‘It is strange to say that God is a logical impossibility, but you don’t know whether God exists. If God is a logical impossibility, then surely She can’t exist, and so you know that She doesn’t exist.’
I don’t get it. Why can’t I be unsure about the truth value of something just because it’s a logical impossibility? My understanding of logic isn’t exhaustive.
BattleGround God is bad arguing. It seems to have been created and tested by one person who had strong ideas about the type of person that was going to take it. The ‘contradictory statements’ that it identifies are 1. not actually contradictory, but 2. not presented in conjunction to each other, meaning that you have to take their re-wording of previous statements as consistent. They are not constant—they replace wording indicating a broad idea with wording requiring a narrow (and specifically Judaic/Christian/Islamic) definition in order to ‘catch you out’. Whacking through all the random things they think that you might believe (mostly wisely chosen if you are taking an exit poll at a church, but not so good on a philosophy site) makes it very boring to find their errors… But errors there are. Whoever wrote it was much more interested in catching out theists with murky ideas of rhetoric and not particularly interested in defining beliefs and testing for contradictions.
This person would not last 5 minutes in a discussion with a real human. This is not a good model of how to talk to theists, nor will any non-rational theist bother to play this game with any intent of taking its conclusions as valid. Nor should they.
Earlier you said that even in the absence of independent evidence, it is justified to base one’s beliefs about the external world on a firm, inner-conviction. But now you do not accept that the serial murderer Peter Sutcliffe was justified in doing just that. The example of the killer has exposed that you do not in fact think that a belief is justified just because one is convinced of its truth. So you need to revise your opinion here. The intellectual sniper has scored a bull’s-eye!
and
Earlier you said that it is justified to base one’s belief about the external world on a firm inner conviction, even in the absence of any independent evidence for the truth of this conviction, but now you say it is not justified to believe in God on just those grounds. That’s a flagrant contradiction!
I answered the first question that way because I believe there are some inner convictions it is justified to base one’s beliefs on (for instance, the belief that there is an external world and that I am not a brain in a vat), but I do not believe this is true for all inner convictions. So that is not actually a contradiction.
I didn’t get any other “contradictions” and I suspect that it’s because I took everything very literally there.
Why can’t I be unsure about the truth value of something just because it’s a logical impossibility?
If you’re using logic to determine truth values, then a logical impossibility is false. The reason is that if something is logically impossible, then its existence would create a contradiction and so violate the Law of Noncontradiction.
Your logic sounds consistent. Thanks, I’m happy to accept the utility of the law of non-contradiction and therefore don’t believe in the logical impossibility of god anymore, not the logical impossibility of anything I conceive.
I’m not certain where the problem lies, but I suspect that you may be misunderstanding the term “logical impossibility”. It would not be used to indicate that you have come up with an argument that shows that something is impossible. Instead it would be used to indicate that something is actually impossible in any consistent universe.
To clarify, if I make the argument that 1. Socrates is a man, and 2. all men are mortal, that does not make it logically impossible for Socrates to live forever; it just means that I can show logically that Socrates won’t die as long as these statements hold.
Logically impossible things are generally things like a square circle (exactly 4 right angles and exactly 0 angles in the same 2d shape); if they exist, it is because you misunderstand the terms being used in some way; if someone claims that this qualifies as a square circle, they have misunderstood what I am trying to communicate.
Likewise, people may say that an entity cannot be perfectly good and have allowed the holocaust; this might qualify god as a logical impossibility—if we accept this judgement of morality, if we believe that god is perfectly good, and if we believe that the holocaust happened.
You could perhaps come up with a scenario in which God, being perfectly good, absolutely needed to implant memories of the holocaust into each of our memories.… or you could simply define god as an evil being. so I would say that “logical impossibility” is a bit strong.
To clarify, if I make the argument that 1. Socrates is a man, and 2. all men are mortal, that does not make it logically impossible for Socrates to live forever; it just means that I can show logically that Socrates won’t die as long as these statements hold.
