago. He hasn't thrown a punch at a real opponent in a long time.

    McGregor isn't even a boxer. He's an MMA fighter. And even he's retired.

    So this is a spectacle for the masses, who are going to pay ninety-nine bucks each to watch this exhibition. What does this say about the masses? They are not interested in actual excellence, or competition. Only in the spectacle. Then what of philosophy? Would a philosopher say that the very falseness of this event, its lack of fundamental integrity, renders it an object to be scorned and criticized?

    Or would they just take the hedonist line and lay down their ninety-nine bucks like the rest of the rubes just to watch the show?
  • Floyd Mayweather vs Conor McGregor
    I'm rooting for whoever is a disappointment or a spontaneous pacifist.Nils Loc

    Well you know Mayweather's boxing style is as close to pacifist as a prizefighter can get. His body seems to adjust in real time to the entire space of physically possible near-future configurations of the two bodies in the ring. He is always just slightly impossible to hit. His mind/body system has totally figured out boxing. His whole style is that he can't be hit.

    Mayweather's a pacifist! But I don't think I'd say that to his face!!
  • Good Partners
    A hard man is good to find. -- Mae West
  • What pisses you off?
    People tailgating me on a four lane freeway. Happened again this morning. Dude if you don't like how I'm driving then pick one of the other three available lanes! And I'm not driving slowly, I'm driving behind someone who's driving behind someone. It's a freeway full of cars all going well over the speed limit to start with. Grrrrrrrr.
  • Trade agreements and cultural products: I am stunned, but I shouldn't be
    Chomsky has documented the machinery of the globalist agenda. What they're doing and how they do it. "Manufacturing consent."
  • The Ingredients of Existence
    The people staring at the shadows have acquired clarity to their existence, they can exist because they know what reality is (the shadows) and how it works, their existence has rules they can follow and exist within. When they are exposed to the reality outside the shadows, they lose that clarity and are completely unable to exist anymore, and thus WILL go back to the shadows anyway.Gentzer

    Gravewise, Plato is spinning.

    RIP Dick Gregory and Jerry Lewis
  • What is the purpose of government?
    Pick up the trash, defend the country from foreign attack. End of story.

    https://en.wikipedia.org/wiki/Minarchism
  • Climate change deniers as flat-landers.
    They discovered that most of the evidence for a round earth has been faked? Cool.
  • Do these 2 studies show evidence that we live in a simulation or a hologram?
    If the world is a simulation ... what is it a simulation of?
  • Cosmological Arg.: Infinite Causal Chain Impossible
    We can use Occam's razor to dismiss it: A hypothesis involving finite things is simpler than one involving infinite things. As such, until it is refuted, we should stick the simpler 'finite chain of causes' hypothesis.Samuel Lacrampe

    If causal chains must be finite then there must be a first cause, who is God.

    Now if Occam leads to the conclusion that it's simpler to believe in an imaginary supernatural being than it is to believe in a naturalistic explanation of the universe ... then Occam's razor needs a new blade.
  • Cosmological Arg.: Infinite Causal Chain Impossible
    Premise-1: Everything in the world has a cause
    ....
    Conclusion: Therefore, it is very probable that a non-contingent first cause exists;
    dclements

    The conclusion violates premise 1. Therefore the chain of reasoning must be wrong.

    Also what do you mean by saying that "is very improbable that there is an infinite chain of causes going back forever?" Why is that improbable? What is the probability? Define your probability model and show your calculations.
  • Objections to the Kalam Cosmological Argument for God
    What you are presuming is that actual infinities really exist. Actual infinity, however is merely an abstract notion , or, if you like, a fiction in the realm of the philosophy of mathematics which proposes that mathematical objects like , say the infinite sequence of negative numbers you refer to above can form a complete totality or "set", I.e. a given object that is a true actual infinity. Actual infinities, though, do not exist, they are not realities. To understand why this is you should google up and read the mathematician David Hibert's famous thought experiment , "Hibert's Hotel".John Gould


    Thanks for your comments.

    I disagree with you on three points, summarized as follows.

    1. Even if I were using actual infinity, so what? After all, actual infinity is no weirder than an all-knowing, all-powerful, benevolent uncaused cause.

    2. However, I am NOT using actual infinity. Your understanding of potential versus actual infinity is different than Aristotle's. My model "..., -3, -2, -1" only uses POTENTIAL infinity as defined by Aristotle. I will expound on this point in a moment.

    3. Hilbert's Hotel (HH) doesn't apply. You are correct that HH assumes actual infinity. But my example only requires potential infinity. I don't need all the numbers (or rooms) to exist all at once. I only need that given one, I can identify the next. I never assume I have them all existing at once. That's potential infinity.

    Here is more detail, especially on point #2.

