• Donald Trump (All General Trump Conversations Here)
    Plausible deniability. Works every time, according to the Biden’s.NOS4A2
    What other conspiracy theories do you embrace?
    Taking everything at face value is not evidence either.NOS4A2
    More conspiracy theory reasoning. There's no evidence for your claim, but you point to an absence of evidence for it being false as somehow relevant.

    But the question as to why Bragg pivoted from not prosecuting the zombie case to prosecuting the case remains, and to me it’s no strange wonder that Bragg announced indictments a few months after Colangelo joined his team.
    I've given you my theory regarding Bragg: there were personal political motivations. And I expect he hired Colangelo for the express purpose of prosecuting Trump. (Don't forget that I have never been a fan of pursuing this).

    Relativist: "It's established that Russia engaged in election interference by illegally accessing DNC emails. Wikileaks also engaged in election interference by leaking those emails at strategic times during the campaign. There's also strong evidence Roger Stone was coordinating that activity with Julian Assange.

    The Russia Investigation (which was in no way, a hoax) became public AFTER the election, so it can't be considered election interference.

    But yes, I can think of others- and I listed some. E.g. Trump's attempt to get Zelensky to say he was investigating Biden. The "catch and kill" conspiracy was election interference (even though aspects of it were legal, it's still interference)."

    Now who is the conspiracy theorist?
    NOS4A2
    You are. I cited established facts that you would be aware of if you ventured outside your Trumpist bubble- which is apparent from your referring to the Russia investigation as a "hoax". If you'd like to challenge anything I said, feel free.

    Note how you never mentioned the Clinton campaign's solicitation of dirt from Christopher Steele...NOS4A2
    Distortion. I've explained this to you before.

    ...which was then used in FISA courts to open up surveillance on Trump's campaign, during the campaign.
    Indeed, exactly 2 FISA warrants were granted that shouldn't have been. These errors do not imply the Russia investigation was unwarranted- even Durham acknowledged an investigation was warranted. Mueller discovered most of the facts I cited, and no one has refuted them. Trumpists like yourself hide behind the FISA errors to avoid facing the facts that were uncovered.
  • Donald Trump (All General Trump Conversations Here)
    You’ve evaded my evidence and tried to pretend I was just accepting claims. The lead prosecutor, Michael Colangelo, was the Acting Associate Attorney General of Biden’s DOJ for two years, working directly under Garland. He’s the same guy that investigated Trump foundation for the New York attorney general, Letitia James. His leaving the DOJ to kick-start Bragg’s “zombie case” gives Biden plausible deniability, which is how he gets out of everything. If Biden’s DOJ chose not to prosecute Trump, why is Biden’s DOJ prosecuting Trump?NOS4A2
    You are "connecting dots", as conspiracy theorists like to do. This particular conspiracy theory is prevalent in the MAGA world.

    The facts you cite demonstrate that Colangelo had relevant experience with Trump, that the DA would deem valuable in mounting the case. Before being named acting assistant US attorney general, he had worked in the NY Attorney General's office investigating Trump Foundation (successfully showing there to be fraud). So it's both knowledge and personal motivation that are the obvious reasons the DA would want him, and that Colangelo would want to take it on.

    If the President had nefariously orchestrated Colangelo's move to prosecute Trump, it would be extremely risky for him politically if this came out. You also conveniently overlook the fact that Biden (through Garland) could have simply allowed the case to proceed, and it would not have their fingerprints on it. But consistent with conspiracy theorists, you ignore the evidence that's inconsistent with your conspiracy theory.

    So as I said, there's no evidence Biden was involved with Colangelo's taking the position to prosecute Trump. Biased speculation is not evidence.

    Another example would be the Russia hoax. I’m sure you could think of others on your own.NOS4A2
    It's established that Russia engaged in election interference by illegally accessing DNC emails. Wikileaks also engaged in election interference by leaking those emails at strategic times during the campaign. There's also strong evidence Roger Stone was coordinating that activity with Julian Assange.

    The Russia Investigation (which was in no way, a hoax) became public AFTER the election, so it can't be considered election interference.

    But yes, I can think of others- and I listed some. E.g. Trump's attempt to get Zelensky to say he was investigating Biden. The "catch and kill" conspiracy was election interference (even though aspects of it were legal, it's still interference).

