• Srap Tasmaner
    4.1k


    That's close.

    The idea is just to show how what is a possible or a necessary result of you picking from a set can be cashed out in terms of what *is* or *is not* there to be picked.

    (This is, to my understanding, the motivation behind possible world semantics: you get to trade in intensions for extensions, and then standard truth functions are available again.)
  • Janus
    13.2k
    Cheers, though I'm not clear what "trading intensions for extensions" means, but then it's probably to be expected since I'm pretty much a modal ignoramus. :smile:
  • Srap Tasmaner
    4.1k
    what "trading intensions for extensions" meansJanus

    Just that classical logic can't deal with propositions of the form "It is possible that you pick a red marble," but can happily deal with propositions like "There is a red marble in the set."
  • Luke
    2.2k
    One predicate is distinct from another if they don't have identical extensions, even if they overlap (as various cases of possibility and necessity do). One predicate is the opposite of another, usually, if one is the complement of the other, includes everything it doesn't and nothing it does. I'm not sure we have an everyday word for only being disjoint, that is, being a subset of the complement.Srap Tasmaner

    Sounds reasonable. Does that imply "possible" is not the opposite of "impossible"?
  • Luke
    2.2k
    It is not impossible to imagine any object being red or not being red. So even if all examples of a certain kind of object were red, it does not follow that a non-red object of that kind could not turn up.Janus

    Right, but if it were necessarily red, then it follows that a non-red object could not turn up. Otherwise, it would be not necessarily red and it follows that a non-red object could turn up.

    Even if (although we could never know it) all objects of a certain kind have been, are and will be red it does not seem to follow that it would be necessary that they were, are or will be red.Janus

    True, but if it were necessary, then they must always be red.

    That they were, are and will be all red could be a contingent matter, that is it just so happens that all of those kinds of objects have been, are and will be red.Janus

    I agree, and I think that regarding temporal events it is a contingent (non-necessary) matter. We were only discussing what's logically necessary, possible and impossible.
  • Merkwurdichliebe
    2.3k
    Sounds reasonable. Does that imply "possible" is not the opposite of "impossible"?Luke

    I would say these are not an example of "opposition" but "negation". A dynamic between the "necessary" and "possibile" would be more of an oppositional relation.
  • Metaphysician Undercover
    10.9k
    Is this ball *this ball* if it is a different color? Is redness essential to it? For comparison, if this ball is flat, we can inflate it, and we will not usually say that being flat is essential to what the ball is, just its temporary state.Srap Tasmaner

    I think this is where things get sticky. In the case of a particular object, such as "this ball", each and every property is an essential property, that's what makes it the unique thing which it is, by the law of identity. That is the identity of the ball itself. But when we move to question "what the ball is", as " a ball", or "a red ball", we are assigning an identity to the object, which is distinct from the identity which the ball has, in and of itself, by the law of identity.

    When talking about particulars, like this specific ball, we can't make modal claims, I think, without considering what is essential and what accidental about that particular.Srap Tasmaner

    I think it is important to note that there is no such distinction in the case of a particular. Each and every property of a particular must be understood as essential to that particular, that's what makes a particular a unique individual, distinct from every other particular. This is what the law of identity recognizes.

    But it is nevertheless true that if it is flat, it is not fully inflated, and that's just the law of noncontradiction. When we say this red ball cannot not be red, are we even saying anything about the ball? Or are we only saying that at this world, as at all others, the law of noncontradiction holds?Srap Tasmaner

    So, let's maintain this distinction, between the identity the ball has, by the law of identity, and the identity which we assign to the ball, through a differentiation between essential and accidental properties. We've assigned essential properties, and have named the ball "red ball", with very good reasons, and we maintain that the ball cannot not be red, for those reasons. However, we need to maintain that the ball in itself might still turn out to be not red, if our reasoning turns out to be wrong. We can't just conclude that the ball cannot not be red because it would be contradictory, because we just have some reasons why the ball must be red, and those reasons might end up being wrong. We cannot impose on the ball that it cannot not be red, just because our reasoning says so, because our reasoning might be wrong.