Given this premise, I now agree that I misunderstood >‘the term “logical impossibility”.’
Though, I unfortunately don’t understand what it does mean. I’ll look it up now and see if that further clarifies.
So from the Wikipedia page, I now understand stand it as something whereby the components of the logical equation in some way denote that the other components are incompatible with it, perhaps they denote some character of the other components at a level of analysis beyond one particular level of characterisation or grouping.
However, if it also comes down to what a particular person can conceive as possibility, doesn’t that come down to a particular person’s ability to visualise, imagine or recombine concepts into a coherent whole—which almost certainly various between those more cognitively flexible and those who aren’t?
In the Wikipedia example, understand why the sky is blue, not just at the physical level but psychological level of description, helps me imagine why someone might claim something apparently absurd like “the sky isn’t a sky”.
btw,w hen I googled for logical impossibility to get the Wikipage it suggested this stack exchange question
if it also comes down to what a particular person can conceive as possibility
I think I see the problem. Whenever any philosopher says that something is logically impossible, they are specifically and openly aware that this is only conditionally true. For example, a square circle is only clearly a logical impossibility if the words square and circle mean the same thing every time I think them, including in the time period that I move from ‘square’ to ‘circle’; if the ideas of ‘square’ and ‘circle’ actually do have a referent, and I am not just deluded into feeling a clear sense of meaning when I think those words, (and including all defining terms [such as ‘right angle’]); if I am correct in believing that two non-identical things are necessarily not one thing; if I am correct in believing language can refer to things other than semantic relationships; and many other fun things, including the big one: the assumption that I exist and am thinking.
However, once you have gotten everyone on the same page, and we all admit that we cannot prove that we exist, we start talking about highly conditional realities, such as those in which BattleGround God is more than a deluded memory, in which the words on the LessWrong are entered by other people, realities in which computers and circles and ‘good’ actually exist in some meaningful sense…
...and we don’t all have the same set of conditionally accepted realities. Nor do we need to in order to make most arguments intelligible to both parties. As a matter of course, most of the things we talk about are propositioned on the existence of the external world as reported by our senses and the media. If we deviate from this, we specify this in some way.
And that explains logical impossibility… but then I realized that I hadn’t read your original question carefully enough.
‘It is strange to say that God is a logical impossibility, but you don’t know whether God exists. If God is a logical impossibility, then surely She can’t exist, and so you know that She doesn’t exist.’
BG has conflated “belief that God is a logical impossibility” and “you know that She doesn’t exist.” The second claim should be “you believe that She doesn’t exist.” BG tried too hard, and it fails. Next time, use a Real Philosopher(TM).
If I’ve understand correct, you’re saying that the probability that x doesn’t exist, can’t less than the probabiltiy that x is logically impossible.
The reason that it can be true, is because I’m not smart enough to interpret that complicated proposition whether it’s in symbolic form or even after I’ve managed to translate it into words.
Therefore, P(x doesn’t exist) may very well be < P(x is logically impossible), I have no idea.
It is definitely true that this could be someone’s subjective probability, if he he doesn’t understand the statement.
But if you do understand it, a thing which is logically impossible doesn’t exist, so the probability that a thing doesn’t exist will be equal to or higher than the probability that it is logically impossible.
I feel like I might understand now. Can I represent your points as follows:
all instances of things which are logically impossible also don’t exist
therefore, there are more things which don’t exist than those that are logically impossible
Assuming statement 1 is correct, without accepting a further premise I don’t feel compelled to accept the second premise. It sounds like things which are logically impossible may in fact be equivelant to things which don’t exist, and vice-versa. And that sounds intuitively compelling. If something was logically possible, it would happen. If it is wasn’t possible, it’s not going to happen. Or, the agent’s modelling of the world is wrong.
Importantly, I don’t accept premise 1, as I’ve indicated in another comment reply (something about how I find I’m wrong about the apparent impossibility of something, or possibility of something.)
