There is no physical process. — fishfry

The scenario describes a fictional, physical process. The lesson is that the defined supertask (the fictional, physical process) is logically impossible, but this isn't apparrent when considering only the mathematical mapping.

Certainly the relationship between time (independent of human control) and physical steps taken over a period of time has ended. — jgill

That's because the physical steps map to an infinite series in an interval with an open boundary. One can't simply declare there's no final step because the mapping implies there isn't. The taking of steps is a repetitive physical process, and if a physical process ends, there has to be a final step.

We of course have the ability to develop our skills of thinking things through, analyzing our opinions and assumptions, and considering other perspectives. But there is a difference between ensuring what you say is correct, and how you conduct yourself in and after saying it. So to say you should “not trust your mind” (yourself)—as I, and Emerson, argue against above—is perhaps different than saying you should not trust the opinions you have or inherited. — Antony Nickles

Consider a devotee of Infowars, who routinely accepts conspiracy theories. Aren't you suggesting they should trust their opinions?

You mention the role of one's conduct, so are you suggesting that the conspiracy theorist just needs to conduct himself in a certain way? Is the right conduct going to lead to him correcting his errors, or are you just suggesting he ought to be polite about his irrational beliefs?

Mathematically, this sequence as a limit of 1.

The sequence never "reaches" 1; nor is there a last step. Neither of these statements is controversial once you understand what a limit is. Sadly, most people have never taken calculus; and most students who take calculus never really learn what a limit is — fishfry

I've taken calculus and I understand what limits are. By definition, a limit is not reached, it is approached. The sequence of steps maps to a mathematical series that approaches, but never reaches 1. The sequence of steps is actually unending (that is how infinity is manifested in this thought experiment)- there is no last term.

However, the clock does reach 1. At time 1, the stairway descent must have ended, because the descent occurs entirely before time 1. The descent is not a mathematical process (even though it can be mapped to a mathematical series), it is a sequence of movements from one step to the next. No movements are occurring AT time 1. If the descent has ended at this time, how can there NOT have been a final step?

Everyone can be rash, everyone can be stupid, misinformed or otherwise malpracticing adequate reason.

My question is how does one know when that is the case - ie they're chatting sh*t. And to the contrary, when they really do know what they're talking about.

What is the litmus test in the realm of discourse with others which may be either just as misinformed or very much astute and correct? — Benj96

You should NOT trust your mind, but you can gain trust in certain beliefs by applying critical thinking: seek out contrary opinions, test your beliefs through discussion with others (like on this forum), attempt to mitigate confirmation bias by trying to identify objective reasons to support or deny some presumption you may have. Learn at least some basics of epistemology (including the limits of each technique).

I don't even understand what the supposed paradox is. — fishfry

The paradox is this:

1.The bottom of the stairs is reached at the 1 minute mark.
2.Reaching the bottom of the stairs entails taking a final step.
3. Therefore there is a final step
4.The steps are countably infinite (1:1 with the natural numbers)
5. There is no final (largest) natural number.
6.Therefore there is no final step

#3 & #6 are a contradiction.

We can also map the steps to the elapsed time (1 → 0.5, 2 → 0.75, 3 → 0.875, etc.). If we conclude that a full minute has elapsed, doesn't this imply that he has traversed all the steps? — keystone

Indeed, the stipulated elapse of a minute implies all the steps would have been traversed, but that implication is contradicted by the fact that the process of counting steps is not completable. The presence of this contradiction implies there's something wrong with the scenario.

Here's what's wrong: a mapping reflects a logical relationship, not an activity. The activity is a stepwise process: step n+1 is counted AFTER step n; the logical relation is present atemporally - it's an entailment of the way the scenario is defined.

Analogously, a limit entails an abstract operation applying to a mathematical series and shouldn't be conflated with a consecutive process.
— Relativist
Why not?

Same as above: it's a logical relation (atemporal) that does not account for the stepwise process that unfolds in sequence (temporally).