    1. For the moment let me grant your (false) premise. Say I did need actual infinity (which I remind you I don't). So what? Craig wants us to conclude that there must be an uncaused cause, which he calls God. What if I call it absoulte infinity? I can't conceive of a worldview that would grant divinity but not infinity.

    Cantor himself thought that his Absolute infinity was God. But Cantor's Absolute infinity is a lot bigger than the infinity of the natural numbers.

    2. But #1 is irrelevant, since I don't use actual infinity, only potential. Let me outline the concept as seen by Aristotle. He said that we all have an intuition of the natural numbers 0, 1, 2, 3, 4, 5, ... Now the "dot dot dot" means something specific as defined by the Peano axioms:

    * Inductive axiom: Given a number n, there is a number n' called the "successor" of n.

    Another notion for the successor of n is n + 1. So if 0 exists, then 1 does. If 1 exists then 2 does. If 2 exists then 3 does.

    So if you want to know, does 43242342 exist? Then you can recursively drill down all the way back to 0, the base of the induction, and you can show that any particular number exists.

    There is never any claim that we have all of them together all at once. We can imagine they don't come into existence till we need them. All I need is n + 1 given n. If I need a million, I make a million. I never have them all at once.

    That is exactly Aristotle's definition of potential infinity. In the following quote, Aristotle is speaking of the endless regress 1/2, 1/4, 1/8, 1/16, etc. He says:


    "For the fact that the process of dividing never comes to an end ensures that this activity exists potentially, but not that the infinite exists separately."
    — Metaphysics, book 9, chapter 6.


    Now the sequence 1/2, 1/4, 1/8, ... may be identified with the the reverse sequence I gave earlier, ..., -3, -2, -1 by the simple mathematical trick of taking the base-2 logarithm of each fraction to get the corresponding negative integer.

    1/2 maps to -1, and 1/4 maps to -2, and so forth. So these two examples are really the same example in different forms.

    Aristotle calls this potential infinity. Does 5 exist? Yes, if 4 exists. So we can prove that any number n exists. But we can't say that ALL the counting numbers exist all at the same time. That would be ACTUAL infinity.

    It was the genius of Cantor to take the huge conceptual leap and say, What if we allow actual infinity into math? That was his brilliant history-changing leap of the imagination.

    Cantor's insight was to write the following notation:

    {0, 1, 2, 3, ...}

    The braces symbolize the COMPLETED SET of natural numbers. The inductive axiom gives us 1 (given 0) then 2, then 3, and so forth.

    The Axiom of Infinity says that there is a set containing all the natural numbers. That's actual infinity.

    We can summarize all this with a table. I apologize that I could not make the right column line up no matter what I did with tabs and spaces. Advice appreciated.

    Potential infinity           Actual infinity
    
    Axiom of induction      Axiom of Infinity
    
    Peano                          Cantor
    
    0, 1, 2, 3, ...           {0, 1, 2, 3, ...}
    
    n+1 given n                All of them at once
    
    Negative integers       Hilbert Hotel
    

    I hope this is helpful.

    3. HH is just a popularized visualization of the fact that an infinite set may be placed into bijection with one of its proper subsets. In fact this can be taken as the definining property of infinite sets.

    You are right that HH does assume actual infinity. But we do NOT need actual infinity to define the natural numbers 1, 2, 3, ... in their usual order, or ..., -3, -2, -1 in their reverse order, or 1/2, 1/4, 1/8, ... if you use base 2 exponentials and logarithms.

    I don't need the strength of the axiom of infinity to give my example. Only the Peano axioms, which define potential infinity. Given n I need n + 1. I never need to complete the process. I only need to take the next step. So Hilbert's Hotel is not relevant here.
  • Cosmological Arg.: Infinite Causal Chain Impossible
    How does the fact that the premise used is specifically picked to make the argument work make the argument any less valid or sound?Chany

    Oh I see. Yes I agree that my objection applies pretty much to every logical argument. After all if I prove that the order of a subgroup must divide the order of a finite group, that's only because of the way I defined a group! (That's a mathematical example for those unfamiliar with group theory).

    So yes I do concede that my objection that Craig's conclusion is baked into his premises is no objection at all, since it applies equally to any logical argument.

    I suppose what I mean here is that some of the moral or persuasive force of Craig's argument is weakened. The phrase "began to exist" carries within it the fact that the universe must have had a cause (if we believe the universe began to exist) hence there must be an uncaused cause which is the all-powerful benevolent God of Christian theology. Although why it couldn't just be the Uncaused Flying Spaghetti Monster, Craig doesn't say.
  • Objections to the Kalam Cosmological Argument for God
    What makes anyone thing the universe "began to exist?" For all we know it's like the negative integers ..., -3, -2, -1. Every element has a predecessor (or "cause" if you like) but there is no first cause.

    What is the evidence for assumption P2?