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Why is the socratic paradox called a paradox?

Why is the socratic paradox called a paradox?

I presume this phrase refers to the "The one thing I know is that I know nothing" remark attributed to Socrates? Well, one form of paradox occurs when you are simultaneously motivated to endorse a contradiction -- i.e. both accept and reject a given proposition, or assign the truth values of both true and false to it. And that seems applicable in this case. On the one hand what Socrates is asserting is that he knows nothing (after all, if he KNOWS that he knows nothing, then since knowledge usually implies truth, it follows that he knows nothing). But then again on the other hand the very assertion seems to disprove it, since he KNOWS it, and therefore knows not nothing, but something. So he simultaneously seems to be asserting that he knows something and that he does not know something. Now you may not find this particularly paradoxical -- you might be tempted to resolve it directly (by rejecting one of the two propositions). But I suppose it's called a paradox because reasonably good cases can be made for both sides of it (even if some individual believes it can be resolved).

hope that helps--

ap

I presume this phrase refers to the "The one thing I know is that I know nothing" remark attributed to Socrates? Well, one form of paradox occurs when you are simultaneously motivated to endorse a contradiction -- i.e. both accept and reject a given proposition, or assign the truth values of both true and false to it. And that seems applicable in this case. On the one hand what Socrates is asserting is that he knows nothing (after all, if he KNOWS that he knows nothing, then since knowledge usually implies truth, it follows that he knows nothing). But then again on the other hand the very assertion seems to disprove it, since he KNOWS it, and therefore knows not nothing, but something. So he simultaneously seems to be asserting that he knows something and that he does not know something. Now you may not find this particularly paradoxical -- you might be tempted to resolve it directly (by rejecting one of the two propositions). But I suppose it's called a paradox because reasonably good cases can be made...

Frequently, I see the statment: "logical truths are trivial". But, what is meant

Frequently, I see the statment: "logical truths are trivial". But, what is meant by the word *trivial*?

Perhaps this: true by definition, v. true by means of some correpondence between their meanings and the world. "Bachelors are unmarried" is logically true, ie true by meaning, because that is how we use the definitions involved; it's a matter of convention and meaning that that sentence is true, and thus one doesn't need to go investigate the world whether it's true -- indeed it's not making a claim primarily about the world at all, if it's truth matter is a function of definition. Contrast with "bachelors live longer on average than average man." Ths is NOT merely logically true, true by definition -- we must go do a study to find out fi it's true, and thus to learn something substantive, some fact, about the world.. Logical truths are trivial because we learn from them no new facts about the world, beyond the meanings of the words involved.

hope that helps--

ap

Perhaps this: true by definition, v. true by means of some correpondence between their meanings and the world. "Bachelors are unmarried" is logically true, ie true by meaning, because that is how we use the definitions involved; it's a matter of convention and meaning that that sentence is true, and thus one doesn't need to go investigate the world whether it's true -- indeed it's not making a claim primarily about the world at all, if it's truth matter is a function of definition. Contrast with "bachelors live longer on average than average man." Ths is NOT merely logically true, true by definition -- we must go do a study to find out fi it's true, and thus to learn something substantive, some fact, about the world.. Logical truths are trivial because we learn from them no new facts about the world, beyond the meanings of the words involved. hope that helps-- ap

Is logic "universal"? For example, when we say that X is logically impossible,

Is logic "universal"? For example, when we say that X is logically impossible, we mean to say that in no possible world is X actually possible. But doesn't this mean that we have to prove that in all possible worlds logic actually applies? In other words, don't we have to demonstrate that no world can exist in which the laws of logic don't apply or in which some other logic applies? If logic is not "universal" in this sense, that it applies in all possible words, and we've not shown that it absolutely does apply in all worlds, how can we justify saying that what is logically impossible means the not possible in any possible world, including our actual world?

I don't understand the question, because I don't understand the phrase 'a world in which the laws of logic don't apply'. I don't think any sense can be attached to that phrase. Is a world in which the laws of logic don't apply also a world in which they do apply? If no, why not? If yes, is that same world also a world in which the laws of logic neither apply nor don't apply? If no, why not? It's as if the questioner had asked, "Don't we have to demonstrate that no world can exist in which @#$%^&*?"