    That’s inaccurate. It was multiple errors. The appeals court described as an “abuse of judicial discretion”, essentially denying him the right to a fair trial.NOS4A2
    I admit that I shouldn't have said "an error", since that connotes a single error. Yes, there were multiple errors, all relating to making decisions regarding what evidence was admissible, and an error in the Sandoval ruling. In both cases, judges have a good bit of discretion, but the appeals court ruled that the judge's rulings exceeded reasonable limits of this discretionary power.

    And despite your claim that they rarely overrule the verdicts of juries, I was just giving you an example off the top of my head of them doing so.
    Wrong. The appellate court didn't rule that the jury got it wrong. It ruled that their verdict may have been influenced by the inadmissible evidence. This is not a revised finding of "not guilty", it's simply negating the trial. Weinstein can be retried, and it's reported that there will indeed be a new trial.
  • Donald Trump (All General Trump Conversations Here)
    Harvey Weinstein’s case was just overturned because the judge could not be just.NOS4A2
    That's inaccurate. I will grant that when any conviction is overturned on appeal, it implies "unfairness", but this is based on there having been an error made. In Weinstein's case, testimony was admitted for prior, uncharged sexual asaults. The trial judge had ruled it admissible, deeming it relevant to establish Weinstein's motive (which is a valid basis, in general). It's not admissible if the purpose is to establish the defendant's character - that is prejudicial, and the appeals cout ruled it that way. IOW, the judge made an error. That certainly doesn't imply "the judge could not be just".

    It simply means they’re interfering with Trump’s campaign, and thus the election.NOS4A2
    So you're going with a special pleading - keeping Trump off from campaigning is the only thing that constitutes election interference. So none of the items I listed count.

    To use your terms, Biden’s campaign is hoping to win the election with the corrupt Justice system’s assistance, which is not in their mandate.
    You're uncritically accepting Trump's allegation that Biden is behind it. There's zero evidence to support that claim. To the contrary, we know Biden's DOJ actually chose NOT to prosecute Trump. You know this, and used this fact to blast Bragg's decision to prosecute- so you're trying to have it both ways. If Biden wanted to behave like Trump promises, and prosecute his political opponents, he would have jumped at the opportunity.
  • Donald Trump (All General Trump Conversations Here)
    If it does get overturned it will be because it’s an unjust and stupid case that will discredit the American justice system for years to come.NOS4A2
    Appellate courts overturn convictions for technical reasons, like interpretations of the law, errors by a judge, inadmissability of evidence. They rarely overrule the verdicts of juries.

    Yes, it’s election interference, meaning they are doing it to stifle Trump’s chances in the election.NOS4A2
    I asked you to define "election interference", because I suspect you apply a double standard. Were the House investigations of Joe and Hunter also election interference? What about Comey's public discussion of Hillary's email practices? Russia's assistance in 2016? Was Pecker engaging in election interference with his "catch and kill" tactics? How about Trump's numerous frivolous lawsuits about the 2020 election? How about his lies that it was stolen, and attempts to get senior DOJ staff to lie about election fraud? How about Trump's attempt to get Zelensky to say he was investigating Biden?

    Do you think this trial cost him votes? If so, won't it be because of the facts that are presented?
  • Is atheism illogical?
    Three persons, like I am one person, but one God. Totally absurd.Fire Ologist
    They needed to rationalize Jesus divinity with monotheism. Aristotelian metaphysics helped them do that.
  • This hurts my head. Can it be rational for somebody to hold an irrational belief?
    Can you choose to become a cult member, or does it just sort of happen to you?RogueAI
    I imagine it happens gradually, but you are making conscious choices along the way, albeit they are naive choices strongly influenced by emotion.
  • This hurts my head. Can it be rational for somebody to hold an irrational belief?
    Do you think that denial can be helpful?Scarecow
    There are cases where it might be, such as if you're diagnosed with a incurable illness and have only weeks to live. Being in denial is better than being in a constant state of depression. I realize there are still healthier ways to cope, but denial might be easier for some.
  • Is atheism illogical?
    Who would have thought of dying humiliated on a cross, to save all of humanity?Fire Ologist
    Zealots suffering from cognitive dissonance after their mentor (and supposed messiah) was executed for high treason.

    it’s really, as an extension of Judaism, many thousands of years old.Fire Ologist
    It's an "extension of Judaism" the same way the Latter Day Saints are an extension of Protestantism (which was an "extension" of Catholicism).