I said “so the probability that a thing doesn’t exist will be equal to or higher than etc.” exactly because the probability would be equal if non-existence and logical impossibility turned out to be equivalent.
If you don’t agree that no logically impossible thing exists, then of course you might disagree with this probability assignment.
Well, the conclusion should read not “more things” but “at least as many”. Things might accidentally not exist.
I feel the fact that you reject premise 1 just means that you don’t really grasp the concept of impossibility, logical or otherwise… Or you have a different concept of existence.
The reason why I used a semi-formal notation was to suggest that if you formalise it all, you can actually prove “P(x doesn’t exist) ≥ P(x is impossible)” as a tautology. (Ignoring the issue that with specifically logical impossibility, you get into a bit of trouble with probability assignments to tautologies.)
Uhm, what? Why? Bla bla bla indeed. (Sorry, I couldn’t resist.) It’s not actually very relevant.
If you don’t believe that logical (or, for that matter, any other sort of) impossibility implies non-existence, then you are understanding either “logical impossibility” or “non-existence” in a way different from just about everybody else. So if there is any point to this discussion, it should be to elucide how you understand them.
Thanks for making that clear to me. I don’t like the idea of having inconstent terminology usage to everyone else, so in that case I’m at deep fault. A few minutes (hours?) ago I had a moment of clarity and I’m pretty sure I’m psychotic right now. I caught myself out in the delusion I’ve been having for a couple of days, which I have had in the past for unfortunately far longer, that society and economies are going to collapse and we’re going to be forced to farm or raid people and because I’m passive and shit at gardening I’ll die a horrible death. Which, I should have good reason to believe is absurd because economic collapses are extremely rare, highly unlikely in developed countries like ours, there are measures in place to intervene in food security crises, so on and so forthe. The point is, this is consistent my prolific shit posting over the last half-day which I will probably go back and perhaps get rid of the ones without comments. Meanwhile, this thread is probably going to be extremely interesting to me when I recover from this because it formalises how it captures, to some extent how I’ve been relating to the world. To some extent I miss that if I had managed to reply to your comment further into this state it might have been very interesting. On the other hand, perhaps if not for it, I wouldn’t have recognised that this indeed is a problem right now and my delusion isn’t just a single odd piece of psychosis admist normal thinking otherwise. Ok I better get off this thing and figure out to get some help so my assignments can still be submitted in time...I’ve lost so much karma in the last half day haha.
Unless this is some kind of self-doubt, or worry/anxiety thing and I’m just making a feel of myself to refuse actually updating my beliefs faced with compelling reason. I don’t know, I feel very odd. I’ll probably update this at some point. Unless something goes very wrong...a little while ago I was thinking of retiring this account and also how interesting it would be if someone wrote a suicide note on lesswrong. Ok I need to stop right now, this isn’t right or relevant. Bye.
“Impossible is just a big word thrown around by small men who find it easier to live in the world they’ve been given than to explore the power they have to change it. Impossible is not a fact. It’s an opinion. Impossible is not a declaration. It’s a dare. Impossible is potential. Impossible is temporary. Impossible is nothing.”
If you already know that square circles cannot exist, it follows that in fact they do not exist; nothing impossible happens, so a proposition like “I saw a square circle” automatically gets a truth value = 0 without having to bother examining it.
The purpose of knowing about confirmation bias is to always keep in mind that you tend to overly favor your own preferred hypothesis, so you must adopt a detached perspective and try to consider all alternative explanations.
But in this case we are dealing with the rules of logic. Unless you’re a follower of one of the many paraconsistent schools, there are no alternative explanations. The rules just work. It’s not confirmation bias to favor an explanation based on the rules of logic.
Denying square circles a priori is not the same as denying black swans a priori: swans are real things in the real universe, and as such can have limitless variations. Swans that fall outside of their former definition force us to update the definition. A black swan is not a logical impossibility. Circles, on the other hand, are abstractions in our heads, and only have one form. Circles that fall outside of their definition are just not circles.
