Seasons
This is a forum or general chit-chat, small talk, a "hey, how ya doing?" and such. Or hell, get crazy deep on something. Whatever you like.
Posts 4,414 - 4,425 of 6,170
a mental concept such as math
What is so mental about Math? Of course, our mathematical concepts are mental entities in some sense, but so are our concepts of physics, sex (at last, my favorite subject), geography, and so on. I cannot see that mathematical concepts are any more mental than any others.
Mathematical objects, such as numbers, are not particularly mental. If numbers were mental entities, then they could not have existed before there were any minds. But there was a whole number between 2 and 4 long before there were any minds in the universe. According to Physics, the universe obeyed certain mathematical laws from the first moment of its existence. Likewise, if all minds in the universe were to die out, not one truth of mathematics would disappear. Pi was a transcendental number long before anyone had the concept of pi or the concept of a transcendental number.
Math appears 'mental' to people because one can do Math just by thinking. This does not imply that the number 2 is somehow in our brains.
The upside to all this is, that we have done our moral duty if we did our best.
I agree. But our best to... what?
I would say our best to avoid committing any evil acts ourselves, since this is the only choice that is truly within our power to make.
It seems you would advocate doing our best to minimize the net evil and maximize the net good by gambling on probable outcomes. But if you employ evil means in this pursuit, you're playing a game you can't know the odds on. And if you play it long enough, you are bound to lose - that's just the nature of gambling.
Given his beliefs at the time, it would have been morally wrong not to have tried to throw the switch.
I agree - he did his best, and throwing a switch with the intention of preventing evil is not only justifiable, but failing to do so would be of itself an evil act. The outcome is not the determining factor - the intention is. The choice here is between killing lots of people or none at all, and if he makes an honest mistake, that does not detract from his good intention (though he will probably still blame himself - that's human nature.)
A choice between good and evil is not the same as a choice between two evils.
would say our best to avoid committing any evil acts ourselves, since this is the only choice that is truly within our power to make.
Well, I imagine that everyone would agree with this. It's hard to believe that someone is going to say, "No, you should commit evil acts now and thhen!" But if two people disagree about what acts are evil, this principle is not going to be of much use, since it does not give any specific criteria. If two people disagree about what is evil, they will disagree about what this principle entails.
It seems you would advocate doing our best to minimize the net evil and maximize the net good by gambling on probable outcomes.
Actually I don't accept minimax as a general rule in morality, although it does apply in some cases.
There is a famous thought experiment called the "Inhospitable Hospital." A man, X, comes in to have his tonsils out. The operation goes well, and he is sleeping in a hospital bed, still knocked out by anesthesia.
5 people are brought into the emergency room: they have been in a terrible auto accident (not their fault). One of them needs a heart transplant, two need kidney transplant, a fourth needs a liver, and the fifth a pancreas. Otherwise they will die.
Unfortunately, the hospital is entirely out of stock on these items!
Then someone says, "But we have Mr. X! He has healthy organs of all those kinds! Let's just use his!" Appealing to maximization, he continues, "If we distribute X's organs, 5 people will live, and one will die. If we don't, one person will live and 5 will die." Clearly the arithmetic is against the survival of Mr. X!
But many people, including myself, have strong intuitions that it would be morally wrong to use Mr. X's organs this way (let us assume that his consent cannot be obtained).
So, since maximizing gives the wrong answer in at least one case, it is not a universaly valid principle.
Well, I imagine that everyone would agree with this. It's hard to believe that someone is going to say, "No, you should commit evil acts now and thhen!"
I would agree that torturing a baby to death is, of itself, evil. But you seem to be saying that if there is a greater good you consider to be achieveable (saving the other babies,) it might under certain circumstances be permissible to torture a baby to death.
I'm just very suspicious of the "greater good" and "lesser of two evils"
if I think they are not useful, that is 'true for me', and if you think they are useful, that is 'true for you',
With respect to morals, you are correct, although I do not like the the phrase "true for you" because it seems to imply that subjective truths are on par with the outside common reality of things that exist with or without humans. When your actions effect others in a common reality of what we think of a the real world, however, I can say that I will work according to what moral or useful in my own view. My view is subjective. I will act on it anyway.
As far as I can see, we don't have the slightest control over whether 2+2=4. How would we go about arranging that 2+2=5
One of my favorite physics/math theorems is 2+2=5 for very large values of 2. It illustrates two principles very well.
On a more serious note, 2+2 is NOT always 4. Mix together 2 gallons of water with 2 gallons of alcohol, and you won't get 4 gallons of liquid. The molecules slide by one another somehow, so that the resulting liquid takes up less space. (I think it's alcohol; it's been a while since I read up on this) On the other hand, the weights will add as expected. So, say, 2 pounds of water plus 2 pounds of alcohol will yield 4 pounds of liquid.