If time is infinitely divisible, the counter would go up to infinity. Not a conclusion that many of us may like, but there doesn't seem to be anything logically absurd with it. — Lionino

I disagree. It's absurd because the counter progresses through natural numbers, and can never reach a final one. Infinity isn't a natural number. In the context of a temporal counting process, infinity = an unending process, not something that is reached (and not a number).

I'm not so sure this will lead to an indictment for Trump. It would be costly to do so, and there's no chance of a trial before the election. If Trump is elected, the case would be put on hold for 4 years - making it all the more questionable as a productive use of resources.

Imagine a universe where not only is everything possible, but that all possibilities must be fulfilled before its natural conclusion.

How might such a universe look? How might you describe it? How would it begin and end? How would it evolve and unfold? What would concepts such as "paradox", "contradiction", "logic", "irrationality", "belief" and "fact" mean in such a universe? How might all these dynamics interact? — Benj96

It seems to me that a universe where everything is possible entails a world with multiple, causally isolated sub-universes. So there wouldn't be a beginning nor end to this universe as a whole, nor would there be a "conclusion" to it. Every possibility is actuallized in one or more sub-universes.

Paradoxes, contractions, logical, irrationality, belief, and facts are epistemological concepts, applying to propositions and reasoning not to ontological reality. The only "dynamics" these apply to are the the processes of reasoning.

What you seem to overlook is that I'm beginning with a premise widely accepted within the mathematical community: the existence of actually infinite objects (like these infinite stairs or the set, N) and the completion of actually infinite operations (such as traversing the stairs or calculating the sum of an infinite series). If you do not accept the concepts of infinite sets or supertasks, then this paradox is not aimed at you. If you claim that an old woman is 2 years old, then you're not basing your argument on any widely accepted concepts of age. — keystone

There's nothing contradictory with the EXISTENCE of an actual infinite, but it's not accepted that an infinity can be traversed in a supertask. In the case of the staircase, there actually is no last step - so it was correct to say the staircase was "endless".That would be analogous to saying the largest natural number can be reached by counting. This same objection has been raised in regard to the Zeno walk (see this SEP article).

We can consider the steps to be implicitly numbered - they map to the natural numbers. Traversal is one step at a time, moving from step n to step n+1. Every such n is a member of the set of natural numbers, but the supertask obviously never runs out of these. The contradiction is introduced by the stipulation that the end (of something endless) is reached by this process.

One reason the thought experiment can be misleading is that we're accustomed to treating infinite sets as mathematical objects. So we can consider the set of natural numbers and discuss it's cardinality (aleph-0). The set of supertask steps (step 0 to step 1, step 1 to step 2...) is also an infinite set with cardinality aleph-0 so it maps 1:1 to the set of natural numbers. The mapping is "complete" because it's defined for each member of the sets, but a supertask is a consecutive PROCESS, not a formulaic mapping identifying the correspondence. So a complete (i.e. well-defined) mapping shouldn't be conflated with a completed PROCESS.

Analogously, a limit entails an abstract operation applying to a mathematical series and shouldn't be conflated with a consecutive process.

I question the meaningfulness of blaming/crediting "Christianity". It's people who are engaging in good/bad behavior. Sometimes they point to scripture to rationalize their behavior (eg slavery), but that's generally post hoc.

Despite the staircase being endless, he reached the bottom of it in just a minute. — keystone

There is a contradiction in the stated scenario: there's an END to the ENDLESS staircase. Better to ask where he is after a minute.

Assess progress after each step he takes by noting the number of steps yet to be taken: there are always infinitely more to take. So at no point does he actually make progress - even after traversing infinitely many steps because that relation holds at all points along the way.

I expect that title to appear after Stormy gives her testimony.

Here's a guy that I could attack both ways: https://www.foxnews.com/video/6329053321112

Instead of attacking the perpetrators of this anti-Trump information (and risking committing a genetic fallacy), why don't you point out some disinformation they've put forth? TBH, I've seen some of their material, and although it's certainly slanted and conveys some wishful thinking when predicting trial outcomes, I haven't noticed factual falsehoods, like we see from Trump-friendly sources. I invite you to disabuse me.