Going back to your original example: IF God is a logical impossibility, no instantiation of a God in the real universe will occur, because, again, nothing impossible happens. You don’t need to bother examining the truth value of something that in principle can’t occur, for the same reason geometrists don’t go on field trips in search for square circles. You can trust logic; it simply won’t happen.
Denying square circles a priori is not the same as denying black swans a priori: swans are real things in the real universe, and as such can have limitless variations. Swans that fall outside of their former definition force us to update the definition. A black swan is not a logical impossibility. Circles, on the other hand, are abstractions in our heads, and only have one form. Circles that fall outside of their definition are just not circles.
You’re implying that square circles are platonic concepts that aren’t empirically verifiable. I would argue that they entirely are, just the task would be too difficult to be worth anyone’s while. Just because something is in someone else’s field of perception, doesn’t make it any less real if it’s a particular hypothesised shape, or a particular hypothesised colour. I could simply ask someone if they’ve seen a square circle and if everyone says no, can comfortably believe there aren’t any till I perhaps see one, just as if I ask about black swans and if everyone says no, comfortable b eleive they don’t exist unless I see one.
nothing impossible happens
This is the assumption made in your last paragraph and I completely disagree. I’ve frequently found that things I thought were impossible happened. That kind of dogmatic certainty sounds awefully dangerous. While thinking about logic in that kind of self-consistent, but externally inconsistent sense seems to be absurd. One can describe a particular mythology that might make sense in a self-consistent way, but when related to other systems of belief isn’t coherent.
There is a difference between things that are impossible per se and things we think are impossible. Logical impossibilities are impossible regardless of anyone’s opinion. Good luck with that square circle survey.
You’re implying that square circles are platonic concepts that aren’t empirically verifiable.
Yes, any real-world circle is imperfect and deviates from being a circle in the mathematical sense. Something that’s square deviates a lot from the circle in the mathematical sense and is thus no real circle.
Absence of evidence is evidence of absence. P(H | E) > P(H) if and only if P(H | ~E) < P(H). Absence of evidence may be very weak evidence of absence, but it is evidence nonetheless. (However, you may not be entitled to a particular kind of evidence.)
You cannot expect[2] that future evidence will sway you in a particular direction. “For every expectation of evidence, there is an equal and opposite expectation of counterevidence.”
Then I may not hold my current attitude. But I don’t see reason to believe those premises.
While I don’t agree with the way they phrased their explanation, it’s akin to saying “I’m not sure if 2 + 2 = 4 is true, but I am sure it can’t equal anything else.” Then falling back to “but there could be oddities in the foundation of mathematics that I’m not aware of” when pressed on the inconsistency.
If you claim that your understanding of logic isn’t exhaustive, I don’t see how you can also claim that X is logically impossible. (“I’m not a car expert but there is no possible way the problem is with the engine”)
Thanks for that analogy, that gives me a new way to think about it.
I believe I can agree with the 2 + 2 = 4 theorem because I already agree with agreement in the summation of the components represented.
To illustrate:
If I put up 2 figures, then another 2 fingers, I can reliable get consensus from a survey of people and my own intuition/memory that it represents 4 fingers, and correspondingly the number 4.
Meanwhile, I don’t have any kind of clear idea of what people are on about when they say god, so doing any logical operation from there is unclear. The reason that understanding the component is important to doing an operation is that it may have an implicit modifier that affects the logical operation in and of itself.
For instance:
2 + (-2) = 4
the (-2), is not the same as 2, it’s a different component which may sometimes appear to be a 2, but getting consensus about it from people, or figuring out what to do with your fingers when you read it, might confuse people into giving an answer that is less consistent.
It appears that I’m using a consensus theory of truth. I guess that’s neccersary for any kind of discussion with more than one participant anyhow.