    So it's not even a case of asking whether the law of non-contradiction holds in this world, it's a case of asking do the reasons for calling the ball "a red ball" hold in this world. Then the question is whether the world described in which the ball must be red, corresponds correctly with the real world. But I would say that we must maintain always, the possibility that it does not. Therefore we ought to allow that the thing itself, with the identity it has within itself, could always be other than the identity we give it. So this would not be a case of violating the law of non-contradiction, it would be a case of us having a misunderstanding of the world.

    Where this becomes difficult is with the assumption that everything must have an identity within itself. That is what Aristotle proposed, but Hegel for instance saw no necessity even for this principle. But if we relinquish the law of identity, then contradiction could inhere right within the world. It would not be necessary that the object has an identity within itself, and it could actually consist of opposing properties.

    To say that there are no worlds at which this ball is both red and not red is to say almost nothing at all. There simply are no such worlds, no worlds at which any ball, this one or another, is both red and not red. If we deem the redness of this ball essential to it, there are no worlds at which this ball is not red, on pain of simply being a different object. If it is inessential that it is red, like being flat, then there are worlds at which it is blue, is green, is white, and so on. And that's what we mean when we say this ball 'might have been' some other color.Srap Tasmaner

    If we let go of the law of identity, then we allow for the possibility of a world in which the ball is both red and not red. Our logic dictates "there simply are no such worlds", but the real world does not conform to our logic, our logic must conform to the world. Therefore we must allow for the possibility that the law of identity is incorrect, and consequently the law of non-contradiction is irrelevant in some circumstances, and it is not accurate to say "there simply are no such worlds".

    See, you say that if this were the case, it would be "a different object". But without the law of identity, there is no reason to believe that the real world even consists of objects. The real world might be 'a different world', outside all of the logically possible worlds, which rely on the law of identity. That's what the law of identity tells us, that the world consists of objects. But if the law of identity is wrong, and the world doesn't consist of objects, then we need a new principle by which we name things as objects, and insist that the law of non-contradiction must hold for these supposed objects.

    We're in very different territory if there's a bin of red playground balls and you're grabbing one of those. In such a case, it's perfectly clear what we mean when we say you cannot pick a ball that is not red: there is no such a ball to pick. To say that you might get the one with "Zeppelin rules" scrawled on it in Sharpie, is to say there is a ball in the bin so adorned, and this inscription makes it unique; to say you might get one bearing those words, is to say this is a thing someone might have done, that it is possible someone has done it.Srap Tasmaner

    The point for you to recognize, I think, is that when we accept the law of identity, then we accept that any ball might be other than the way we name it. In fact, the object is designated as necessarily other than how we name it. That's what the law of identity recognizes, that we name it by essentials, not by accidentals, while accidentals are what gives identity to the individual. So any particular object, by the law identity, is necessarily inconsistent with how we identify it.

    Now I have moved from the claim that we must accept the possibility that the world is other from how we describe it (above), to the claim that it is necessarily other than how we describe it. We do not identify the accidentals, but the accidentals are what are essential to the particulars. And since we do not acknowledge the accidentals, we cannot even name them as possibilities. They are unknown possibilities. And once we see the reality of unknown possibilities, then we must allow for possible worlds which are outside the realm of "logically possible", such as a world with no objects and no law of identity. "Possible worlds" is a restriction imposed by logic which is necessarily inconsistent with reality.

    But how do we get necessity out of the law of noncontradiction? That if something is red, it cannot not be red? Since the law of noncontradiction holds at each world, restricting to worlds at which "The ball is red" is true automatically embodies the necessity we were looking for: for any world w in that set, the ball is red at every world accessible (under this restriction) from w. That's our definition of necessity. No world at which it is not red, or also not red, can sneak in.Srap Tasmaner

    The law of non-contradiction, in this sense, is just an artificial restriction imposed on possibility, by us. It only applies to produce a set of possible worlds which is created by our minds. But what the law of identity indicates to us, is that the real world is a world which is necessarily outside this set of possible worlds. The true identity of the particular is within the aspects (accidentals) which we ignore when we assign an identity to the object. Therefore the real world is necessarily inconsistent with the "possible worlds".
  • Luke
    2.2k
    I would say these are not an example of "opposition" but "negation". A dynamic between the "necessary" and "possibile" would be more of an oppositional relation.Merkwurdichliebe