    Absurd, yet it works - shows me something more at work than the human mind, interests, cultures - this absurdity should have died within years, even if he did rise from the dead. Why the absurdity?Fire Ologist
    Was it really more absurd than other religions of the time in which it became popular? Few taught there was an afterlife (Judaism was ambiguous on this) - that had its appeal. But in general, it's an interesting historical question.
  • Is atheism illogical?
    ...atheism couldn't possibly gain you any divine favor, and therefore it is irrational to hold atheist beliefs.Scarecow

    One can't just turn on a belief, so let's say I take a pill that causes me to believe in a god, because I want to have that chance at getting a reward. Is my belief in a god rational?

    A belief that is established by reason is rational. It was rational to create a chance of getting the reward, so one might argue that my belief was indeed established by reason. However, it was actually the pill that established the belief - not a reasoning process.

    So it's actually irrational to believe in a god in order to have a chance at a reward.
  • Donald Trump (All General Trump Conversations Here)
    I've previously acknowledged that a conviction might get overturned on appeal, but it won't be because there's no precedent, nor because you consider it election interference, or political persecution.

    There's no evidence of involvement by the Biden campaign. In fact, we know Biden's DOJ chose to drop it.

    Is this really "election interference"? Define the term.
  • Donald Trump (All General Trump Conversations Here)
    Another misdemeanor with a two-year statute of limitations.NOS4A2
    Irrelevant. The charge for falsifying business records rises to a felony because it allegedly entailed intent to commit the conpiracy crime. The statute of limitations explains why he wasn't indicted for that conspiracy crime.

    I know you feel the indictment shouldn't have been made, but I hope you at least see there's a legal basis for it.
  • Donald Trump (All General Trump Conversations Here)
    So will you hazard a guess as to what the other crime may have been, federal or otherwise?NOS4A2
    Assistant District Attorney Joshua Steinglass said in court that one of the crimes Trump intended to commit was a conspiracy to promote or prevent an election. Here's the law:

    Any two or more persons who conspire to promote or prevent the election of any person to a public office by unlawful means and which conspiracy is acted upon by one or more of the parties thereto, shall be guilty of a misdemeanor.

    Both the DOJ and the FEC examined the case and no charges were brought.NOS4A2
    Exercise of prosecutorial discretion does not mean a crime wasn't committed.
  • Philosophy as a prophylaxis against propaganda?
    Not so sure philosopher and critical thinker are one and the same.jgill
    That's true. IMO, teaching critical thinking is the priority. It could be taught in a more general philosophy class, but it wouldn't need to be.
  • Donald Trump (All General Trump Conversations Here)
    That, I think, was the point all along: a campaign favor for Trump's opponents. What else could explain why they waited past the statute of limitations so that it could happen as close to election as possible?NOS4A2
    The state waited because the feds told them to stand down, because they were investigating. The federal investigation stopped when Biden took office. Many of the investigators were pissed, and pressured Bragg to indict Trump (e.g Mark Pomerantz wrote a book about Trump's financial crimes- and this got the public's attention). DA is an elected position, so this constituted political pressure.

    As you know, it is the misdemeanor that has passed the statute of limitations. Trump is charged with a felony, based on the fraud being associated with another crime. So although there was a political element to the decision to prosecute, there do seem to have been actual felonies.

    If he's found guilty, the appeals court may rule that he would need to have been indicted for those "other crimes", although that's not stated in the statute. There's a smaller vulnerability that one of the "other crimes" is a federal crime, so the appeals court may decide it must be a state crime. However, there is also state election law that tracks the same act.

    In the meantime, it's still an interesting case to watch, as Trump continues to flout the law.
  • Donald Trump (All General Trump Conversations Here)
    I was already aware the actual facts, as well as the Trumpist spin.

    As I've mentioned before, I think the prosecution's legal basis is weak, so there's a good chance of overturning it on appeal. But the coverage of the case provides a good reminder of Trump's sleazy character (irrespective of the legality).
  • Donald Trump (All General Trump Conversations Here)
    Have you never heard of the phrase "hatchet man"?NOS4A2
    You're deflecting. But thanks for sharing your opinion about the judge. FYI: I disagree.
  • Donald Trump (All General Trump Conversations Here)
    I learned about Colangelo from the New York Times and Merchan’s daughter from a gagged Donald Trump. One place you won’t hear of it is in your little echo chamber.NOS4A2
    I seriously doubt the NY Times called Colangelo Biden's "hatchet man". I read similar claims on the Fox News website.(part of my "bubble", I guess).

