Right, but it's not a paradox - it's a conundrum. It's not just that the person saying it is part of the first group, but that they necessarily are.
Since people want to believe that they "know better," there's a strong urge to count oneself among the second group, which immediately places one in the first.
In classical logic, trichotomy on the reals (any given numbers is either >0, <0 or =0) is provably true; in intuitionistic logic it is probably false. Thanks to Godel’s incompleteness theorem, we’ll never know which is right!
Ok, so let’s start with the following number, I need you to tell me if it is greater than, or equal to, 0:
0.0000000000000000000000000000…
Do you know yet? Ok, let’s keep going:
…000000000000000000000000000000…
How about now?
Will a non-zero digit ever appear?
The Platonist (classical mathematician) would argue “we can know”, as all numbers are completed objects to them; if a non-zero digit were to turn up they’d know by some oracular power. The intuitionist argues that we can only decide when the number is complete (which it may never be, it could be 0s forever), or when a non-zero digit appears (which may or may not happen); so they must wait ever onwards to decide.
Such numbers do exist beyond me just chanting “0”.
A fun number to consider is a number whose nth decimal digit is 0 if n isn’t an odd perfect number, and 1 of it is. This number being greater than 0 is contingent upon the existance of an odd perfect number (and we still don’t know if they exist). The classical mathematician asserts we “discover mathematics”, so the question is already decided (i.e. we can definitely say it must be one or the other, but we do not know which until we find it). The intuitionist, on the other hand, sees mathematics as a series of mental constructs (i.e. we “create” mathematics), to them the question is only decided once the construct has been made. Given that some problems can be proven unsolvable (axiomatic), it isn’t too far fetched to assert some numbers contingent upon results like this may well not be 0 or >0!
It’s a really deep rabbit hole to explore, and one which has consumed a large chunk of my life XD
I’m gonna be honest, I just don’t see how a non-Platonic interpretation makes sense. The number exists, either way. Our knowledge about it is immaterial to the question of what its value is.
To the Platonist, the number exists in a complete state “somewhere”. From this your argument follows naturally, as we simply look at the complete number and can easily spot a non-zero digit.
To the intuitionist, the number is still being created, and thus exists only as far as it has been created. Here your argument doesn’t work since the number that exists at that point in the construction is indeterminate as we cannot survey the “whole thing”.
Both points of view are valid, my bias is to the latter - Browser’s conception of mathematics as a tool based on human perception, rather than some notion of divine truth, just felt more accurate.
Actually I’ve done some more reading and frankly, the more I read the dumber this idea sounds.
If a statement P is provable, then P certainly cannot be refutable. But even if it can be shown that P cannot be refuted, this does not constitute a proof of P. Thus P is a stronger statement than not-not-P.
This reads like utter deranged nonsense. P ∨ ¬P is a tautology. To assert otherwise should not be done without done extraordinary evidence, and it certainly should not be done in a system called “intuitionist”. Basic human intuition says “either I have an apple or I do not have an apple”. It cannot be a third option. Whether you believe maths is an inherent universal property or something humans invented to aid their intuitionistic understanding of the world, that fact holds.
Actually, AvA’ is an axiom or a consequence of admitting A’'=>A. It’s only a tautology if you accept this axiom. Otherwise it cannot be proven or disproven. Excluded middle is, in reality, an axiom rather than a theorem.
The question lies not in the third option, but in what it means for there to be an option. To the intuitionist, existance of a disjunct requires a construct that allocates objects to the disjunct. A disjunct is, in essence, decidable to the intuitionist.
The classical mathematician states “it’s one or the other, it is not my job to say which”.
You have an apple or you don’t, god exists or it doesn’t, you have a number greater than 0 or you don’t. Trouble is, you don’t know which, and you may never know (decidability is not a condition for classical disjuncts), and that rather defeats the purpose! Yes we can divide the universe into having an apple or not, but unless you can decide between the two, what is the point?
So, obviously there’s a big overlap between maths and philosophy, but this conversation feels very solidly more on the side of philosophy than actual maths, to me. Which isn’t to say that there’s anything wrong with it. I love philosophy as a field. But when trying to look at it mathematically, ¬¬P⇒P is an axiom so basic that even if you can’t prove it, I just can’t accept working in a mathematical model that doesn’t include it. It would be like one where 1+1≠2 in the reals.