    I take it you meant to say that a dynamic between the "necessary" and "impossible" would be more of an oppositional relation?
  • Luke
    2.2k
    We cannot impose on the ball that it cannot not be red, just because our reasoning says so, because our reasoning might be wrong.Metaphysician Undercover

    If the entire linguistic community agrees that this ball is "red", then how might our "reasoning" be wrong? What "reasoning" is involved when we teach someone how to use the word "red"?
  • Metaphysician Undercover
    10.9k
    If the entire linguistic community agrees that this ball is "red", then how might our "reasoning" be wrong? What "reasoning" is involved when we teach someone how to use the word "red"?Luke

    There is actually many examples if you look for them. Someone, I believe it was Srap, earlier gave the example of Pluto being a planet. The linguistic community agreed to this, but it turned out to be wrong. We can also say for example that "the sun rises", and "sunrise" are misleading usage, and wrong, because the sun doesn't rise, the earth spins. There is clearly "reasoning" involved in teaching how to use words. One must decide how to approach the task. And the required technique differs depending on whether the student is beginner or advanced. Learning how to use "red" would generally be more toward the beginner level, prior to the complex logical concepts required for science and mathematics. I've never really taught language use, but I think the reasoning involved in teaching the use of "red", might involve deciding how to demonstrate the concept of colour, and deciding how to properly demonstrate a specific colour, "red". There are judgements which must be made.
  • Agent Smith
    9.2k
    Is p is true IFF p the simplest way of expressing the correspondence theory of truth?
  • Srap Tasmaner
    4.1k
    Each and every property of a particular must be understood as essential to that particular, that's what makes a particular a unique individual, distinct from every other particular. This is what the law of identity recognizes.Metaphysician Undercover

    So now we're back to @Isaac's teapot and the missing screw. In that discussion, the question was only about successfully referring to a particular that (might or) might not possess a property you believe (or don't believe) it does. I think it's plain that you can; for some cases, I'm leaning on the causal theory of names, and for others on how demonstratives work: you can clearly demand someone get "that" off your kitchen table even when you know very little about what "that" is. Exactly how that works may be unclear; that it works, I believe, is not. (We may come back to the double-bind theory of reference eventually.)

    Here, we might start with the question of whether "being on my kitchen table" is a property of the object in question. It can be expressed as a predicate, as I've just done, but we could just as well express the situation as my kitchen table having the property of "having that on it," assuming again that "that" will manage to refer to the object. Or we could define a two-place predicate "on" such that "on" is true of an ordered pair <that, my kitchen table>. For either of the one-place predicates (of that, or of the table), I would be asking you to make something that is true of one of them false; for the two-place predicate, I would be asking you to make something that is true of the two of them false.

    There are a couple ways to take that: I described "on" as a relation not just of two objects but of two objects in a particular order, so that on(table, thing) was already false, but on(thing, table) was true and I want it to be false. on(table, thing) and on(thing, table) describe different states of the world; in this case, the demand to make whichever is true false needn't concern itself with the order, because context will take care of that. But if I asked you to put that thing on the table, my demand would not be satisfied by you putting the table on that thing. So if we want on/2 to carry the same meaning across different uses, we can't rely on context in that way, and have to build in the required order. How do we do that?

    Do we say that "on" takes three objects, the two from before and a third that specifies the order? If so, the third would look something like this: "1 = thing, 2 = table". Such a list can be presented in any order, so we don't have a regress, only a rule about each natural number up to the arity of the predicate being used, so this is a genuine option. But our new on/3 takes two concrete objects and a third which, whatever it is, is not like that. I say "whatever it is," because the semantics of the ordering list are unclear at this point: are those objects in the list, or expressions referring to objects? I guess either would do, but we're still building in a lot of other stuff, some of which looks suspiciously abstract, so we could just give in and have "on" take a single abstract object which is the ordered pair <thing, table>.