Are there things in the physical universe that we can never find out? — Vera Mont

Absolutely. For example: what is the ontological bedrock of physical reality? No matter how deeply we explore, we can't know we've reached rock bottom.

the truth is that they have been planning for such a war since at least 2009. — Tzeentch

I watched the video, and read the Brookings report. The person in the video grossly misrepresents the report. Brookings does not state a plan, it lists options - and identifies potential negative and positive consequences of each. The author's premise is that there is some secret plan to go to war with Iran, and he interprets points in the Brookings document to in light of this premise. The fact that certain events have unfolded with some of the anticipated consequences is a testament to Brookings' analysis, not an implication that one particularly nefarious path has been chosen by the US, among all the permutations of paths outlined by Brookings.

I agree, but chip availability is critical to national security.

I agree we need to address the trade imbalance with China, but a sudden, across the board 60% tarriff would hurt consumers and be inflationary. The results of the current tarriffs have been mixed (see this). Going forward, we need to carefully target them to minimize consumer price impacts and avoid supply chain distuptions.

Biden has generally retained Trump's tarriffs on China, even increasing them in some areas. So in practice, there may be little difference between them on tarriffs, although Biden's subsidies for building chip factories is a positive in his corner. The "60%" threat may be campaign talk to create a contrast that's not real. If real, it seems dumb.

Yeah, you're right about it being about perception.

Regarding taxes, it appears that Trump has only promised to extend the current tax schedule that's soon to expire - not lower current taxes. By contrast, Biden says he'll keep current tax rates for everyone making under $400K. Trump has also said he's thinking about lowering corporate tax rates. So I don't see a real benefits for most folks.

Trump has also talked about imposing more tarriffs, including 60% on imports from China, and 10% on all others. This will increase the costs of many things, and likely lead to a trade war.

The culture wars issue sounds more like offering rhetorical support.

Trump is charged with a felony because, per state law, the falsification of the records was allegedly undertaken with the intent to commit another crime: the scheme to keep the public from becoming aware of the allegations of his sexual conduct. The scheme was executed prior to the election, Cohen made the payments before the election. Critically, these payments were approved by Trump prior to the election - and in the indictment, this constitutes Trump's "causing" the false business records to be produced - albeit that the actual false recording occurred after the election.

Nevertheless, I do think it's a tenuous case, because of the legal technicalities involved. The prosecution has a difficult burden to meet.

the crime you're alleging is what the Clinton campaign did when they funnelled money through Perkins Coie to fund the Steele dossier, which they then hid as "legal fees — NOS4A2

It's misleading to call this "funelling money... to fund the Steele dossier" because it suggests intent by the Clinton campaign. The campaign was not involved with the decisions on what to investigate (other than approving opposition research) nor on whom to hire to conduct that research, nor did they direct anyone on invent facts to support a narrative.

The fact that the DNC and Clinton campaign funded opposition research was not withheld from the public. The expenditure wasn't associated with a crime or coverup, nor was it improper: conducting opposition research is normal. The crime was simply a failure by the campaign to properly report the purpose of an expense by Perkins Coie. It was reported only as "legal services". The FEC ruled that it should have been reported as opposition research. The Clinton campaign argued that it was correct to consider this a legal expense, since it was an expense incurred by the law firm they used, but the FEC ruled against that interpretation.

Help me understand why one would vote for Trump

I live in Texas, and know more people who support Trump than who oppose him. I would like to better understand their point of view by hearing rational reasons why one might vote for him.

I'm not interested in hearing praise or condemnation for Trump's personality traits (e.g. lecherous, lying, bullying, insulting, xenophopic, racist, conspiracy-theory minded, etc), crimes he's committed (or alleged to have committed) such as sexual assault, fraud, election interference, conspiracy.

I'm mostly interested in hearing what policies you expect him to implement that may be perceived as positive by supporters. You don't have to be a supporter to understand why some would find policies attractive to supporters, even if you don't agree it's a good idea.