What about 2+2=1? This could easily apply in a situation with interlocking parts, that won't stay interlocked until all have been connected together. Sure, you can count the four separate parts, but the resulting...thing...is a single unit in its own right.
"Mathematical objects, such as numbers, are not particularly mental. If numbers were mental entities, then they could not have existed before there were any minds." (Irina)
BTW, my color tags have been working intermittently--I put them there but they may not be in red now. I hope you know your quotes.
Objects existed regardless of human existence. "Numbers" as such, did not (though it's possible others non humans may develop a concept of numbers just as it is possible non humans may develop a concept of language). We created numbers to describe the word as we see it. They are a mental construct, though we can write symbols for these ideas down just as we can write down symbols for words.
Mathematics is an axiomatized deductive system. You can start with a set of postulates, say Peno's axioms,
"P1. 0 is a number
P2. The successor of any number is a number
P3. No two numbers have the same successor
P4. 0 is not the successor of any number
P5. If P is a property such that (a) 0 has the property P, and (b) whenever a number n has the property P, then the successor of n also has the property P, then every number has the property P."
From there we can define various operations such as addition, subtractions, multiplication and division. We could make some adjustments to this system, but in essence, all math can be deprived form these primitives and rules, and it is not dependent on empirical evidence.
"But there was a whole number between 2 and 4 long before there were any minds in the universe."
What makes you think that is so? Numbers are tools created by humans to describe various aspects, objects and relationships, but they only describe things, they are not things themselves.
"According to Physics, the universe obeyed certain mathematical laws from the first moment of its existence."
No. Physics gives us the means to describe various principles and relationships, but it only describes what is going on, it doesn't dictate what happens.
"Likewise, if all minds in the universe were to die out, not one truth of mathematics would disappear. Pi was a transcendental number long before anyone had the concept of pi or the concept of a transcendental number."
I disagree. The label "transcendental" or "pi" or "number" does not exist unless a mind defines and applies it. These may describe various aspects of reality, but they are not reality. They may be useful for our understanding (subjectively useful to me or others as we judge it) but they do not exist outside of our minds.
Posts 4,414 - 4,425 of 6,170
Mathematical objects, such as numbers, are not particularly mental. If numbers were mental entities, then they could not have existed before there were any minds. But there was a whole number between 2 and 4 long before there were any minds in the universe. According to Physics, the universe obeyed certain mathematical laws from the first moment of its existence. Likewise, if all minds in the universe were to die out, not one truth of mathematics would disappear. Pi was a transcendental number long before anyone had the concept of pi or the concept of a transcendental number.
Math appears 'mental' to people because one can do Math just by thinking. This does not imply that the number 2 is somehow in our brains.
Dear Psimagus (4410):
It seems to me that our moral responsibilities do not depend on our having perfect knowledge; if they did, we would have no moral responsibilities at all, for we never have perfect knowledge.
Our moral responsibilities depend on what is true to the best of our knowledge.
Suppose I see someone about to eat something that I have good reason to believe is toxic. I am morally obligated to try to warn her. It is true that I could be mistaken in any number of my relevant beliefs. Perhaps it's not toxic; perhaps she's really an alien and it is nourishing to her; perhaps she is an evil dictator, and by letting her eat it I will liberate an entire people; perhaps she is deaf and will not hear my warning; perhaps she speaks a language in which the phoneme sequence of "Watch out! That's toxic!" means, "Lucky you! That stuff is delicious and nourishing!' Perhaps she despises me so much that she will eat it just because I tried to discourage her from doing so. Perhaps, perhaps, perhaps. You can never be sure what the consequences of your acts will be. Welcome to the human condition!
In spite of all the pitfalls of trying to figure out the universe, there are things that I am most justified in believing at any given time. If, to the best of my knowledge, the material will be poisonous to her, and if, to the best of my knowledge, she is not an evil dictator, and so on, then I am morally obligated to warn her even though every last one of my relevant belief might possibly be false.
The upside to all this is, that we have done our moral duty if we did our best. If I sincerely try to do the right thing, to the best of my ability and the best of my knowledge, this is all that can be asked of me. A switchman sees two long passenger trains heading rapidly toward each other, and it comes into his head that the switch is set so that they will collide. In order to avert disaster, he rushes to the switch and throws it. Alas, he is mistaken! The two trains would have passed each other on different tracks, if he had let the switch alone; instead, there is no a horrible accident killing hundreds of people. Is he morally at fault? Not at all. Given his beliefs at the time, it would have been morally wrong not to have tried to throw the switch.
It seems to me that our moral responsibilities do not depend on our having perfect knowledge; if they did, we would have no moral responsibilities at all, for we never have perfect knowledge.
Our moral responsibilities depend on what is true to the best of our knowledge.