But on the philosophy, I still also come back to the issue of the name. You say this point of view is called “intuitionist”, but it runs completely counter to basic human intuition. Intuition says “I might not know if you have an apple, but for sure either you do, or you don’t. Only one of those two is possible.” And I think where feasible, any good approach to philosophy should aim to match human intuition, unless there is something very beneficial to be gained by moving away from intuition, or some serious cost to sticking with it. And I don’t see what could possibly be gained by going against intuition in this instance.
It might be an interesting space to explore for the sake of exploring, but even then, what actually comes out of it? (I mean this sincerely: are there any interesting insights that have come from exploring in this space?)
I would say mathematics is a consequence of, or branch of philosophy in its own right. The name intuitionism derives from the source of this branch of mathematics - “2 primal intuitions”.
Twoity - we are able to perceived time, and are thus able to split the universe into two, three, four etc parts. Counting is not something we just learn, it is something built into us as humans.
Repetition - we can repeat operations and not stop, just as we can never stop counting.
From these two (heavily paraphrased) ideas we can derive all of mathematics.
The first is actually enough to give us everything up to the rationals, the second grants us the reals and beyond.
While we lose excluded middle, we gain things such as “all total real functions are uniformly continuous on the unit interval” (Brouwer), the removal of the information paradox in physics (someone used Posey’s take on intuitionism to rewrite all physics to see where it led), and the wonder of lawless sequences (objects we cannot predict entirely, but still work with).
The intuitionist is very very formal “you are either alive or not alive” is a very nice statement to make, but entirely worthless if one cannot tell which you are! Excluded middle is not universally false in intuitionism; it is true for decidable statements, of which having an apple or not does seem to fall within (though here we can question how “apple-like” must something be to be considered an apple if we wish to be peverse). However, to argue it is true for any statement means your disjunct (or) must be very weak indeed - the classical mathematician is happy with this, the intuitionist demands that a disjunct not only present two options, but provide a way of determining which if the two applies on a case to case basis (hence excluded middle applying for decidable things).
Simplifying your example of an apple, you can think of it as a Platonist just having the statement that everything is either and apple or not. Meanwhile, the Intuitionist also demands there be a guide on how to sort everything into “apple” or “not apple” before they make that statement.
Classical mathematics does also have a huge unintuitive step - mathematics must exist independently of humanity. Every theorem ever proved, and ever to be proved, exists somewhere. Where you ask? The platonic plane of ideal forms beckons, with all the madness it entails!
I read an interview with her once that was kind of funny and humanizing. She wrote and recorded that song before she was famous and had no idea that it would ever be heard. Then it blew up and people have been giving her shit about it for decades now.
Could you imagine if you wrote a shitty Lemmy comment that became extremely viral and people were like, “you fucking moron, how could you have written something so dumb?!”
Not sure if its what you’re talking about but I really like the Ship of Theseus thought experiment, if an object is the same object after having had all of its original components replaced. Always makes me think of if an exact clone of you is created (same thoughts, memories, etc…) should that be considered you?
Even in the trek universe, some people refuse to take transporters. I’d pry be one of them. You have no idea if you’re killing yourself every time, and its just clones out the other side.
If and when we figure out human cloning, it’s sure going to bring up a near infinite number of legal issues. Is the clone a new person? Is their birthday yours or the day they were cloned? Are they the same age as you? Or is a clone a new born?
If they are a copy of you, are they beholden to any legal agreements you’ve made? Are they liable for crimes you commit?
I read a good sci-fi book called “Six Wakes” by Mur Lafferty that touches on this topic, you might enjoy it.
In the distant future cloning has become commonplace, but is used as a continuation of a person’s life. Ie a person is born, lives there life, and at the end they are cloned and their memories transferred over to the new body, and life goes on. Also, a person would make “backups” of their consciousness in case they were killed/died accidentally, and would be “reinstalled” in a clone.
Honestly though, that sounds like the only way to do cloning without completely redoing every single law in every single country, city, state, Providence, county, parish, etc. The implications of cloning fascinates me way more than the cloning itself
And I would venture that the answer to your question is yes, but no. The moment your exact clone experiences something you don’t, you two are no longer exactly the same. And I would wager that moment would happen very fast.