I'm open to hearing about things he did while President (policies implemented by law or executive order) - but explain what this has to do with future policies he's promised to implement.

If you point to differences in conditions (e.g. inflation, deficits, immigration rates...), explain what he did (and/or what Biden did) to create those differences in conditions.

I hope NOS4A2 takes advantage of this to make his case, but it's a useful exercise for everyone to try and understand the attraction.

"The signed statement with the denial was publicly released on Jan. 30, 2018. Not long after, Daniels recanted the statement and said that an affair had occurred. She said her denials were due to a non-disclosure agreement and that she signed the statement because parties involved “made it sound like I had no choice.”" -source

The statement will certainly be brought into evidence, and Daniels (Clifford) will probably testify that the affair did occur. It will be up to the jury to assess whether her in-court testimony (under oath) will convince the jury.

But I'm not sure it matters a great deal. Worst case, it's like the doorman who claimed to have knowledge of a "love-child" of Trump's, and similarly got paid off to prevent going public with it. Even after it was shown to be a false accusation, Trump still wanted the story killed until after the election. It is the killing of these stories, and reporting these as legal expenses, that is the crime. Not any affairs.

But if a child's alleged memories of a previous life can be validated against documentary records and witness testimony, that amounts to some form of verification. — Wayfarer

I'm not challenging the fact that it's verification that the child has some knowledge of someone who's dead, and the knowledge was not obtained from contemporary sources, but rather due to something paranormal. Although it's consistent with reincarnation, it could be some other mechanism - and I was lamenting that there's no way to test what is actually going on- to know if it is reincarnation, or some form of ESP.

In the Teletransporter cases, someone who is not you, is exactly continuous with you. — AmadeusD

Or it could be considered a discontinuity: you are being destroyed and a new entity, an exact physical copy, is being produced. I tend to think there's no right answer; all answers are paradigm dependent.

It's fascinating, but frustrating. How best to account for these, metaphysically?

If actual reincarnation, it implies some (traumatic) memories are stored non-physically.

But it could be some telepathic connection across time, implying something about the nature of time and of mental activities.

It's frustrating because there seems to be no way to test any theories.

:grin:
Corrected.

But you can never be identical to yourself in even the shortest amounts of time — RogueAI

In terms of strict identity, we can consider ourselves AT a point of time: RogueAI at t1 is identical to RogueAI at t1.

RogueAI at t1 has the same loose (perduring) identity as RougueAI at t2, t3, ...tn. This holds even if memory loss commences at some point - all are on a unique causal chain.

Let's suppose you die at tn, and all your memories cease to exist. Should we consider your loose identity to continue existing? The paradigm doesn't dictate an answer; it's a matter of semantics - what do we wish to refer to. We could talk about (loose identity) RogueAI in any of 3 ways:

1. The living person (which ceases to exist at death)
2. The physical body (which gradually decomposes after death)
3. A bare identity (a haeccity) that is your propertyless essense.

I don't believe in haeccity, so I generally wouldn't use sense #3. But we've been discussing an afterlife in which one's memories are gone. This seems to be a bare identity. Perhaps it reincarnates in a new infant.

To be ME at this point in time, 100% of my memories must be present.

Me (now) is not identical to the me of yesteday, much less to the infant me of 70 years ago.

I take the identity of indiscernibles seriously: entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa

In terms of having an identity over time, it is a looser sort of identity. Perdurantism makes some sense: my identity has temporal parts: today's me was caused by yesterday's me, in a temporal chain that goes back to whatever we might call my origin. But there's a vast difference between 70 year old me and zygote me. Zygote me lacks an entire lifetime of my memories. Similarly with losing memories from dementia or trauma. In some sense, it's stll me - but a vastly different me depending on how much is lost, and if it's sudden or gradual. If it's gradual, then it's the mirror image of growing up and gaining memories- each day not much different from the last. But loss of all memories at death is a discontinuity. I don't see any sense that it's me. It's similar to zygote-me, but without the temporal connections to the subsequent temporal parts the zygote has. We'd label it me only if we choose to define individual identity that way, but that's arbitrary.