This is a great question, which deserves a book-length answer. (And in some possible world, perhaps, I would give such an answer.) For many philosophers the 'logically possible' means something like the 'non-contradictory', which (for many) also yields something like the 'limits of intelligibility.' That is, you may imagine the possibility of a world in which logic does not apply, but that is not a world we can grasp, make sense of, in any way. (I can imagine a 'round square' or a 'married bachelor,' I can say those words, but as soon as I try to make sense of such a thing I pretty much have to give up.) So it's not really apparent that we can even meaningfully entertain the notion you're working with, that there are/might be 'possible worlds' in which logic doesn't apply. In light of that it seems plausible to hold, instead, that by 'possible world' we mean 'logically possible world,' i.e. worlds the description of which does not involve any contradicitons (and worlds in which logic is applicable)....

Do we have a duty to strive towards a life without contradiction? Can a person,

Do we have a duty to strive towards a life without contradiction? Can a person, for example, both eat meat and hold the belief that animals should not be willfully killed for private gain?

Well, one CAN do that, since I myself in fact do (and many, many others) .... But of course what you're asking is more like "is it morally permissible to violate one's own principles?", or something like that ... Assuming that one's principles are correct (i.e. that you are right to believe that animals shouldn't be willfully killed etc.), then it seems clear that the answer must be no, because it's not morally permissible to do that which is morally impermissible! But that seems so clear that I wonder if that really is, ultimately, your question. Weakness of will is a well-known (and much discussed phenomenon), and a paradigm case of weakness of will is precisely that where you cannot bring yourself to do that which is right (and so when I succumb, and eat meat, I condemn myself for not being able to live up to my own standards). But you seem to be getting at a much deeper question, which the weakness of will case is merely a simple case of: is there a moral obligation to avoid contradictions, to seek truth, etc. The possible contradictions in question, here, aren't between your beliefs and your actions (which aren't strictly contradictions, actually, but close enough), but between beliefs -- and here I don't have any clear intuitions about what to say. If we are morally obliged to do the right thing then, presumably, we have some moral obligation to form the correct moral beliefs; but, aside from morality/behavior, do we have any moral obligation to seek truth and avoid error? If that is, ultimately, what you're asking, then it strikes me as a really deep and hard question about which I have nothing substantial to say .... (Would be interesting to explore this question both within, and without, religious frameworks ....)

ap

Well, one CAN do that, since I myself in fact do (and many, many others) .... But of course what you're asking is more like "is it morally permissible to violate one's own principles?", or something like that ... Assuming that one's principles are correct (i.e. that you are right to believe that animals shouldn't be willfully killed etc.), then it seems clear that the answer must be no, because it's not morally permissible to do that which is morally impermissible! But that seems so clear that I wonder if that really is, ultimately, your question. Weakness of will is a well-known (and much discussed phenomenon), and a paradigm case of weakness of will is precisely that where you cannot bring yourself to do that which is right (and so when I succumb, and eat meat, I condemn myself for not being able to live up to my own standards). But you seem to be getting at a much deeper question, which the weakness of will case is merely a simple case of: is there a moral obligation to avoid contradictions, to...

When someone says "That seems(or does not seem) logical" it is not always easy

When someone says "That seems(or does not seem) logical" it is not always easy to know how they define "logical". Is it meaningful at all? I guess the question relates to the use of something that seems to be a looser term than e.g. "deductively valid" or the like, which refers to a particular system of inference and specific rules for determining truth or falsehood of propositions. Do you have any idea as to what the term commonly refers to?