With that in mind, it really just comes down to if the original gets destroyed, for a lack of better words, before that moment even happens in order for it not to be considered just a copy.
Edit: this honestly kinda helped me understand the problem more I really appreciate it.
The moment of divergence is instantaneous between the clone and original. The only way it could not be instantaneous, is if both were just a brain connected to the exact same simulation, experiencing the exact same inputs. If they didn’t respond the same, then they aren’t an exact clone. Even then, the brains would be sustained with different blood, made up of trillions of slightly different atoms — although similar, not 100% identical due to quantum mechanics — with a slightly different fluid dynamics. Actually the only way they could be identical is if they weren’t brains but identical code, running in an identical simulation, with the exact same boundaries, and no possibility of probability, chaos or divergence from that code… Oh no I’ve gone cross eyed.
Ship of Theseus applies to every human, because all our cells get replaced over and over until we die. At a cellular level, you’re wholly different from yourself 10 years ago. Are you still you?
One thought is that “You” is just an unbroken string of consciousness. Which means you cease to be every time you sleep, and the person that wakes up just has the memories of being you.
A different perspective,seen in buddhism and similar worldviews, is that the only “you” that exists is the consciousness experiencing reality at any given moment.
I don’t think you’ve quite clocked it. It’s not that one of the statements has to be wrong, because that’s just a point in the cycle. If A is wrong, then B is right, which means A is right, which means B is wrong, which means A is wrong and the cycle begins anew.
They aren’t wrong, they’re contradictory. There is no logical way to parse the two statements together. That’s what a paradox is.
Neither statement can be true OR false. If statement A is true, statement B is true, which means statement A is false. To simplify, if statement A is true, statement A is false.
“This statement is false” can be neither true nor false. That is the most basic paradox there is.
The Monty Hall problem is not a paradox, and I’m hesitant to call it a conundrum. It has a very simple solution. The “point” of it is that people inherently don’t like that solution because it challenges their instinct to stick with their first choice.
Because when you first picked 27, it was 1 out of 100 choices. Then I tell you that you either got it right, or it’s this other number. None of the others are correct, only 27 or 44.
So you think your 1/100 choice was better than the one I’m giving you now? On average, you’ll be right 1% of the time if you don’t switch. If you do switch, you’ll be correct 99% of the time.
Another way to think of it is: you choose 27 or you choose ALL of the other 99 numbers knowing that I’ll tell you that 98 of them are wrong and you’ll be left with the correct one out of that batch. One of those clearly has better odds, no?
In this example, there were 100 choices in the beginning, and later you reduced to 2 choices. Clearly an advantage. Does the same apply to the 3 door problem?
Let’s take this question in another angle. Instead of 3, there are only 2 doors. I am to choose one out of 2, which has a prize. After I choose one, you show me a third door which is empty. Now, should I change my option?
Yes, it’s the same concept. The same math/logic behind it doesn’t change. You’re choosing 1/3 or you are choosing 2/3 and I’ll tell you which of the two is incorrect. It’s just easier to visualize with 100 doors instead.
I’m not sure I’m following the other angle…there are 3 correct possibilities at the start but I can only choose 2? Or there are 2 possibilities and then you introduce a 3rd door that is never correct?
Do you know the third door is never correct? Because then the probability doesn’t change.
Scenario 1: You chose 1/2 at first with a 50% chance of being correct, I introduce a 3rd door (but it isn’t a legit possibility), so the actual choice for you is still 50/50 (between doors 1 and 2)
Scenario 2: If you think it’s possible that 3 could be correct (but it actually never is) then, no, you wouldn’t want to switch. By staying with your first choice has a 50% chance of winning, by switching it only has a 33% chance. But there’s no way to know this ahead of time (because as soon as you know you shouldn’t switch bc 3 is the wrong door, then you’re back in scenario 1)
Scenario 3: For completeness, let’s say the 3rd door can be correct sometimes. Then it doesn’t matter if you switch or not. It’s a 33% chance of winning either way. If there is a chance it can be correct, then your first choice doesn’t matter at all and the second choice is the ‘real’ choice bc that’s the only time you’re able to choose from all real possibilities.