Consciousness doesn't, on it's face, consist in memories, so I see no reason to have them at-base — AmadeusD

If memories aren't preserved in my after-life consciousness, in what sense is that still me? It hardly seems like something to look forward to.

This touches on the concept the individual identity, and essence. It sounds like Penelope Mackie's minimal essentialism - which entails a bare identity with no attached properties.

The ability to criticize is a precious right. — NOS4A2

Criminal defendants forfeit some of their liberties, as noted in the Appellate court ruling:

"after indictment, criminal defendants are frequently subjected to 'substantial liberty restrictions as a result of the operation of our criminal justice system.'"

there is little to no evidence these threats even occurred — NOS4A2

The Special Counsel's filing on that appeal listed a number of instances in which these have occurred (see pages 3-7). Trump's attorneys did not dispute these allegations.

It's only through voting for a third party that corruption will be held accountable. — boethius

How does voting for a 3rd party (that has zero chance of winning) hold either the winner or loser accountable? Ross Perot received a whopping 19% of the popular vote in 1992. Walk me through how Clinton and/or Bush were held accountable (and for what)?

The threats, if there really are any, are strictly caused by the motives of the threatener. — NOS4A2

I'm not sure what it means to be "strictly caused", but there's a clear, predictable connection between Trump's verbal attacks on named individuals and threats by Trump supporters to that individual. Do you deny that? Do you seriously think Trump is unaware? For that matter, it wouldn't even matter if Trump were too stupid to see this - the effect is obvious.

This comment is pertinent:

If they didn’t abuse their power they wouldn’t get threats. It’s as simple as that. What I applaud is retributive justice. — NOS4A2

So... it seems you feel they deserve to be threatened, irrespective of its impact on the administration of justice. So I don't take your legal analysis seriously - you grope for all available rationalizations.

Then lets discuss a few of your examples.

Biden said Trump was "sort of like [Joseph] Goebbels".

Goebbels was Nazi Germany's chief propogandist, who spewed disinformation. Trumps pews a great deal of disinformation.
Seems an apt comparison.

You mentioned Hillary saying "half of Trump supporters are racist, sexist, homophobic, xenophobic, Islamophobic". The "half" was an exaggeration (which Hillary regretted the next day) but it's accurate that Trump attracts those sort of people.

You mentioned AOC saying, ""Trump is compared to Hitler because he demonizes immigrants and refugees, denies science and facts, and promotes hate and division."
Again, that sounds accurate (Immigrants are "destroying the blood of our country. That's what they're doing. They're destroying our country" )

Omar: "The President is an open racist, a bigot, and has repeatedly showed strong shades of Hitler in his policies and actions."
Trump's degrading comments about immigrants sure sound racist, and his Muslim ban sure seemed bigoted. But even if he's not truly racist in his heart, these words and policies clearly appeal to those who are- so it's worthwhile drawing attention to them and discussing.

Sanders:"Trump's authoritarian tendencies and attacks on minorities are reminiscent of Hitler's tactics."
Is he wrong?

"Trump is a dictator in the making, following in Hitler's footsteps with his racist and xenophobic policies." - Tlaib
A bit over the top, but his immigration talk certainly sounds racist and xenophobic (He has
lamented that people were not immigrating to the United States from “nice” countries “like Denmark”).

Cohen: "What he has done and what he is doing goes to the Joseph Goebbels playbook. The big lie. You say the lie over and over and over, again and again, and it becomes the truth."
100% accurate. About 70% of Republicans believe the "stolen election" lie, and that he was completely exonerated in the Muelller probe.

So what's your take on these?

All your examples entail various people attacking one individual: Trump, based on things he has actually said. The comparisons could be debated. By contrast, Trump (and Trumpists) are making assertions about classes of citizens based on their party affiliation - displaying and encouraging bigotry toward the group. That's quite different.