Thanks, that’s an interesting point, but I don’t think it can get a probability of being true or false because that would imply that the underlying concept can somehow be demonstrated true or false.
If it can be demonstrated true or false, then it’s logical impossibility would be 0%, because anything that is testable and has yet to be tested has a possibility of being true or false, however small that may be, or else it’s self-evident (100%).
Else, it cannot be demonstrated true or false, in which case the logical impossibility is 100%.
But the whole point of the original post was that you had logical uncertainty. That’s why in Bayesian reasoning you can’t have probabilites of 0 and 1 - to allow for the possibility, however small, of updating.
Thanks, I don’t really understand where I was coming from before. Maybe my new found understanding of the terminology around uncertainty has finally updated my intuitions :)
I just tried this ‘battleground god’ thing and it told me:
I don’t get it. Why can’t I be unsure about the truth value of something just because it’s a logical impossibility? My understanding of logic isn’t exhaustive.
BattleGround God is bad arguing. It seems to have been created and tested by one person who had strong ideas about the type of person that was going to take it. The ‘contradictory statements’ that it identifies are 1. not actually contradictory, but 2. not presented in conjunction to each other, meaning that you have to take their re-wording of previous statements as consistent. They are not constant—they replace wording indicating a broad idea with wording requiring a narrow (and specifically Judaic/Christian/Islamic) definition in order to ‘catch you out’. Whacking through all the random things they think that you might believe (mostly wisely chosen if you are taking an exit poll at a church, but not so good on a philosophy site) makes it very boring to find their errors… But errors there are. Whoever wrote it was much more interested in catching out theists with murky ideas of rhetoric and not particularly interested in defining beliefs and testing for contradictions.
This person would not last 5 minutes in a discussion with a real human. This is not a good model of how to talk to theists, nor will any non-rational theist bother to play this game with any intent of taking its conclusions as valid. Nor should they.
It was so painful!
I just took that.
and
I answered the first question that way because I believe there are some inner convictions it is justified to base one’s beliefs on (for instance, the belief that there is an external world and that I am not a brain in a vat), but I do not believe this is true for all inner convictions. So that is not actually a contradiction.
I didn’t get any other “contradictions” and I suspect that it’s because I took everything very literally there.
If you’re using logic to determine truth values, then a logical impossibility is false. The reason is that if something is logically impossible, then its existence would create a contradiction and so violate the Law of Noncontradiction.
Your logic sounds consistent. Thanks, I’m happy to accept the utility of the law of non-contradiction and therefore don’t believe in the logical impossibility of god anymore, not the logical impossibility of anything I conceive.
I’m not certain where the problem lies, but I suspect that you may be misunderstanding the term “logical impossibility”. It would not be used to indicate that you have come up with an argument that shows that something is impossible. Instead it would be used to indicate that something is actually impossible in any consistent universe.
To clarify, if I make the argument that 1. Socrates is a man, and 2. all men are mortal, that does not make it logically impossible for Socrates to live forever; it just means that I can show logically that Socrates won’t die as long as these statements hold.
Logically impossible things are generally things like a square circle (exactly 4 right angles and exactly 0 angles in the same 2d shape); if they exist, it is because you misunderstand the terms being used in some way; if someone claims that this qualifies as a square circle, they have misunderstood what I am trying to communicate.
Likewise, people may say that an entity cannot be perfectly good and have allowed the holocaust; this might qualify god as a logical impossibility—if we accept this judgement of morality, if we believe that god is perfectly good, and if we believe that the holocaust happened.
You could perhaps come up with a scenario in which God, being perfectly good, absolutely needed to implant memories of the holocaust into each of our memories.… or you could simply define god as an evil being. so I would say that “logical impossibility” is a bit strong.
Given this premise, I now agree that I misunderstood >‘the term “logical impossibility”.’
Though, I unfortunately don’t understand what it does mean. I’ll look it up now and see if that further clarifies.