The only reason that the Monty Hall problem changes probability in the second choice is because you are provided more information before the switch (that the opened door is absolutely not the one with the prize)
In scenario 1, legit or not, you said the chance is still 50-50. In other scenarios also you shouldn’t change or it wouldn’t matter. That’s what I say, just in the opposite direction. But the problem of probability depends on the wordings and phrases, which means I may not have understood the ques well.
Another angle: You explained the Monty Hall problem at the end that the probability changes because in second choice we have more information. So you are implying that the initial 1/3 probability of the now-open door adds to the door we did not choose - making the switch advisable. Here I also say the probability does change from initial 1/3, but to 1/2-1/2 for each remaining doors; why should the probability be poured to the unselected single door?
In the original the possibilities for a prize behind the doors 1,2,3 are:
A) YNN B) NYN C) NNY
In (A) - A.1 you choose door 1 and then stay, you win A.2 you choose door 1 and switch, you lose A.3 you choose door 2 and stay, you lose A.4 You choose door 2 and switch, you win A.5 you choose door 3 and stay, you lose A.6 you choose door 3 and switch, you win
By staying, you lose in 2 of 3 cases (A.3 and A.5)
This isn’t a trick or anything, the math is pretty clear and you can actually write out all the scenarios and count it up yourself. It’s just a little counterintuitive because we aren’t used to thinking in terms of conditional probabilities this way.
Another way to think about it is the probability of losing. If the contestant loses, it means that they picked correctly on their first choice and then swapped. This will happen 1/3rd of the games, because there is a 1 in 3 chance of picking correctly the first time. So, if you have a 1/3rd chance of losing by swapping, then it follows that you have a 2/3rds chance of winning by swapping (choosing incorrectly at the start and then switching to the correct door)
God clearly can’t exist because an omnipotent, omniscient, and just God is a paradox already. Omnipotence and omniscience means that God, if they exist, would have full control of every moment of the universe (even if they only “acted” initially). Some (I’d argue nearly all) people suffer for reasons out of their control. Only deserved suffering is just. Since undeserved suffering exists then God cannot exist (at least omniscient, omnipotent, and just - as we understand those terms). God could be an omniscient, omnipotent asshole or sadist… God could be omniscient and just (aka the martyr God who knows of all suffering but is powerless to prevent it)… or God could be omnipotent and just (aka the naive God who you could liken to a developer running around desperately trying to spot patch problems and just making things worse).
Alternatively, by omnipotent maybe the scriptures are just hyping them up - “God is so fucking buff - this one time they lifted up this rock that was like this big. Fucking amazing.”
As you said, that does depend entirely on God having those properties, exactly as you define them.
Alternatively, if definitive property is “universal consciousness”, then God clearly must exist. Either consciousness is an emergent property of sufficiently complex systems, in which case the entire universe is obviously more complex than the human nervous system and consciousness should certainly emerge within it; or, consciousness is some external field, like gravity or electromagnetism, that complex systems can channel. Either way, the existence of your own consciousness implies a universal one.
I don’t think your alternative proposal makes sense, at least not to me. An emergent property being present in one complex system doesn’t imply that it must be present in all complex systems.
What does imply it’s presence, then? The emergence of comparable effects is implied by isomorphic complexities. If you can’t define the foundational structure which implies emergence, you can only fall back on a probabilistic approach.
Unless you can define exactly what structure it is that belies the emergence of consciousness, you must acknowledge that the comparative complexity of a more complex system is undoubtedly probabilistically suggestive of at least comparable, if not far more complex, emergent behavior.
The proposition that consciousness is emergent, but only at a very specific and narrow band of complexity, falls quickly to Occam’s razor. It’s logically and probabilistically ridiculous.
My point is that not all complex systems are the same. Maybe it depends on your definition of consciousness but from what I know we have only ever observed that in a very specific set of complex systems which is brains and possibly fungi. Two different systems being complex isn’t enough in my view to infer that they would have the same properties unless there are other similarities.
It absolutely depends on your definition of consciousness. Every conversation about a concept depends on the definition of that concept. My definition is based upon sensation, processing, and decision-making, in regards to the self and the environment. I’d argue that plants and even cells exhibit simple forms of consciousness. If you take the emergent-property perspective, I’d argue even molecules and individual particles have a broad and abstract consciousness, although certainly several orders of magnitude less sophisticated than yours or mine.