I don't really, but it is one of my biggest pet peeves, from the perspective of one grading students' philosophy papers! ... My guess would be that on many such occasions, the person means something like "valid" -- where "valid" does NOT mean the technical deductive notion but something closer to "true"! (They will often say, "P is not logical," clearly meaning that P is false ...) Occasionally people use it with a defeater: "P seems logical, and yet here's why it's false ..." On such uses they seem to mean "apparently true, even if not really true." Rarely do they use it with anything very close to its basic sense, if not quite "deductively valid" then at least bearing some relationship to arguments and conclusions (where to say "P is logical" would be to say "P is based on some form of argument") ....

ap

I don't really, but it is one of my biggest pet peeves, from the perspective of one grading students' philosophy papers! ... My guess would be that on many such occasions, the person means something like "valid" -- where "valid" does NOT mean the technical deductive notion but something closer to "true"! (They will often say, "P is not logical," clearly meaning that P is false ...) Occasionally people use it with a defeater: "P seems logical, and yet here's why it's false ..." On such uses they seem to mean "apparently true, even if not really true." Rarely do they use it with anything very close to its basic sense, if not quite "deductively valid" then at least bearing some relationship to arguments and conclusions (where to say "P is logical" would be to say "P is based on some form of argument") .... ap

Recently I tried to explain to a friend what interested me about Hume's 'problem

Recently I tried to explain to a friend what interested me about Hume's 'problem of induction.' I told him how if we want to give an argument for the superiority of inductive reasoning (concluding x's are always P, based on observed instances of x's that are P) over, say, anti-inductive reasoning (concluding x's are not always P, based on observed instances of x's that are P) then we would have to give either an inductive argument or else a deductive argument. We cannot give such a deductive argument, I told him, and to give an inductive argument like 'inductive reasoning has led to good results in every observed instance' would be circular. He replied with the question 'why is there no problem of deduction?' He asked why he couldn't give a similar argument that any defense of deductive reasoning (concluding C based on premises that logically entail C) over, say, anti-deductive reasoning (concluding not C based on premises that logically entail C) needs to be either deductive or inductive. A deductive...

Rather than offer a response to this excellent question, let me just refer you to a paper whcih essentially raises and discusses the very same problem: Susan Haack's "A Justification of Deduction," from the journal Mind in 1976 (try vol 85, n. 337 I believe). Also, Lewis Carroll (as in "Alice in Wonderland" has a similar, more fun version of it -- "What the Tortoise said to Achilles" -- also in Mind, in 1895 or so ... Check them out!
ap

Rather than offer a response to this excellent question, let me just refer you to a paper whcih essentially raises and discusses the very same problem: Susan Haack's "A Justification of Deduction," from the journal Mind in 1976 (try vol 85, n. 337 I believe). Also, Lewis Carroll (as in "Alice in Wonderland" has a similar, more fun version of it -- "What the Tortoise said to Achilles" -- also in Mind, in 1895 or so ... Check them out! ap

Let's say I have a machine with a button and a light bulb where the bulb lights

Let's say I have a machine with a button and a light bulb where the bulb lights up if and only if I press the button. I don't know anything about it's inner workings (gears, computers, God), I only know the "if and only if" connection between button and light. Can I say that by pressing the button I cause the bulb to light up? (I would say yes). It seems to me that for the causal connection it doesn't matter that I don't know the exact inner workings, or that I don't desire the effect (maybe I press the button just because I enjoy pressing it, or because there is strong social pressure to press it, ...), and that I consider it very unfortunate that the bulb lights up wasting electric energy. Let's now change the terms: instead of "pressing the button" we insert "having a kid" and instead of "the bulb lights up" we have "the kid dies" (maybe when adult). I think the "if and only if" relationship still holds, and so does the causal connection. It would seem to me that parents are causally connected to...