    Regarding the use of Trump for information, that's probably the least credible source one could use. Are you also upset that the gag order prevents him from testifying? :lol:

    Loren Merchand's company has certainly made millions from Dem candidates, but she's not involved in Trump's legal case. The ethics board ruled her business constituted no conflict of interest for the judge, which was perfectly appropriate. Of course, Trump will nevertheless seize every opportunity to attack.
  • Donald Trump (All General Trump Conversations Here)
    Bragg’s current prosecutor, Matthew Colangelo, previously served as acting associate attorney general in Biden’s Justice Department and also led New York Attorney General Letitia James’s civil inquiry into Trump. He’s Biden’s hatchet man.

    Add this to the fact that the judge’s daughter received millions from the Biden/harris campaign, is it just not possible to find someone in the justice system who is impartial, and not a Biden/obama stooge with a vested interest in Trump’s conviction?
    NOS4A2
    I seem to recall you complaining about media propoganda, and yet here you are- regurgitating (right-wing) media propoganda.
  • Infinite Staircase Paradox
    Sorry, I overlooked that part.
  • Infinite Staircase Paradox
    Can we not count the intervals starting with 1? Would that number not tend towards infinity given time is infinitely divisible or approach a certain value and terminate given a smallest sliver of time exists?ToothyMaw
    "Tending towards infinity" means counting through the natural numbers - the set is infinite. The process has no end.
  • Donald Trump (All General Trump Conversations Here)
    So they don't want a better government, better economic policies, or better anything. What they want, is to bring down the whole system, because they don't accept the principles on which it was founded.Wayfarer

    What I can't figure out is, what Trump voters think they're voting for.Wayfarer

    My theory is that are motivated to halt, or roll back social changes (e.g.normalization of the LGBTQ communities, perceived special treatment for minorities), and are fed up with the way the goverment works - the negative impacts of government bureaucracy, as well as foreign entanglements. They want a superman who uses his superpowers to solve our most important problems. Trump promises to do the impossible, and thus appeals to their wishes. As example: in 2016, building a (Mexico funded) border wall that was perceived as a solution to many problems (eg unwanted migration, drug trafficking)- an alleged simple solution to a complex set of problems.

    It's not that they actively want to do unconstitutional or illegal things, per se, it's that Trump doesn't concern himself with those impediments, so they don't have to even think about those things. They trust Trump will find a way.
  • Does no free will necessarily mean fatalism or nihilism?
    I don’t think it entails nihilism and fatalism, but it does set the grounds for them.NOS4A2
    I agree with this much, but disagree with suggesting that the
    ... implications of determinism...[are] that they have zero responsibility.
    I disagree because this sense of responsibility is a part of our mechanism, and contributes to our choices. This is in spite of the fact that all of our decision-making components originated outside ourselves. Indeed, we aren't responsible for our genetic makeup, don't fully control what we learn, are (somewhat) slaves to our conditioned responses, etc, but we still make the choices that we make. As the decision-maker, there is inherent responsibility for those decisions. We hold others accountable, and we ought to hold ourselves accountable. Accountability never means the past can be changed; it is only about the future decisions we (or others) will make. So what if we couldn't have made a different decision in that instant within its circumstances? We can learn from the consequences, and this can result in better decisions in the future.

    I actually question the notion that Libertarian Free Will (LFW) entails the Principle of Alternative Possibilities (PAP) - the notion that LFW implies there's true contingency to our choices. Even under LFW, we are guided by our impulses, knowledge, assumptions, etc. Given some series of deliberative thoughts, how could there be a different outcome? We have followed some chain of reasoning, and are subject to the same impulses.
  • Infinite Staircase Paradox
    Since x reaches infinity at time 1, all steps are completed at that time, so the task is completenoAxioms
    Infinity is not reached. You're not considering what it means to be infinite in this context: it means continually dividing the remaining time (prior to the 1-minute mark) in half. Because the remaining time corresponds to a real number line, the process proceeds without ending because the remaining time is infinitely divisible. It's limited by the fact that all points of time that are reached by the process are less than 1 minute- so it is logically impossible for this process to reach the point of time of 1 minute.

    The source of confusion is that the clock does hit the 1-minute mark. You are incorrectly interpreting this as implying the the process reaches that point. It can't, because it is logically impossible.

