Somethings to think about today, or not.

[Solitary]

https://youtu.be/3x1q5_lYMRA

[Baruch]

1. Reality isn't strictly logical.  Logic was invented to make "reductio ad absurbum" arguments ... like the arrow paradox.  Later Aristotle and the Stoics invented positive logic, thus making Euclid's work possible (math organized by deduction, rather than just random statements).  The problem is, that logic only works, as long as its axioms are true ... but in some cases they are not.  Similarly Euclidean geometry works, as long as its axioms are true, which in case of the Earth's surface, they are not.  Logic isn't true ... it simply is a way to make fewer mistakes while reasoning.  There are plenty of fallacies still available to step in, that logic won't save you from.

2. in the first example, this is true of your own body.  Science has now shown that no cell of yours, not even the neural cells, are the same as you started with, after three years.  So are you still you?  Buddha would answer ... of course not!

[Munch]

I'm subbed to Santoro's channel. He's freaky, especially that grin of his, but he does some interesting lists.

paradox's are always fun to create speculation around, but they more seem to just serve as plot dynamics for fictional writing more then anything ever testable.

For example the surprise exam paradox.

A maths teacher says to the class that during the year he'll give a surprise exam, so the students need be prepared the entire year. One student starts thinking though:

1 - The teacher can't wait until the last day of school, because then the exam won't unexpected. So it can't be the last day.
2 - Since we've removed the last day from the list of possible days, the same logic applies to the day before the last day.
3 - By applying 1) and 2) we remove all the days from the list of possible days.
4 - So, it turns out that the teacher can't give a surprise exam at all.

Following this logic, our student doesn't prepare for this test and is promptly flunked when the teacher does give it somewhere during the middle of the year (but that's my own creative addition to the problem).

in smaller cases perhaps testable theory can be applied, but so many paradox's are made from what has already occurred, and put into its own instance. I just think a paradox as just something applied as a logic solving riddle in order to join the loop. The grandfather paradox being one of the best examples, but again, unless you can time travel, not really testable.

[Baruch]

"join the loop" as in theological "reasoning".  Whether as a physical idea or as a verbal idea ... circularity defies Western thinking, which is completely linear by assumption.  This is less of a problem in India.

[dtq123]

"Lazy" ways to solve each paradox

1. Both ships are the original
2. There is no such thing as omnipotence
3. Poor assessment of reality
4. Recursion eliminates possibilities until base case is reached. Judge uses another case that is not base case. (Base Case = No Execution)
5. Everything that can, has always happened/Multiverse
6. A girl shaves him
7. The sum of infinite series does not need to be infinite, Constant is reached
8. Both can occur, and will occur
9. Definition of Heap is too vague to be a definition
10. Just flat out poor logic

[Hakurei Reimu]

A more apt description of a paradox is "a paradox is a deep truth turned on its ear."

1. The Ship of Theseus reveals that there is something a bit screwy with our notion of identity. In practice, it's nothing to actually worry about. Both ships float just as well as the other (assuming the old planks haven't rotted away), and which one to label "the Ship of Theseus" is a matter of how you resolve our notions of identity against the scenario.

2. The Omnipotence Paradox reveals that our notion of "omnipotence" is so ill-defined that it does not admit even the most casual argumentation.

3. The Monty Hall "Paradox" is actually a counterintuition. The mathematics are actually unambiguous that the correct strategy is to switch doors (though there are idiots who insist otherwise) â€" at least if you want a car rather than a goat. Explaining why is also easy: with the staying strategy, you only win if you initially chose the door with the car, which has a probability of 1/3; with the switch strategy, you only lose if you initially chose the door with the car, which again has a probability of 1/3.

4. The Unexpected Hanging Pardox hinges on what constitutes an 'unexpected hanging.' Even if the prisoner were to end his argument with excluding Friday only, once he has logically excluded Friday as his exectution day, then he no longer expects the hanging on Friday, which means that his own logic has folded back and destroyed itself. The conclusion that Friday would be excluded is dependent on the fact that the prisoner could still expect Friday to be a possible day of execution, and once that changed, that particular argument has had removed from it one of its vital premises and so its conclusion has lost its support. In other words, there's nothing wrong with logic, just with the prisoner's argument.