So from the Wikipedia page, I now understand stand it as something whereby the components of the logical equation in some way denote that the other components are incompatible with it, perhaps they denote some character of the other components at a level of analysis beyond one particular level of characterisation or grouping.
However, if it also comes down to what a particular person can conceive as possibility, doesn’t that come down to a particular person’s ability to visualise, imagine or recombine concepts into a coherent whole—which almost certainly various between those more cognitively flexible and those who aren’t?
In the Wikipedia example, understand why the sky is blue, not just at the physical level but psychological level of description, helps me imagine why someone might claim something apparently absurd like “the sky isn’t a sky”.
btw,w hen I googled for logical impossibility to get the Wikipage it suggested this stack exchange question
I think I see the problem. Whenever any philosopher says that something is logically impossible, they are specifically and openly aware that this is only conditionally true. For example, a square circle is only clearly a logical impossibility if the words square and circle mean the same thing every time I think them, including in the time period that I move from ‘square’ to ‘circle’; if the ideas of ‘square’ and ‘circle’ actually do have a referent, and I am not just deluded into feeling a clear sense of meaning when I think those words, (and including all defining terms [such as ‘right angle’]); if I am correct in believing that two non-identical things are necessarily not one thing; if I am correct in believing language can refer to things other than semantic relationships; and many other fun things, including the big one: the assumption that I exist and am thinking.
However, once you have gotten everyone on the same page, and we all admit that we cannot prove that we exist, we start talking about highly conditional realities, such as those in which BattleGround God is more than a deluded memory, in which the words on the LessWrong are entered by other people, realities in which computers and circles and ‘good’ actually exist in some meaningful sense…
...and we don’t all have the same set of conditionally accepted realities. Nor do we need to in order to make most arguments intelligible to both parties. As a matter of course, most of the things we talk about are propositioned on the existence of the external world as reported by our senses and the media. If we deviate from this, we specify this in some way.
And that explains logical impossibility… but then I realized that I hadn’t read your original question carefully enough.
BG has conflated “belief that God is a logical impossibility” and “you know that She doesn’t exist.” The second claim should be “you believe that She doesn’t exist.” BG tried too hard, and it fails. Next time, use a Real Philosopher(TM).
How can P(x doesn’t exist) < P(x is logically impossible)? That’s… well, logically impossible.
If I’ve understand correct, you’re saying that the probability that x doesn’t exist, can’t less than the probabiltiy that x is logically impossible.
The reason that it can be true, is because I’m not smart enough to interpret that complicated proposition whether it’s in symbolic form or even after I’ve managed to translate it into words.
Therefore, P(x doesn’t exist) may very well be < P(x is logically impossible), I have no idea.
It is definitely true that this could be someone’s subjective probability, if he he doesn’t understand the statement.
But if you do understand it, a thing which is logically impossible doesn’t exist, so the probability that a thing doesn’t exist will be equal to or higher than the probability that it is logically impossible.
I feel like I might understand now. Can I represent your points as follows:
all instances of things which are logically impossible also don’t exist
therefore, there are more things which don’t exist than those that are logically impossible
Assuming statement 1 is correct, without accepting a further premise I don’t feel compelled to accept the second premise. It sounds like things which are logically impossible may in fact be equivelant to things which don’t exist, and vice-versa. And that sounds intuitively compelling. If something was logically possible, it would happen. If it is wasn’t possible, it’s not going to happen. Or, the agent’s modelling of the world is wrong.
Importantly, I don’t accept premise 1, as I’ve indicated in another comment reply (something about how I find I’m wrong about the apparent impossibility of something, or possibility of something.)
A purple dog with octopus arms is logically possible, but does not exist.
I said “so the probability that a thing doesn’t exist will be equal to or higher than etc.” exactly because the probability would be equal if non-existence and logical impossibility turned out to be equivalent.
If you don’t agree that no logically impossible thing exists, then of course you might disagree with this probability assignment.
Well, the conclusion should read not “more things” but “at least as many”. Things might accidentally not exist.