Suppose I see someone about to eat something that I have good reason to believe is toxic. I am morally obligated to try to warn her. It is true that I could be mistaken in any number of my relevant beliefs. Perhaps it's not toxic; perhaps she's really an alien and it is nourishing to her; perhaps she is an evil dictator, and by letting her eat it I will liberate an entire people; perhaps she is deaf and will not hear my warning; perhaps she speaks a language in which the phoneme sequence of "Watch out! That's toxic!" means, "Lucky you! That stuff is delicious and nourishing!' Perhaps she despises me so much that she will eat it just because I tried to discourage her from doing so. Perhaps, perhaps, perhaps. You can never be sure what the consequences of your acts will be. Welcome to the human condition!
In spite of all the pitfalls of trying to figure out the universe, there are things that I am most justified in believing at any given time. If, to the best of my knowledge, the material will be poisonous to her, and if, to the best of my knowledge, she is not an evil dictator, and so on, then I am morally obligated to warn her even though every last one of my relevant belief might possibly be false.
The upside to all this is, that we have done our moral duty if we did our best. If I sincerely try to do the right thing, to the best of my ability and the best of my knowledge, this is all that can be asked of me. A switchman sees two long passenger trains heading rapidly toward each other, and it comes into his head that the switch is set so that they will collide. In order to avert disaster, he rushes to the switch and throws it. Alas, he is mistaken! The two trains would have passed each other on different tracks, if he had let the switch alone; instead, there is no a horrible accident killing hundreds of people. Is he morally at fault? Not at all. Given his beliefs at the time, it would have been morally wrong not to have tried to throw the switch.
I agree. But our best to... what?
I would say our best to avoid committing any evil acts ourselves, since this is the only choice that is truly within our power to make.
It seems you would advocate doing our best to minimize the net evil and maximize the net good by gambling on probable outcomes. But if you employ evil means in this pursuit, you're playing a game you can't know the odds on. And if you play it long enough, you are bound to lose - that's just the nature of gambling.
I agree - he did his best, and throwing a switch with the intention of preventing evil is not only justifiable, but failing to do so would be of itself an evil act. The outcome is not the determining factor - the intention is. The choice here is between killing lots of people or none at all, and if he makes an honest mistake, that does not detract from his good intention (though he will probably still blame himself - that's human nature.)
A choice between good and evil is not the same as a choice between two evils.
There is a famous thought experiment called the "Inhospitable Hospital." A man, X, comes in to have his tonsils out. The operation goes well, and he is sleeping in a hospital bed, still knocked out by anesthesia.
5 people are brought into the emergency room: they have been in a terrible auto accident (not their fault). One of them needs a heart transplant, two need kidney transplant, a fourth needs a liver, and the fifth a pancreas. Otherwise they will die.
Unfortunately, the hospital is entirely out of stock on these items!
Then someone says, "But we have Mr. X! He has healthy organs of all those kinds! Let's just use his!" Appealing to maximization, he continues, "If we distribute X's organs, 5 people will live, and one will die. If we don't, one person will live and 5 will die." Clearly the arithmetic is against the survival of Mr. X!
But many people, including myself, have strong intuitions that it would be morally wrong to use Mr. X's organs this way (let us assume that his consent cannot be obtained).
So, since maximizing gives the wrong answer in at least one case, it is not a universaly valid principle.
I would agree that torturing a baby to death is, of itself, evil. But you seem to be saying that if there is a greater good you consider to be achieveable (saving the other babies,) it might under certain circumstances be permissible to torture a baby to death.
I'm just very suspicious of the "greater good" and "lesser of two evils"
With respect to morals, you are correct, although I do not like the the phrase "true for you" because it seems to imply that subjective truths are on par with the outside common reality of things that exist with or without humans. When your actions effect others in a common reality of what we think of a the real world, however, I can say that I will work according to what moral or useful in my own view. My view is subjective. I will act on it anyway.
??? As far as I can see, we don't have the slightest control over whether 2+2=4. How would we go about arranging that 2+2=5?
2 plus 2 equals 5 because of how we define numbers, addition and equal. I am basing my views primary on the works of Hempels' "On the Nature of Mathematics"
http://www.ditext.com/hempel/math-frame.html. Hemple said, for example, "In the light of this remark, consider now a simple "hypothesis" from arithmetic: 3 + 2 = 5. If this is actually an empirical generalization of past experiences, then it must be possible to state what kind of evidence would oblige us to concede the hypothesis was not generally true after all. If any disconfirming evidence for the given proposition can be thought of, the following illustration might well be typical of it: We place some microbes on a slide, putting down first three of them and then another two. Afterwards we count all the microbes to test whether in this instance 3 and 2 actually added up to 5. Suppose now that we counted 6 microbes altogether. Would we consider this as an empirical disconfirmation of the given proposition, or at least as a proof that it does not apply to microbes? Clearly not; rather, we would assume we had made a mistake in counting or that one of the microbes had split in two between the first and the second count. But under no circumstances could the phenomenon just described invalidate the arithmetical proposition in question; for the latter asserts nothing whatever about the behavior of microbes; it merely states that any set consisting of 3 + 2 objects may also be said to consist of 5 objects. And this is so because the symbols "3 + 2" and "5" denote the same number: they are synonymous by virtue of the fact that the symbols "2," "3," "5," and "+" are defined (or tacitly understood) in such a way that the above identity holds as a consequence of the meaning attached to the concepts involved in it."