5. The Grandfather Paradox assumes that your own grandfather could be killed by yourself or as the direct consequence of anything you did in the past. This paradox actually has yielded somewhat to analysis. It involves the theoretical construction of a wormhole time machine and asking what kinds of boundary conditions can lead to a ball from the future knocking itself in the past off a path into the wormhole. Turns out, there are only two possible outcomes: the future ball misses altogether, and the past ball continues unmolested to miss itself; or the future ball hits the past ball, but not only does not prevent itself going into the wormhole mouth, but proturbs it in just the right way so that it hits itself in the future in such a way to send it careening into the wormhole at just the right angle to knock itself... well, you get the idea.

So the tentative conclusion is that you cannot kill your own grandfather this way â€" physics will simply not allow it to happen. Some circumstance will prevent his death: you will miss the fateful moment, your grandfather will survive your assault, the time machine will simply fail to function, or will kill you outright. If you survive the experience, you will find that the future condition of the world will be absolutely consistent with your experience in the past: there are signs that you were there, in the past; and/or your grandfather will recount a miraculous survival with some crazed maniac.

6. The Barber Paradox is not an infinite regression, because the casual analysis simply oscillates between two distinct states, not cause the unrestricted spawning of a chain of new propositions that support earlier propositions. There's only one issue to resolve: does the barber shave himself or not?

The resolution to the paradox is the same as the resolution to Russel's paradox, because the barber paradox is Russel's paradox in disguise: the barber cannot exist as described. Either there is a barber where the rule does not extend to himself (in which case, he's free to shave himself or not at his pleasure) or there is no barbar at all and you have been told a fib.

7. The Fletcher's Paradox is just straight-up sophistry. The scenario as described is one in which all states of motion are indistinguishable. And when I say all states of motion, I do mean all states of motion, including the arrow being stationary. You cannot in the situation described say that the arrow is moving, but you also cannot say that it is stationary either, because that's also a state of motion and to say the arrow is stationary requires exactly the same look-ahead or -behind that would allow you to say that the arrow is in motion. There is no paradox, but rather you have been presented with a situation where there simply isn't enough information to answer the question.

8. The Epimenides Paradox is again not an infinite regression, because again the only issue at stake is whether the statement "this statement is false" is false or not, and does not spawn an infinite number of propositions. Raymond Smullyan has I think the most thorough deconstruction of this paradox by recognizing that the truth or falsity of a statement depends on what the statement means. Only when you have deciphered what the statement means can you then decide on the truth or falsity of the statement by comparing its meaning to the actual state of affairs presented. But, for the statement "this statement is false," the truth of the statement depends on its own meaning, but that meaning depends on the truth of the statement itself. Smullyan resolved the paradox by pointing this out and claiming (I think sensibly) that the only statements that can be said to be true or false are those that are well-founded â€" where it is possible to decide the meaning of a statement without knowing whether it is true or false. "This statement is false" is not well-founded, and therefore cannot be said to be either true or false.

This simple form of the Epimenides Paradox is the most interesting because here is where we get to some real philosophical meat. The classic forms are less interesting: the clasic Epimenides Paradox is that Epimenides, a Cretan, states, "All Cretans are liars!" The proper resolution is that Epimenides is lying and that there is at least one honest Cretan â€" just not him at that particular moment. The other form is, on the Island of Knights and Knaves, an inhabitant is claimed by Smullyan to have said, "I am a knave." The resolution to this paradox is that Smullyan is not a knight. Of course, having told a truth sometime in his life, Smullyan is not a knave either.

9. The Sorites' Paradox comes from treating a fuzzy notion like a "heap" as if it were a precise one. As you take away grains of sand, the pile becomes less and less heap-like. When you get to a few grains, you're much less inclined to consider the collection a "heap" as you were when there were a million grains. If you haven't recinded your designation that the collection is a heap yet, you will be more likely to do so with each grain removed and nobody at that point could fault you for it, and almost all participants would have recinded their designation by the time the collection reached one grain. This is the proper conclusion, not "A heap can be a single grain of sand, or there's no such thing as a heap."

10. The Raven Paradox is only a 'paradox' because logicians are trying to evaluate empirical evidence, which logic is ill-equipped to do.

Thing is, if you had absolute assurance that you have seen all non-black objects and observed them to be not ravens, then you can indeed say logically that all ravens are black, because you have exhausted the pool of non-black objects and have not found a single raven amongst them. The only group where you can find ravens is then in the black objects.