I feel the fact that you reject premise 1 just means that you don’t really grasp the concept of impossibility, logical or otherwise… Or you have a different concept of existence.
The reason why I used a semi-formal notation was to suggest that if you formalise it all, you can actually prove “P(x doesn’t exist) ≥ P(x is impossible)” as a tautology. (Ignoring the issue that with specifically logical impossibility, you get into a bit of trouble with probability assignments to tautologies.)
Seems undecidable, circa Godel bla bla bla.
Uhm, what? Why? Bla bla bla indeed. (Sorry, I couldn’t resist.) It’s not actually very relevant.
If you don’t believe that logical (or, for that matter, any other sort of) impossibility implies non-existence, then you are understanding either “logical impossibility” or “non-existence” in a way different from just about everybody else. So if there is any point to this discussion, it should be to elucide how you understand them.
Thanks for making that clear to me. I don’t like the idea of having inconstent terminology usage to everyone else, so in that case I’m at deep fault. A few minutes (hours?) ago I had a moment of clarity and I’m pretty sure I’m psychotic right now. I caught myself out in the delusion I’ve been having for a couple of days, which I have had in the past for unfortunately far longer, that society and economies are going to collapse and we’re going to be forced to farm or raid people and because I’m passive and shit at gardening I’ll die a horrible death. Which, I should have good reason to believe is absurd because economic collapses are extremely rare, highly unlikely in developed countries like ours, there are measures in place to intervene in food security crises, so on and so forthe. The point is, this is consistent my prolific shit posting over the last half-day which I will probably go back and perhaps get rid of the ones without comments. Meanwhile, this thread is probably going to be extremely interesting to me when I recover from this because it formalises how it captures, to some extent how I’ve been relating to the world. To some extent I miss that if I had managed to reply to your comment further into this state it might have been very interesting. On the other hand, perhaps if not for it, I wouldn’t have recognised that this indeed is a problem right now and my delusion isn’t just a single odd piece of psychosis admist normal thinking otherwise. Ok I better get off this thing and figure out to get some help so my assignments can still be submitted in time...I’ve lost so much karma in the last half day haha.
Unless this is some kind of self-doubt, or worry/anxiety thing and I’m just making a feel of myself to refuse actually updating my beliefs faced with compelling reason. I don’t know, I feel very odd. I’ll probably update this at some point. Unless something goes very wrong...a little while ago I was thinking of retiring this account and also how interesting it would be if someone wrote a suicide note on lesswrong. Ok I need to stop right now, this isn’t right or relevant. Bye.
If you already know that square circles cannot exist, it follows that in fact they do not exist; nothing impossible happens, so a proposition like “I saw a square circle” automatically gets a truth value = 0 without having to bother examining it.
thats confirmation bias
And how do we compensate for confirmation bias?
“Wait, I must not yet discard the chance I’m wrong, because for all I know, square circles can—”
No, they can’t. Ergo, they don’t.
Sorry I don’t follow. Please use baby steps for me.
The purpose of knowing about confirmation bias is to always keep in mind that you tend to overly favor your own preferred hypothesis, so you must adopt a detached perspective and try to consider all alternative explanations.
But in this case we are dealing with the rules of logic. Unless you’re a follower of one of the many paraconsistent schools, there are no alternative explanations. The rules just work. It’s not confirmation bias to favor an explanation based on the rules of logic.
Denying square circles a priori is not the same as denying black swans a priori: swans are real things in the real universe, and as such can have limitless variations. Swans that fall outside of their former definition force us to update the definition. A black swan is not a logical impossibility. Circles, on the other hand, are abstractions in our heads, and only have one form. Circles that fall outside of their definition are just not circles.
Going back to your original example: IF God is a logical impossibility, no instantiation of a God in the real universe will occur, because, again, nothing impossible happens. You don’t need to bother examining the truth value of something that in principle can’t occur, for the same reason geometrists don’t go on field trips in search for square circles. You can trust logic; it simply won’t happen.