    The clock reaching the 1-minute mark implies the process ends, but since the process cannot reach the 1-minute mark, the process must be terminated at some point. Laws of nature would clearly provide a limit to how small we divide the time, but even setting that aside - a stopping point is logically necessary. The math doesn't identify any particular stopping point, but it does imply there has to be one.
  • Infinite Staircase Paradox
    I also think you are misinterpreting the meaning of limit.
    — Relativist

    On a forum our words must speak for themselves. But in this instance I can assure you that nothing could possibly be farther from the truth.
    fishfry

    You explained your interpretation:

    You can think of it that way. Or you can think of it "reaching" its limit at a symbolic point at infinity. Just as we augment the real numbers with plus and minus infinity in calculus, to get the extended real numbersfishfry
    So...you're thinking of a limit in a vauge way ("symbolic"), and vaugely asserting the series "reaches" infinity, and then rationalize this with a mathematical system that defines infinity as a number.

    Although it's true that there are such mathematical systems, it doesn't apply to the supertask. Time is being divided into increasingly smaller segments approaching, but never reaching, the 1 minute mark. There is a mathematical (and logical) difference between the line segments defined by these two formulae:
    A. All x, such that 0<=x < 1
    B. All x, such that 0<=x <= 1

    Your blurred analysis conflates these, but it is their difference that matters in the analysis. The task maps exactly to formula A, but not to formula B (except in a vague, approximate way). Mathematics is about precise answers.
  • Infinite Staircase Paradox
    ...like physics is somehow exempt from mathematics (or logic in Relativist's case) or something.noAxioms
    Physics indeed is not exempt from logic. It's logically impossible to reach the 1 minute mark when all steps (even if there are infinitely many of them) fall short of the 1 minute mark.

    Calculating the limit does not entail a process that reaches that limit. This is a misinterpretation of the concept of limit.This article describes it this way:
    In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value...

    The formal definition intuitively means that eventually, all elements of the sequence get arbitrarily close to the limit, since the absolute value |an − L| is the distance between an and L.
  • Does no free will necessarily mean fatalism or nihilism?
    But you don't get to "give meaning to the factors" if it's all deterministic. Your genetic makeup, experiences, etc., give everything meaning to the group of cells referred to as Relativist.Patterner
    This ignores the fact that your genetic makeup, experiences, etc comprise you. That particular group of cells performs functions, including the cognitive functions of making choices.

    when you are in a situation where different directions are taken by different people, the meaning that all those factors have determined you have determine which direction you take.
    I agree that the process is, in one sense, programmed, but you are the program. There's also a sense in which you aren't programmed: you aren't the product of design. You weren't built in order to perform the functions you execute.
  • Does no free will necessarily mean fatalism or nihilism?
    You do go through a "process" yes. But (while I'm not saying you did so deliberately) note how your wording even implies ultimate passivity.ENOAH

    You're reading passivity into it; that certainly was not what I was trying to convey. The mental processes are under your control, not someone or something else. Determinism implies the process is mechanistic, but even a machine still has to do the work to produce its output - the machine isn't "passive".

    The fact that we lack the freedom to refrain from things like breathing seems irrelevant- not everything we contemplate involves a real choice, and that applies even if we have libertarian free will.
  • Infinite Staircase Paradox
    Agreed.

    You are falling into the trap of thinking a limit "approaches" but does not "reach" its limit. It does reach its limit via the limiting process, in the same sense that 1/2, 3/4, 7/8, ... has the limit 1, and 1 is a perfectly good real number, and we all have had literally billions of experiences of one second of time passing.fishfry
    You're pointing to the limit of a mathematical series. A step-by-step process does not reach anything. There is no step that ends at, or after, the one-minute mark. Calculating the limit does not alter that mathematical fact.

    I also think you are misinterpreting the meaning of limit. This article describes it this way:
    In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value...

    The formal definition intuitively means that eventually, all elements of the sequence get arbitrarily close to the limit, since the absolute value |an − L| is the distance between an and L.


    You just said to me that one second of time can't pass; and this, I reject. Am I understanding you correctly?fishfry
    No, I didn't. I said the stair-stepping PROCESS doesn't reach the 1 second mark. Are you suggesting it does?
  • Does no free will necessarily mean fatalism or nihilism?
    But if the choices are determined, then are they really choices?Patterner
    You do go through a choice-making process, don't you? For important decisions, you may deliberate for a time, weighing the pros and cons of alternatives. Your beliefs and whims will factor in, as will your hopes, desires, risk tolerance - all influenced by your genetic makeup. But all those factors are intrinsic to who you are.