Great set of thoughts, here. But maybe one quick mode of response is to remark that much depends on just what you take the word "cause" to mean. You could take it to mean something like this: "x causes y" = "y if and only if x", as you've suggested. Then, granting that both cases above are cases fulfilling the "if and only if", sure, giving birth would count as a cause of the later death. But now two things. (1) Why should "cause" mean precisely that? Wouldn't it be enough if the x reliably yielded the y, even if things other than x could yield the y too? (i.e. couldn't you drop the 'only if' part, so 'x causes y' would mean 'if x, then, y', even if it might also be true (say) that 'if z, then y'?) Going this route would preserve your intuition that both cases above are cases of causation, but focus on whether your particular definition is the best one. (2) Perhaps more importantly, though, one might examine the 'pragmatics' of causation -- how people actually use the word, different from how very precise philosophers or scientists might define it. So, for example, we often restrict the word 'cause' not just to every factor which may be necessary or sufficient or both for an effect, but to the most salient factors, the most explanatorily relevant ones, the most proximate ones, etc. So, you strike a match and it lights; strictly speaking many things are at least necessary for that (the presence of oxygen, the existence of the match, the laws of physics, etc.) but we often say 'the striking caused the lighting', even though all those other factors were necessary. Indeed the striking was neither necessary nor sufficient for the lighting -- the match could have been lit other ways, and striking on its own (without oxygen etc) wouldn't light. So our ordinary use of 'cause' is far looser than some technical philosophical definition. So the question for you is: how, ultimately, are you going to use the word 'cause', and are you justified in choosing that use in light of competing uses?

hope that's useful ...

ap

Great set of thoughts, here. But maybe one quick mode of response is to remark that much depends on just what you take the word "cause" to mean. You could take it to mean something like this: "x causes y" = "y if and only if x", as you've suggested. Then, granting that both cases above are cases fulfilling the "if and only if", sure, giving birth would count as a cause of the later death. But now two things. (1) Why should "cause" mean precisely that? Wouldn't it be enough if the x reliably yielded the y, even if things other than x could yield the y too? (i.e. couldn't you drop the 'only if' part, so 'x causes y' would mean 'if x, then, y', even if it might also be true (say) that 'if z, then y'?) Going this route would preserve your intuition that both cases above are cases of causation, but focus on whether your particular definition is the best one. (2) Perhaps more importantly, though, one might examine the 'pragmatics' of causation -- how people actually use the word, different from how...

Is it logical to infer a higher power given how extraordinary human life is?

Is it logical to infer a higher power given how extraordinary human life is?

If by 'logical' you mean 'a decent argument can be constructed of this form' then i would say the answer is yes -- but if you mean 'an absolutely convincing argument ...' then, well, you don't find too many of those anywhere in philosophy -- my favorite version of the kind of argument that Allen Stairs mentions is some version of the fine-tuning argument -- which observes how perfectly fine-tuned features of the universe seem to be, such that they could easily have been otherwise, and yet had they been otherwise then human life (conscious, rational, moral life) would not have been possible -- and goes from there to argue that it is reasonable to think this didn't occur by chance -- a good source on this topic would be any of Paul Davies' recent books ...

best, ap

If by 'logical' you mean 'a decent argument can be constructed of this form' then i would say the answer is yes -- but if you mean 'an absolutely convincing argument ...' then, well, you don't find too many of those anywhere in philosophy -- my favorite version of the kind of argument that Allen Stairs mentions is some version of the fine-tuning argument -- which observes how perfectly fine-tuned features of the universe seem to be, such that they could easily have been otherwise, and yet had they been otherwise then human life (conscious, rational, moral life) would not have been possible -- and goes from there to argue that it is reasonable to think this didn't occur by chance -- a good source on this topic would be any of Paul Davies' recent books ... best, ap

I have been reading discussions on this site about the Principia and about Godel

I have been reading discussions on this site about the Principia and about Godel's incompleteness theorem. I would really like to understand what you guys are talking about; it seems endlessly fascinating. I was an English/history major, though, and avoided math whenever I could. Consequently I have never even taken a semester of calculus. The good news (from my perspective) is that I have nothing to do for the rest of my life except for working toward the fulfillment of this one goal I have: to plow through the literature of the Frankfurt School and make sense of it all. Understanding the methods and arguments of logicians would seem to provide a strong context for the worldview that inspired Horkheimer, Fromm, et al. So yeah, where should I start? Do I need to get a book on the fundamentals of arithmetic? Algebra? Geometry? Or do books on elementary logic do a good job explaining the mathematics necessary for understanding the material? As I said, I'm not looking for a quick solution. I...