The statement “we have only ever observed that in a very specific set of complex systems which is brains and possibly fungi” tells me less about consciousness than it does about our ability to observe it.
Ah, the Epicurean Trilemma. This was my answer too. Weirdly attributed to a guy from before monotheism was the predominant belief.
Alternatively, by omnipotent maybe the scriptures are just hyping them up
The scriptures don’t use that word, and it’s notable because the Old Testament didn’t believe that to be the case, either. Early Israelites were henotheistic. They believed other gods might exist (hence the need for “thou shalt have no other gods before me”), but only worshipped the one. When multiple gods exist, it is by definition necessary that they cannot be omnipotent.
It’s pretty clear that he is not meant to be omnibenevolent either. The god of the Tanakh is wrathful. Christians later reinterpreted him as omnibenevolent, but this was clearly not the authors’ intent. I believe Jewish scholars still don’t think he’s omnibenevolent today.
Religious scholars have come up with a number of other proposed solutions to the trilemma. Ones involving free will are quite popular, though not the only ones. I have yet to find any argument that is remotely convincing, however. Saying “free will” just means god either cannot or chooses not to enable people to have a form of free will that does not involve them desiring to do evil. It also ignores the very many evils not created by human action. Child cancer, earthquakes, drought-induced famine (today humans have the technological ability to solve this last one and might simply choose not to, but historically it has been an insurmountable problem not caused by human free will).
I recommend you read “Religion of the Apostles” by Stephen De Young. He explains the common misconceptions of the early Israelite beliefs. The “Gods” are lesser divine beings that were meant to protect the 70 tribes after the Tower of Babel fell. The deities rebelled against God and led the nations astray and were worshipped. The tribe of Israel worshipped the God of “Most high” which is the one true God above all divine beings. So they aren’t henotheistic because there is only one God. The term “Gods” was used because they were divine beings but they were created whereas God the Father is not. Everything proceeds from him.
A great podcast that explains evil and suffering is “Whole Counsel of God” with the same guy. In short, suffering is unavoidable because man falls from Eden after sinning and the consequence of sin is death. Making death the consequence is a mercy because man can become sanctified during his life and through death re-enter the kingdom of God. Consequently suffering draws people closer to God than anything else.
I’m not a theologian and wrote this on my phone but that’s my quick recap. The book is way more thorough of course.
I haven’t read the book, but I did some reading about it, and it seems like it’s come against some significant criticism for being poor academics and its author criticised for presenting his own one academic idea as a fact.
So while it’s certainly interesting to hear his theory from your summary of it, and to learn that there are competing theories out there, I don’t think it’s going to change my understanding of where scholars more broadly stand on it. The fact that I can’t really find anyone talking about de Young’s interpretation of early Israelite monolatry (which I’ve just realised is possibly a more accurate term than henotheism, though the lines between the two are blurred) concerns me from that perspective. Which is not to say that’s it’s necessarily wrong. It especially could have been a phase they went through on the way from monolatry to Second Temple Judaism’s monotheism.
But in general I’m very wary of non-academic books presenting grand theories that cannot be well backed-up by academic sources, even when by an author with academic credentials. Reminds me too much of Guns, Germs, and Steel.
“His” main critique is against evolutionary theology which is common amongst reformers and Christian critics. “God was seen this way. Then it changed and he was seen this way. OT God is angry. NT God is compassionate etc” This is not a new idea and has been held by the Orthodox church since it’s inception and has been codified for the last 1200-1300 years. The Orthodox view everything consistently through a Christological lens which is why their view of sotieriology etc is so different than what you will get from Protestants or even Roman Catholics.
Fr. Stephen De Youngs book is just a readily consumable encapsulation of ancient arguments, historical findings (such as the Rosetta stones) with his own analyses and contributions. Would you be better off reading the church fathers and primary sources yourself? Possibly but you’d also need to know ancient Greek and Hebrew.
Christians and academics love to argue and I’m not surprised to see that people are critical of the book. I don’t think there is any religious commentary that hasn’t received criticism.
At any rate I encourage you to look at Orthodox theology more generally. You will find a logical consistency and depth of analysis that the secular world usually says is lacking in the Christian worldview.