I disagree.
You’re implying that square circles are platonic concepts that aren’t empirically verifiable. I would argue that they entirely are, just the task would be too difficult to be worth anyone’s while. Just because something is in someone else’s field of perception, doesn’t make it any less real if it’s a particular hypothesised shape, or a particular hypothesised colour. I could simply ask someone if they’ve seen a square circle and if everyone says no, can comfortably believe there aren’t any till I perhaps see one, just as if I ask about black swans and if everyone says no, comfortable b eleive they don’t exist unless I see one.
This is the assumption made in your last paragraph and I completely disagree. I’ve frequently found that things I thought were impossible happened. That kind of dogmatic certainty sounds awefully dangerous. While thinking about logic in that kind of self-consistent, but externally inconsistent sense seems to be absurd. One can describe a particular mythology that might make sense in a self-consistent way, but when related to other systems of belief isn’t coherent.
There is a difference between things that are impossible per se and things we think are impossible. Logical impossibilities are impossible regardless of anyone’s opinion. Good luck with that square circle survey.
Square circles exist in the Manhattan metric.
It is not really interesting that a circle can be X if you first change the definition of circle.
It’s not arbitrary redefinition, though. like the old joke about “calling a tail a leg doesn’t make it one”; it’s actually a consistent geometry.
Yes, any real-world circle is imperfect and deviates from being a circle in the mathematical sense. Something that’s square deviates a lot from the circle in the mathematical sense and is thus no real circle.
Maybe it’s because I’m not bayesian enough:
If I accepted that:
Then I may not hold my current attitude. But I don’t see reason to believe those premises.
While I don’t agree with the way they phrased their explanation, it’s akin to saying “I’m not sure if 2 + 2 = 4 is true, but I am sure it can’t equal anything else.” Then falling back to “but there could be oddities in the foundation of mathematics that I’m not aware of” when pressed on the inconsistency.
If you claim that your understanding of logic isn’t exhaustive, I don’t see how you can also claim that X is logically impossible. (“I’m not a car expert but there is no possible way the problem is with the engine”)
Thanks for that analogy, that gives me a new way to think about it.
I believe I can agree with the 2 + 2 = 4 theorem because I already agree with agreement in the summation of the components represented.
To illustrate:
If I put up 2 figures, then another 2 fingers, I can reliable get consensus from a survey of people and my own intuition/memory that it represents 4 fingers, and correspondingly the number 4.
Meanwhile, I don’t have any kind of clear idea of what people are on about when they say god, so doing any logical operation from there is unclear. The reason that understanding the component is important to doing an operation is that it may have an implicit modifier that affects the logical operation in and of itself.
For instance:
2 + (-2) = 4
the (-2), is not the same as 2, it’s a different component which may sometimes appear to be a 2, but getting consensus about it from people, or figuring out what to do with your fingers when you read it, might confuse people into giving an answer that is less consistent.
It appears that I’m using a consensus theory of truth. I guess that’s neccersary for any kind of discussion with more than one participant anyhow.
It makes more sense to think in terms of probabilities here, than “is or isn’t”. To what probability would you give god being a logical impossibility?
Thanks, that’s an interesting point, but I don’t think it can get a probability of being true or false because that would imply that the underlying concept can somehow be demonstrated true or false.
If it can be demonstrated true or false, then it’s logical impossibility would be 0%, because anything that is testable and has yet to be tested has a possibility of being true or false, however small that may be, or else it’s self-evident (100%).
Else, it cannot be demonstrated true or false, in which case the logical impossibility is 100%.
But the whole point of the original post was that you had logical uncertainty. That’s why in Bayesian reasoning you can’t have probabilites of 0 and 1 - to allow for the possibility, however small, of updating.
See also: How to convince me that 2+2 =3
Thanks, I don’t really understand where I was coming from before. Maybe my new found understanding of the terminology around uncertainty has finally updated my intuitions :)