The Supreme Court has deemed gag orders constitutional only where it protects the right to a fair trial. — NOS4A2

I recommend reading the DC Appellate Court ruling that upheld Chutkin's gag order. It provides important context that is applicable to all the gag orders imposed on Trump.

For example:


"after indictment, criminal defendants are frequently subjected to “substantial liberty restrictions as a result of the operation of our criminal justice system.” More specifically, as a less restrictive alternative to pre-trial detention, Congress granted courts the authority to release indicted defendants under the “least restrictive * * * condition, or combination of conditions [of release], that * * * will reasonably assure the appearance of the person as required and the safety of any other person and the community[.]” 18 U.S.C. § 3142(c)(1)(B). Such conditions commonly include measures that burden criminal defendants’ ability to act, associate, and speak...
...like any other criminal defendant, Mr. Trump does not have an unlimited right to speak. “Although litigants do not surrender their First Amendment rights at the courthouse door, those rights may be subordinated to other interests that arise in [the trial] setting.

...The record before the district court and its factual findings demonstrate that some of Mr. Trump’s speech poses a significant and imminent threat to the fair and orderly adjudication of the criminal proceeding against him...

...The record also shows that former President Trump’s words have real-world consequences. Many of those on the receiving end of his attacks pertaining to the 2020 election have been subjected to a torrent of threats and intimidation from his supporters...

...The former President has repeatedly attacked both the presiding judge and his law clerk in a New York state-law lawsuit. Since those attacks, the judge’s chambers have been “inundated with hundreds of harassing and threatening phone calls, voicemails, emails, letters, and packages.” New York v. Trump, No. 452564/2022, NYSCEF No. 1631 at 2 (N.Y. Sup. Ct. Nov. 3, 2023). In addition to threatening death or serious harm, callers have labeled the judge and clerk “Nazi[ s],” “dirty Jews,” and child molesters...

...Mr. Trump himself recognizes the power of his words and their effect on his audience, agreeing that his supporters “listen to [him] like no one else.”...

...Mr. Trump’s documented pattern of speech and its demonstrated real-time, real-world consequences pose a significant and imminent threat to the functioning of the criminal trial process in this case in two respects

Mr. Trump’s right to a fair trial does not give him “the right to insist upon the opposite of that right”—that is, a trial prejudiced in his favor. See Singer v. United States, 380 U.S. 24, 36 (1965)...”

The defendant has the constitutional right to a fair trial, but in this case he was gagged using prior restraint — NOS4A2

A non-point. All gag orders entail prior restraint.

You appeal to authority to guide your reasoning. — NOS4A2

"Guide my reasoning"? It's perfectly rational to rely on authorities, as long as one doesn't treat them as infallible and remains open to revising one's view when there are compelling reasons to do so. A Trumpist dogmatically stating their opinion isn't compelling.

The problem is you’ll defer to them even when they’re wrong or unjust...not applying a single thought of your own. — NOS4A2

Re-read that post and you'll see that I'm open to argument and evidence. You seem upset that I don't simply embrace your dogmatic statement.

If you don’t know or understand why free speech is preferable to censorship — NOS4A2

I don't think censorship is preferable to free speech, but it's a leap to call the gag order "censorship". As I mentioned, there are no withheld facts, the gag order is narrow, and the constraint is temporary, and it has not caused Trump harm. You've provided no facts or reasoning to support your contention, and have ignored what I said about the Constitution. Dogmatism is not persuasive.

Being a conservative, to an anti-conservative, is tantamount to being a literal Nazi. — AmadeusD

I'm sure there are such people, but I haven't noticed Democratic leaders promoting that sort of thing. On the other hand:

Trump ha promoted the message "the only good democrat is a dead democrat" (see this)

Trump's 2020 campaign sent a faux survey to supporters asking if they were "American or democrat?"

Trump has called Democrats "treasonous" for failing to applaud his SOTU.

He's called Democrats "fascists" and he's called them "vermin".