Logic does not deal well with trends that show up only in the aggragate, as empirical evidence often does. You have to go to more powerful tools to properly evaluate such evidence. Statistics is one field that does so. Sure, that green apple is only one of many, many non-black objects that may have been chosen, but if sufficient randomization conditions for sampling can be satisfied, you can show that observing that green apple absolutely gives you some non-zero support for the plausibility that all non-black objects are not crows (albeit slim), and consequently for the contrapositive hypothesis that all crows are black.

Practically, I have very good assurance that "all crows are black" is likely wrong, because albinoes exist in all vertibrate animals (crows are vertibrate animals), and an albino cannot sensibly be called "black." Therefore, an albino crow is quite likely to have existed at some point in time, and can be fairly called a "non-black crow."

[dtq123]

A more apt description of a paradox is "a paradox is a deep truth turned on its ear."

1. The Ship of Theseus reveals that there is something a bit screwy with our notion of identity. In practice, it's nothing to actually worry about. Both ships float just as well as the other (assuming the old planks haven't rotted away), and which one to label "the Ship of Theseus" is a matter of how you resolve our notions of identity against the scenario.

2. The Omnipotence Paradox reveals that our notion of "omnipotence" is so ill-defined that it does not admit even the most casual argumentation.

3. The Monty Hall "Paradox" is actually a counterintuition. The mathematics are actually unambiguous that the correct strategy is to switch doors (though there are idiots who insist otherwise) â€" at least if you want a car rather than a goat. Explaining why is also easy: with the staying strategy, you only win if you initially chose the door with the car, which has a probability of 1/3; with the switch strategy, you only lose if you initially chose the door with the car, which again has a probability of 1/3.

4. The Unexpected Hanging Pardox hinges on what constitutes an 'unexpected hanging.' Even if the prisoner were to end his argument with excluding Friday only, once he has logically excluded Friday as his exectution day, then he no longer expects the hanging on Friday, which means that his own logic has folded back and destroyed itself. The conclusion that Friday would be excluded is dependent on the fact that the prisoner could still expect Friday to be a possible day of execution, and once that changed, that particular argument has had removed from it one of its vital premises and so its conclusion has lost its support. In other words, there's nothing wrong with logic, just with the prisoner's argument.

5. The Grandfather Paradox assumes that your own grandfather could be killed by yourself or as the direct consequence of anything you did in the past. This paradox actually has yielded somewhat to analysis. It involves the theoretical construction of a wormhole time machine and asking what kinds of boundary conditions can lead to a ball from the future knocking itself in the past off a path into the wormhole. Turns out, there are only two possible outcomes: the future ball misses altogether, and the past ball continues unmolested to miss itself; or the future ball hits the past ball, but not only does not prevent itself going into the wormhole mouth, but proturbs it in just the right way so that it hits itself in the future in such a way to send it careening into the wormhole at just the right angle to knock itself... well, you get the idea.

So the tentative conclusion is that you cannot kill your own grandfather this way â€" physics will simply not allow it to happen. Some circumstance will prevent his death: you will miss the fateful moment, your grandfather will survive your assault, the time machine will simply fail to function, or will kill you outright. If you survive the experience, you will find that the future condition of the world will be absolutely consistent with your experience in the past: there are signs that you were there, in the past; and/or your grandfather will recount a miraculous survival with some crazed maniac.

6. The Barber Paradox is not an infinite regression, because the casual analysis simply oscillates between two distinct states, not cause the unrestricted spawning of a chain of new propositions that support earlier propositions. There's only one issue to resolve: does the barber shave himself or not?

The resolution to the paradox is the same as the resolution to Russel's paradox, because the barber paradox is Russel's paradox in disguise: the barber cannot exist as described. Either there is a barber where the rule does not extend to himself (in which case, he's free to shave himself or not at his pleasure) or there is no barbar at all and you have been told a fib.

7. The Fletcher's Paradox is just straight-up sophistry. The scenario as described is one in which all states of motion are indistinguishable. And when I say all states of motion, I do mean all states of motion, including the arrow being stationary. You cannot in the situation described say that the arrow is moving, but you also cannot say that it is stationary either, because that's also a state of motion and to say the arrow is stationary requires exactly the same look-ahead or -behind that would allow you to say that the arrow is in motion. There is no paradox, but rather you have been presented with a situation where there simply isn't enough information to answer the question.