    Sure, every one of those factors were caused (by your genetic makeup, upbringing, experiences, education...), but they are bundled together in a unique way to comprise YOU.

    If determinism is true, and the person's genetic makeup, upbringing, other past experiences, health at the moment, and all other factors, will allow only one optionPatterner
    Of course, whatever choice you make could not have been different at the point you make it, given your life-history. But you will also learn from the consequences of your decision, adding factors that will influence future choices. This is why I have previously argued that moral accountability is at least somewhat reasonable: future behavior is influenced by reward/punishment.

    So, although there are causes that necessitate the choices you make, those causes didn't conspire to make the choice. The machinery that is YOU had to do the processing that led to the result (the choice).

    And your choices aren't meaningless. You give meaning to the factors, and those meanings influence the choice. The person who chooses to keep the money you drop is doing so because of what money means to him.
  • Does no free will necessarily mean fatalism or nihilism?
    If it really is the case that everything that happens couldn’t help but happen and people’s choices aren’t truly free, then those who believe life is meaningless and morality doesn't exist have no choice but to believe that. And nobody has any choice but to live their lives as they do in response to that.Patterner
    Even if determinism is true, we still make choices. It's true that those choices are a product of prior events, but the choices are still made - and we are the agents making them.
  • Does no free will necessarily mean fatalism or nihilism?
    As hotly contested as the topic is I can’t recall a philosopher ever using the deterministic nature of the universe as evidence that good and evil don’t exist and the lives of sentient beings have no actual value.Captain Homicide
    First of all, I agree with everything you said. Regarding the above, I don't think determinism (per se) is inconsistent with the existence of objective moral values (OMVs). On the other hand, materialism is inconsistent with OMVs, because OMVs are not material objects.
  • Infinite Staircase Paradox
    The task consists of a sequence of actions occurring at intervals of time that decrease by half at each step: 1/2 minute, 1/4, 1/8,.... It is logically impossible for this sequence of actions to reach the 1 minute mark (the point in time at which the descent is considered completed), it just gets increasingly close to it.
  • Infinite Staircase Paradox
    That's true, but that just makes it physically impossible. I think it's stronger: logically impossible.
  • Infinite Staircase Paradox
    1. A given halfway step cannot reach the goal.
    2 There is a specific step that reaches the goal (per PSA)
    3 Therefore this final step is not a halfway step (1 & 2)
    4 Any given step is halfway (per Zeno)

    You don't find this contradictory?
    noAxioms

    Of course it is, but the the contradiction can be resolved by denying either one of two premises. You chose to deny the PSA, and I responded that the PSA could be true - we'd merely have to reject the other relevant premise - that the goal is reached. You have not made an argument that shows it is more reasonable to deny the PSA than to deny the reaching of the goal. I don't think it make sense to deny that a completed task entails a final step.


    Demonstration that immediate contradictions arise from denying either of the premises or presuming your conclusion 3 is also more than just handwaving.noAxioms
    Sure. You have to agree the PSA is true for finite tasks. Is there something different about infinite tasks? It doesn't seem so: consider the process: stepping increasingly closer to temporal point in time 1, but the process never actually reaches it. So the goal is unreachable by the process.

    I'm not enough of the mathematician to regurgitate all the axioms and processes involved in the accepted validity of the value of a convergent series.noAxioms
    No need. I understand that the math shows that the series reaches a point of convergence at time 1. However: the kinematic process never actually reaches time 1. That's why the series doesn't adequately account for the kinematic process -and why I've stressed we need to examine the process, not just do the math on the mathematical series.

    no impediment to the reaching of the goal has been identified,noAxioms
    On the contrary, there's a logical impediment to reaching the goal through the process: the process does not reach time 1.
    You do seem to heavily rely on definitions that come only from finite logicnoAxioms
    I'm actually basing my claims on real analysis, which analyzes the characteristics of real numbers - including the associated infinities.

    There is a temporal end to it, a final moment if not a final step.noAxioms
    That makes no sense. The process does not have a final moment. because there are infinitely many moments prior to time 1. There is no end to the series of kinematic steps, in spite of the fact that the mathematical series converges.
    Relativist: "But this process has a 1:1 correspondence to the supertask -- for every step taken in one scenario, there's a parallel step taken in the other. This suggests that either they both complete, or neither completes."