1. I don't think there is any reason to suppose that learning about mathematical logic from Principia to Gödel will be any help at all in understanding what is going on with the Frankfurt School. (The only tenuous connection I can think of is that the logical positivists were influenced by developments in logic, and the Frankfurt School were concerned inter alia to give a critique of positivism. But since neither the authors of Principia nor Gödel were positivists, it would be better to read some of the positivists themselves if you want to know what the Frankfurt School were reacting against).

2. Of course, I think finding out a bit about mathematical logic is fun for its own sake: but it is mathematics and to really understand I'm afraid there is not much for it other than working through some increasingly tough books called the likes of "An Introduction to Logic" followed by "Intermediate Logic" and then "Mathematical Logic". Still, you can get a distant impression of what's going on by following links on Wikipedia etc. And on Gödelian matters, Hofstadter's long book is entertainingly illuminating and somewhat annoying in about equal measure. Goldstein's book, though, is hopeless as a guide: see http://math.stanford.edu/~feferman/papers/lrb.pdf for an authoritative demolition (which indeed pulls its punches). If I was going to recommend one book on Gödel as a way in for the non-mathematical, it would be Torkel Franzen's Gödel's Theorem, an Incomplete Guide to its Use and Abuse.

lucky you, with so much time on your hands and with such interesting interests! there are numerous secondary expositions of Godel etc. -- I personally love Douglas Hofstadter's way of explaining it (in Godel Escher Bach and also his more recent Strange Loops) ... but Rebecca Goldstein has a recent book on it (haven't read it, can't speak to its quality) -- http://www.rebeccagoldstein.com/books/incompleteness/index.html good luck ap

My teacher claims that he is utterly emotionless; according to him, he isn’t

My teacher claims that he is utterly emotionless; according to him, he isn’t clouded by emotions of any form, and has no emotional desire. He argues that any emotions he appears to possess are simply superficial occurrences, with the purpose of manipulating others. He argues that he is utterly objective and consequently, completely exclusive from any form of bias. My question is that surely somebody who objectively chooses to use logic over any form of emotional guidance and has “no emotional desire whatsoever”, is therefore exhibiting a desire in itself? Surely, if one assumes logic as their only form of reasoning, the logic must be based upon basic desires and principles, therefore denoting an emotional presence? I would be grateful if somebody could enlighten me!

I worry that framing the question this way begs the question -- you seem to assume that any 'choice' comes from or out of 'desire', but isn't that precisely what's at issue? I think we'd need to get a lot clearer on what a 'desire' is before we could answer the question in a satisfactory way ... For example, you seem to consider 'desire' a kind of 'emotion', but philosophers of mind typically would distinguish the two in various ways -- perhaps desires share a kind of 'qualitative character' or 'qualia' with emotions, but desires are typically characterized by having an object or content, one often expressible in words, in a way emotions are typically characterized as 'raw feelings' that may or may not have a specific object or content -- Once you separate desires from emotions, you then need to define desire in such a way as to make it clear that every choice comes from some desire ..... (Charles mentions Spock -- consider this thought. Suppose you could program a computer to do all sorts of complex tasks, including navigating its environment successfully. Maybe it's a robot that's programmed to explore the surface of Mars and send back data. That robot seems to have to make all sorts of 'choices' -- as it navigates its terrain, taking samples of some things, not others -- but do you want to say it has any desires? If not, why must all human choices come from desire?)

AP

I worry that framing the question this way begs the question -- you seem to assume that any 'choice' comes from or out of 'desire', but isn't that precisely what's at issue? I think we'd need to get a lot clearer on what a 'desire' is before we could answer the question in a satisfactory way ... For example, you seem to consider 'desire' a kind of 'emotion', but philosophers of mind typically would distinguish the two in various ways -- perhaps desires share a kind of 'qualitative character' or 'qualia' with emotions, but desires are typically characterized by having an object or content, one often expressible in words, in a way emotions are typically characterized as 'raw feelings' that may or may not have a specific object or content -- Once you separate desires from emotions, you then need to define desire in such a way as to make it clear that every choice comes from some desire ..... (Charles mentions Spock -- consider this thought. Suppose you could program a computer to do all sorts of complex...