2 plus 2 equals 5 because of how we define numbers, addition and equal. I am basing my views primary on the works of Hempels' "On the Nature of Mathematics"
http://www.ditext.com/hempel/math-frame.html. Hemple said, for example, "In the light of this remark, consider now a simple "hypothesis" from arithmetic: 3 + 2 = 5. If this is actually an empirical generalization of past experiences, then it must be possible to state what kind of evidence would oblige us to concede the hypothesis was not generally true after all. If any disconfirming evidence for the given proposition can be thought of, the following illustration might well be typical of it: We place some microbes on a slide, putting down first three of them and then another two. Afterwards we count all the microbes to test whether in this instance 3 and 2 actually added up to 5. Suppose now that we counted 6 microbes altogether. Would we consider this as an empirical disconfirmation of the given proposition, or at least as a proof that it does not apply to microbes? Clearly not; rather, we would assume we had made a mistake in counting or that one of the microbes had split in two between the first and the second count. But under no circumstances could the phenomenon just described invalidate the arithmetical proposition in question; for the latter asserts nothing whatever about the behavior of microbes; it merely states that any set consisting of 3 + 2 objects may also be said to consist of 5 objects. And this is so because the symbols "3 + 2" and "5" denote the same number: they are synonymous by virtue of the fact that the symbols "2," "3," "5," and "+" are defined (or tacitly understood) in such a way that the above identity holds as a consequence of the meaning attached to the concepts involved in it."
One of my favorite physics/math theorems is On a more serious note, 2+2 is NOT always 4. Mix together 2 gallons of water with 2 gallons of alcohol, and you won't get 4 gallons of liquid. The molecules slide by one another somehow, so that the resulting liquid takes up less space. (I think it's alcohol; it's been a while since I read up on this) On the other hand, the weights will add as expected. So, say, 2 pounds of water plus 2 pounds of alcohol will yield 4 pounds of liquid.
What about 2+2=1? This could easily apply in a situation with interlocking parts, that won't stay interlocked until all have been connected together. Sure, you can count the four separate parts, but the resulting...thing...is a single unit in its own right.
BTW, my color tags have been working intermittently--I put them there but they may not be in red now. I hope you know your quotes.
Objects existed regardless of human existence. "Numbers" as such, did not (though it's possible others non humans may develop a concept of numbers just as it is possible non humans may develop a concept of language). We created numbers to describe the word as we see it. They are a mental construct, though we can write symbols for these ideas down just as we can write down symbols for words.
Mathematics is an axiomatized deductive system. You can start with a set of postulates, say Peno's axioms,
"P1. 0 is a number
P2. The successor of any number is a number
P3. No two numbers have the same successor
P4. 0 is not the successor of any number
P5. If P is a property such that (a) 0 has the property P, and (b) whenever a number n has the property P, then the successor of n also has the property P, then every number has the property P."
From there we can define various operations such as addition, subtractions, multiplication and division. We could make some adjustments to this system, but in essence, all math can be deprived form these primitives and rules, and it is not dependent on empirical evidence.
What makes you think that is so? Numbers are tools created by humans to describe various aspects, objects and relationships, but they only describe things, they are not things themselves.
No. Physics gives us the means to describe various principles and relationships, but it only describes what is going on, it doesn't dictate what happens.
I disagree. The label "transcendental" or "pi" or "number" does not exist unless a mind defines and applies it. These may describe various aspects of reality, but they are not reality. They may be useful for our understanding (subjectively useful to me or others as we judge it) but they do not exist outside of our minds.
Irnia, no doubt we have. 
I was just thinking that this was starting to sound like the quantum physics debate because we are returning to similar issues involving whether mechanism merely describes a phenomenon, or is itself the phenomenon. Not that I want to start that again.
Don't worry, soon we'll be able to upload again and I'll leave the boards alone.
I was just thinking that this was starting to sound like the quantum physics debate because we are returning to similar issues involving whether mechanism merely describes a phenomenon, or is itself the phenomenon. Not that I want to start that again.Don't worry, soon we'll be able to upload again and I'll leave the boards alone.
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