    There is a bijection yes. It does not imply that both or neither completes.
    noAxioms
    Why not?

    Relativist: "The number line in question is an interval that is open on the right: i.e. it includes all points <1, but not including 1. There are infinitely many points in this interval, but the point "1" isn't one of them. So the process cannot reach 1, and 1 is the goal of the process."

    The 'process' can go beyond the end of the line despite it ending before the goal.
    noAxioms
    No it can't - that is logically impossible. The process entails taking steps with increasing shorter durations: 1/2 second, 1/4, 1/8,.... The process can only approach 1, it can never reach it.

    . The kinematic process isn't restricted to only points on the number line.
    No! Each new step is half the duration of the last step, and this halving process has no end.
  • What is 'Right' or 'Wrong' in the Politics of Morality and Ideas of Political Correctness?
    Moral law is an invention of mankind for the disenfranchisement of the weak.Jack Cummins
    I disagree with this. IMO, morality is rooted in empathy. It feels wrong to hurt another person, because we empathize with the one who is hurt. The golden rule formalizes this into a "moral law" of sorts. Assessing what is morally good becomes trickier as situations become more complex, and often there's moral ambiguity - partial goods and partial evils. This opens the door for the perceived "disenfranchisement of the weak" in those cases. It's worthwhile to debate those cases, but I disagree that all moral law should be assumed to motivated by such a cynical motive.

    She said that as it is a charity supporting children, they will not stock CDs, in case there has been any exploitation of children in the making of the music'.Jack Cummins
    She's not being immoral, she's being cautious - perhaps overly cautious. Why deal in materials that she has suspicions about? Perhaps her suspicions are irrational, but is that relevant?

    It made me think of the previous movement of the 'moral right', as represented by Mary Whitehouse, which argued against pornography and art forms which showed forms of violence. It is based on forms of moral absolutism and what is acceptable being enshrined as 'moral law'.Jack Cummins
    This is similar to the charity lady scenario only in that it seems rooted in ignorance and irrationality, but it differs from from the charity scenario in that it represents a movement to generally restrict access to pornography, whereas the charity lady was just choosing not to participate in something she was suspicious about.

    "Political correctness" has both positive and negative connotations. On the positive side, it may deter people from offending others. On the negative side, it can be based on false assumptions and become a sword to shame people (sometimes appropriately, sometimes inappropriately).
  • Infinite Staircase Paradox
    Or the PSA is correct, and the goal can't be met.
    — Relativist
    I showed that for a supertask, the PSA is not correct. So no, this cannot be for a supertask.
    noAxioms
    No, you didn't. You merely asserted: "The PSA statement (that there is a step that reaches the goal) directly violates the premise that any given step gets only halfway to the goal." There is no direct violation.

    Here's valid logic:
    1. A halfway step cannot reach the goal.
    2. All steps are halfway
    3. Therefore the goal cannot be reached.

    You merely asserted the goal is reached (directly contradicting #3) but didn't explain how the sequence of halfway steps somehow reaches the goal. Labeling the process a "supertask" is handwaving, not proof. Show your logic.

    If the process continues forever, by definition it isn't a supertask.noAxioms
    Fair enough, I misstated it. The process does not continue forever, however there is no end to the process.

    Let's compare the supertask to a scenario in which the time interval between each step is a constant (e.g. 1 second). You'll agree that this process does not complete, right? But this process has a 1:1 correspondence to the supertask -- for every step taken in one scenario, there's a parallel step taken in the other. This suggests that either they both complete, or neither completes.

    Points on a number line exist concurrently (in effect).
    — Relativist
    I don't know what is meant by this. 'Concurrently' means 'at the same time' and there isn't time defined for a number line.
    A number line seems to be a set of ordered points represented by a visual line. It can be defined otherwise, but functionally that seems sufficient. It being a visual aid, it seems physical, but a reference to the simultaneity of the positions along the line seems irrelevant to the concept.
    noAxioms
    My point was that the kinematic stair-stepping process has a temporal element that is not reflected in a number line.

    The number line in question is an interval that is open on the right: i.e. it includes all points <1, but not including 1. There are infinitely many points in this interval, but the point "1" isn't one of them. So the process cannot reach 1, and 1 is the goal of the process. The goal is therefore unreachable by the kinematic process.
  • Infinite Staircase Paradox
    The PSA statement (that there is a step that reaches the goal) directly violates the premise that any given step gets only halfway to the goal.noAxioms
    Or the PSA is correct, and the goal can't be met.