8. The Epimenides Paradox is again not an infinite regression, because again the only issue at stake is whether the statement "this statement is false" is false or not, and does not spawn an infinite number of propositions. Raymond Smullyan has I think the most thorough deconstruction of this paradox by recognizing that the truth or falsity of a statement depends on what the statement means. Only when you have deciphered what the statement means can you then decide on the truth or falsity of the statement by comparing its meaning to the actual state of affairs presented. But, for the statement "this statement is false," the truth of the statement depends on its own meaning, but that meaning depends on the truth of the statement itself. Smullyan resolved the paradox by pointing this out and claiming (I think sensibly) that the only statements that can be said to be true or false are those that are well-founded â€" where it is possible to decide the meaning of a statement without knowing whether it is true or false. "This statement is false" is not well-founded, and therefore cannot be said to be either true or false.

This simple form of the Epimenides Paradox is the most interesting because here is where we get to some real philosophical meat. The classic forms are less interesting: the clasic Epimenides Paradox is that Epimenides, a Cretan, states, "All Cretans are liars!" The proper resolution is that Epimenides is lying and that there is at least one honest Cretan â€" just not him at that particular moment. The other form is, on the Island of Knights and Knaves, an inhabitant is claimed by Smullyan to have said, "I am a knave." The resolution to this paradox is that Smullyan is not a knight. Of course, having told a truth sometime in his life, Smullyan is not a knave either.

9. The Sorites' Paradox comes from treating a fuzzy notion like a "heap" as if it were a precise one. As you take away grains of sand, the pile becomes less and less heap-like. When you get to a few grains, you're much less inclined to consider the collection a "heap" as you were when there were a million grains. If you haven't recinded your designation that the collection is a heap yet, you will be more likely to do so with each grain removed and nobody at that point could fault you for it, and almost all participants would have recinded their designation by the time the collection reached one grain. This is the proper conclusion, not "A heap can be a single grain of sand, or there's no such thing as a heap."

10. The Raven Paradox is only a 'paradox' because logicians are trying to evaluate empirical evidence, which logic is ill-equipped to do.

Thing is, if you had absolute assurance that you have seen all non-black objects and observed them to be not ravens, then you can indeed say logically that all ravens are black, because you have exhausted the pool of non-black objects and have not found a single raven amongst them. The only group where you can find ravens is then in the black objects.

Logic does not deal well with trends that show up only in the aggragate, as empirical evidence often does. You have to go to more powerful tools to properly evaluate such evidence. Statistics is one field that does so. Sure, that green apple is only one of many, many non-black objects that may have been chosen, but if sufficient randomization conditions for sampling can be satisfied, you can show that observing that green apple absolutely gives you some non-zero support for the plausibility that all non-black objects are not crows (albeit slim), and consequently for the contrapositive hypothesis that all crows are black.

Practically, I have very good assurance that "all crows are black" is likely wrong, because albinoes exist in all vertibrate animals (crows are vertibrate animals), and an albino cannot sensibly be called "black." Therefore, an albino crow is quite likely to have existed at some point in time, and can be fairly called a "non-black crow."

Deserves donations: 

[Solitary]

1. Reality isn't strictly logical.  Logic was invented to make "reductio ad absurbum" arguments ... like the arrow paradox.  Later Aristotle and the Stoics invented positive logic, thus making Euclid's work possible (math organized by deduction, rather than just random statements).  The problem is, that logic only works, as long as its axioms are true ... but in some cases they are not.  Similarly Euclidean geometry works, as long as its axioms are true, which in case of the Earth's surface, they are not.  Logic isn't true ... it simply is a way to make fewer mistakes while reasoning.  There are plenty of fallacies still available to step in, that logic won't save you from.

2. in the first example, this is true of your own body.  Science has now shown that no cell of yours, not even the neural cells, are the same as you started with, after three years.  So are you still you?  Buddha would answer ... of course not!

Buddha answers: " I may not be my same physical self, but I am still the same me created by a physical brain that is not my same physical self.   He! He! Is a candle flame always the same candle flame, and where does it go when it goes out?

[Baruch]

Hakurei Reimu ... very impressive.

Solitary ... technically Buddha wouldn't answer that way, but many materialists would.  Buddha was not a materialist.  Next time ascribe to Confucius and put it in a random fortune cookie ;-)  I can't agree with you regarding the candle flame either ... Heraclitus would have a fit if I did.

[GSOgymrat]

paradox's are always fun to create speculation around, but they more seem to just serve as plot dynamics for fictional writing more then anything ever testable.

For example the surprise exam paradox.

If the instructor gave an exam on the next to last day of class and then a different exam on the last day of class the second exam would certainly come as a surprise.