Roku's basilisk just doesn't make sense to me because any semi-competent AI would be able to tell that it is not punishing the people that failed to help create it it's just wasting energy punishing a simulacrum.
We are not going to suddenly be teleported into a future of torment. If the AI had the ability to pluck people out of the past it should have no reason to waste it on torture porn.
Then AI already exists and you have no memory or recollection of either helping to create it or accidentally contributing to its non-creation and therefore you being tormented by the AI would serve no moral purpose.
Any torture you would be experiencing in that simulation would simply be that the AI desires to torture, and you happen to be one of its victims.
Any person alive during the time when the Basilisk is being created is at risk. Also, if you create a good AI instead, then you didn’t help build the Basilisk so if anyone else does, you’re screwed.
The Unexpected Hanging Paradox: A man is sentenced to death, but the judge decides to have a little fun with it. The man will be killed at noon on a day of the judge’s choosing in the next week, from Monday to Friday. The only stipulation is that the man will not expect it when he’s called to be killed.
The man does some quick logic in his head. If Friday is the last day he could be killed, then if he makes it to Friday without dying, he knows he must die on that day. And since that wouldn’t be a surprise, he cannot be killed on Friday.
He then extends the logic. Since he can’t be killed on Friday, the last day he can be killed is on Thursday. Thus, all the prior logic regarding Friday applies, and he cannot be killed on Thursday either. This then extends to Wednesday, then Tuesday, and then Monday. At the end, he grins with the knowledge that, through logic, he knows he cannot be killed on any of the days, and will therefore not be killed.
Therefore, the man is astonished when he’s called to be killed on Wednesday.
This is how I proposed to my wife. I said I’d propose at some point in the next year, and that according the the unexpected hanging paradox, we’re doomed to break up at the end of the year. Then I proposed on a random day in the year and she was totally surprised.
Cannot be properly defined? “Expecting it” means “regarding it likely to happen”, according to the dictionary. He regarded it as impossible to happen, so he was not expecting it. His own logic disproving the event (him being surprised) allowed the event to happen (he was surprised).
Why does the paradox suffer if he lies about the solution? The paradox has already played out, and anything after that is just set dressing.
Just off the top of my head, maybe the judge has a camera set to gauge his reaction to the knock on the door? Or maybe he goes into denial and tries to explain his logic, thus proving the paradox? Or maybe the judge doesn’t actually care as much as he said, but trusts the logic to hold out and make for a funny story?
My dude. The paradox doesn’t change based on whether or not the judge knows the truth, or even if the man dies.
The truth is the man was made not to expect a thing by his own logic proving he would always expect a thing. The paradox is based on his own prediction being wrong because of his prediction. In this instance, his prediction was what his emotions would be.
A horse walks into a bar, and the barman says “why the long face?” I haven’t said how they remove the horse from the bar, so does that mean I didn’t tell a joke? Or does horse removal not actually matter to the joke?
No. A paradox is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
In this case, there is no true premesis.
That’s the core of the problem. Your incorrect interpretation of the joke metaphor demonstrates that you don’t understand this.
I find it funny that you directly quoted wikipedia to write that (exact wording from the paradox article, I checked), but ignored the sentence immediately before it (…or a statement that runs contrary to one’s expectation). Also, the linked articles at the bottom include the unexpected hanging page. Maybe read the entire wiki page before citing it?
A driveway is named because it was originally a circle that you could use to drive right up to the house. Think old mansions in movies.
Parkways had separated lanes with shrubberies and plants on between and around, basically parks with a road through them.
A driveway that is straight and ends in a garage isn’t really a driveway. Separated lanes with no plants or parks isn’t really a parkway. But the names both stuck around.
Jokes aside, I have baked my bacon and it works really well for preparing an awful lot of bacon very quickly.
Once you do that, you have bacon that you can quickly microwave and slap on a sandwich, plus you can easily collect all of the grease for making gravies or general cooking purposes if you so desire.
I’d go so far as to say baking is superior- it never reaches temp to make the oil pop and makes a mess inside the oven, and you’re only limited on how much bacon you can cook by how many cookie sheets you own (and maybe how much bacon you have stored away in the freezer 😁). Great point on the grease, easy to collect afterwards! Makes great rice!
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