    Relativist: "Simply denying a final step is necessary doesn't make it so."
    Simply asserting that such a step is necessary doesn't make it so
    noAxioms
    I'm not merely asserting it. You have to agree that a final step is necessary for completion when there are finitely many steps. Why would it matter if the number of steps is infinite?

    Most importantly: What does it even mean for a kinematic process to be infinite? My answer: it means the process continues forever and does not end. What's your answer?

    Relativist: "you have to explain why it's not necessary for a kinetic task to require a final step in order to be completed."
    I don't know how the task being 'kinetic' changes the argument.
    noAxioms
    Here's how: the infinity is manifested as a never-ending kinetic process.

    Points on a number line exist concurrently (in effect). Steps in a kinetic process do not: they occur sequentially, separated by durations of time.

    I'm going to defer commenting on the Achilles/tortoise problem. It just clouds the issue with the stairway supertask.
  • Infinite Staircase Paradox
    Doing successive steps does not get you past the tortoise unless the passing of the tortoise is done by one of the steps. That's the same as suggesting a final step, which suggests that infinity is a number.noAxioms
    Yes, the PSA entails taking a final step. We agree infinity is not a number, so there is no final step.

    I cannot buy into that PSA statement.
    Show the PSA is false.

    But I'm making the stronger claim that it is logically impossible.
    — Relativist
    I'm trying to get a justification of that claim without the addition of the necessity of a final step, which would by definition be contradictory.
    noAxioms
    Why? The claim is indeed justified by the necessity of a final step for completion. Simply denying a final step is necessary doesn't make it so - you have to explain why it's not necessary for a kinetic task to require a final step in order to be completed.
  • Infinite Staircase Paradox
    In the case of Achilles, we know that the task can be completed, but it is presented to us in a form in which it cannot be completed. I mean that we know that Achilles will pass the tortoise and even calculate when with simple arithmetic (no infinities required).Ludwig V

    It depends on how the race is framed. It CAN be described as a supertask, wherein Achilles runs to a series of destinations, each established by where the tortoise is located when he begins each leg of the race. In that case, Achilles never actually reaches the turtle, he just gets increasingly closer. If you frame it in terms of constant speeds by both, then it's not a supertask - it's a different kind of puzzle.
  • Infinite Staircase Paradox
    Countably infinite means that any step can be assigned a number. It does not in any way mean that there is a meaningful count of steps.noAxioms
    We can assign those numbers as we take each step. That's counting, and it's perfectly meaningful.

    Perhaps you mean there's no way to say we can meaningfully complete the counting of all the steps. That's true, but it seems to be contradicted by the fact that the infinite process completes before the 1 minute mark. .

    Physical (fixed size) stairs are of infinite length, and such a distance cannot be traversed in finite time. If the stairs get smaller as we go, then we get into the physical problem of matter being discreet, not continuous. Hence the steps have a minimum size. That's what I mean about physical stairs not qualifying as a supertask.noAxioms
    OK, but speed of light limitations put a physical limit on how fast the stairs can be descended, so that it eventually becomes physically impossible to descend a step in the prescribed period of time. The minimum size limitation also relates to a physical impossibility. But I'm making the stronger claim that it is logically impossible.


    Relativist:"The mathematical series completes, but this is an abstract, mathematical completion. The kinetic activity of descending the stairs does not complete."
    Again, the stairs is utterly abstract. There's no kinematics to it.
    noAxioms
    The entire exercise is abstract, but the scenario is written in terms of the kinematic (not abstract) process of descending stairs: each step is a motion, taking place in a finite amount of time.

    PSA:The performance of a sequence of successive acts does not complete a particular task unless it is completed by the performance of one of the acts in the sequence.

    I cannot parse this. What is an 'act' that is distinct from a 'task'? The word 'sequence' seems to refer to the entire collection.
    A 'task' (what, one of the steps??) is not completed by a performance unless 'it' (what, the performance?, the task?) is completed I cannot follow it at all.
    noAxioms
    Taking a single step is an act. The acts are performed in a sequence (from step n to step n+1). The term (sequence) is not referring to the entire collection. The task is to reach the bottom of the stairs (as stated in the description in the first post of this thread). Perhaps you can already see that it's trivial: it's actually impossible to reach the bottom of the stairs, since there is no bottom to a staircase with infinitely many stairs.