[Solitary]

Hakurei Reimu ... very impressive.

Solitary ... technically Buddha wouldn't answer that way, but many materialists would.  Buddha was not a materialist.  Next time ascribe to Confucius and put it in a random fortune cookie ;-)  I can't agree with you regarding the candle flame either ... Heraclitus would have a fit if I did.

The only teachings of Buddha I take seriously are those agreed upon by the Buddhist council of 241 BC, that are accepted as genuine, all the various Buddhist schools have been corrupted by Christianity, Hinduism, and even Islamic teachings. Also, Buddha was not static in his beliefs and only his latest beliefs should be considered. I'm not going to list them because I believe you know what I mean.

He proposed a theology without a deity, a psychology without a soul; he repudiates animism in every form, even in the case of man. He agrees with Heraclitus and Bergson about the world, and with Hume about the mind. Even the ego is not an entity distinct from those mental states; it merely the continuation of those states, the remembrance of earlier by later states, together with the mental and moral habits, the dispositions tendencies, of the  organism. The succession of the mythical will superadded to them, by the determinism of heredity, habit, environment and circumstances.

The mind is only mental states, this ego or soul is only a character or prejudice formed by helpless inheritance and transient experience, can have no immortality in  any sense  that implies the continuance of the individual. What about Nirvana? His followers have given the word every meaning under the sun. But Buddha said it was the complete annihilation of self: the reward of the highest saintliness is never to be reborn. When we have learned to love not our separate life, but all men and all living things, then at last we shall find peace. He hardly sounds like he isn't a materialist to me.

[Mike Cl]

The only teachings of Buddha I take seriously are those agreed upon by the Buddhist council of 241 BC, that are accepted as genuine, all the various Buddhist schools have been corrupted by Christianity, Hinduism, and even Islamic teachings. Also, Buddha was not static in his beliefs and only his latest beliefs should be considered. I'm not going to list them because I believe you know what I mean.

He proposed a theology without a deity, a psychology without a soul; he repudiates animism in every form, even in the case of man. He agrees with Heraclitus and Bergson about the world, and with Hume about the mind. Even the ego is not an entity distinct from those mental states; it merely the continuation of those states, the remembrance of earlier by later states, together with the mental and moral habits, the dispositions tendencies, of the  organism. The succession of the mythical will superadded to them, by the determinism of heredity, habit, environment and circumstances.

The mind is only mental states, this ego or soul is only a character or prejudice formed by helpless inheritance and transient experience, can have no immortality in  any sense  that implies the continuance of the individual. What about Nirvana? His followers have given the word every meaning under the sun. But Buddha said it was the complete annihilation of self: the reward of the highest saintliness is never to be reborn. When we have learned to love not our separate life, but all men and all living things, then at last we shall find peace. He hardly sounds like he isn't a materialist to me.

Do you really think Buddha was one particular man?  From what I've learned (which is kind of slim, really) Buddha is also a myth.  The says of Buddha have been collected much like the Gospel of Thomas, only with more structure.

[Solitary]

I have thought of that too after reading what his followers have said about him, even now. But what he said had to come from someplace, even if not from him it is pretty profound in his original form.  I think, like Jesus, he has been mythicized whether he existed or not. I have compared the original teachings of his to modern teachings of Buddhism, and it is obvious they have been updated to the times and modern religious teachings. For some reason people have to make him and Jesus into a miracle worker and a god. The way Buddhism is taught now doesn't resemble what he taught---there were no gods, God, prayers, rituals, shall not's, black and white thinking or rules, just a philosophy for living free of pain and suffering if one wants to. And he never thought he was divinely inspired or a God, even if the Hindu's think he is. He never thought life in his later life was sacred either with so much pain and suffering. Those Magic Mushrooms finally did him in. He was kind of an ass to leave his wife and children to find out why there was so much pain and suffering in the world, even if he did discover not to form attachments to anything, even life and death.

[Baruch]

Extra credit to ... Solitary.  Very nice outline.  But you are surprisingly orthodox in your tastes, for an atheist ;-)

I like Thich Nhat Han's version of the bio of Buddha ... Old Path White Clouds.

As best I can tell, the Buddha was regarded as a historical person in the time of Emperor Ashoka ... but then Emperor Ashoka was promoting his own version as a state religion.  Constantine may have copied this 500 years later.

https://www.youtube.com/watch?v=Veldz5-80aE