    If we do that, my asking you to get that thing off my kitchen table would be asking you to make "on" false of the ordered pair <thing, table>. No properties of the concrete objects will change when you do so. We've added a step, so that "on" is not true of the concrete objects themselves, but of an ordered pair of the objects, which is a bit of a surprise. I'm not sure how much that should count against the scheme.

    Can we do something similar with other cases? For instance, if my bike tire is flat, is it a different object once it's inflated, or is it just a different arrangement of tire and air, the tire itself never changing? (In this case, we may or may not have any specific batch of air in mind.) But then what would we say about the shape of the tire, that surely changes when it's inflated? If anything is a property of an object, surely its shape is. But I make different shapes when I sit and when I stand — does that make me a different person? What all of these examples have in common is that there are at least two different times considered: the tire is never flat and inflated at the same time, I am never sitting and standing at the same time, and so on. So a first attempt at distinguishing what is essential to an object from what is accidental is, naturally, distinguishing what is constant or invariant about it, what does not change from one time to another, and what does or can change from one time to another. Essential is what is time-less, and accidental is what is time-dependent. The same dog barks at one time and not at another.

    But Isaac's screw-missing teapot raises a batch of familiar problems: evidently material constitution is not a great candidate for the timeless identity of an object. If we replace the missing screw with another of the same size, we have the Teapot of Theseus: is it the same teapot after as before the installation of the new screw? (It's considerations like this, if memory serves, that drove Peter van Inwagen to conclude that inanimate objects lack identity altogether, and thus do not, strictly speaking, exist.) One solution offered, in a sort of conventionalist spirit, is that this is all a collective fiction: there are no things with identities that we come along afterward and refer to; rather, our various acts of reference, intended and accepted by us as such, and our deeming these acts successful, is all there really is here. Thus, the slight oddity of Russell's account of definite descriptions — that they involves implicit existence claims — is vindicated, because indeed we are asking others to accept , at least for the duration of this exchange, what amounts to a stipulation that there is a dog when we say "the dog is barking."

    The conventionalist account doesn't automatically undermine a distinction between essential and accidental properties, of course; you could take it as simply falsifying all claims of essence, or you could conversely take essence as whatever we tacitly agree it is. We generally count me as being the same person sitting or standing, and since that's all there is, that's enough.

    But there's an odd wrinkle to all this. If I, like Isaac's teapot, do have an identity, then a proper semantics of me would require everyone to speak of me as if I do, and we would expect the corpus of attempted references to me to roughly, and only roughly, follow this requirement. That means the conventionalist will argue that our broad agreement in how to talk is just that, and nothing more; while the identitarian will argue that our broad agreement is a consequence of there being objects with identities. The conventionalist would seem to have parsimony on their side, and can allow or disallow the hypothesis of concrete self-identical objects as their mood dictates; but the base position is that it is more perspicuous to venture only that we say what we say. The object-identitarian offers a theory that explains why we talk the way we do, and the conventionalist can just say he doesn't need one.

    That means there are two overlapping arguments here: on the one hand, the conventionalist can keep poking holes in whatever theory of object identity the other side comes up, because he needs no such theory anyway, and may even think no such theory is possible; on the other hand, the object-identitarian has to come up with a theory that works and show that it is needed, which means he also has to find some flaw in the conventionalist account of our referential speech acts — not for the sake of his theory but to show that some theory is even needed. What's not clear in any of this is how the evidence is to be handled: I'll venture that most people's pre-theoretical intuition is that we talk the way we do because things are the way they are, and that our talking the way we do is in fact evidence that things are the way we say they are.

    But we have those pesky scientific refutations of how we talk: sunrise, solidity, and so on. That doesn't show that how we talk is never evidence of how things are, but it does show that it isn't always such evidence. On the other hand, the conventionalist can shift from the claim that how we talk is only evidence of how we talk, and nothing more only for methodological reasons, to a claim that how we talk is only we how talk — now meaning our agreement is precisely evidence that there is nothing more.

    If that were true, it would not only deny the object-identitarian what was counted pre-theoretically as evidence but change the character of what's to be explained by any such theory. If the mean girls call you a loser, that's just a thing they say: the truth-value of their statement matters to you, but not to them; what matters to them is producing some effect, of hurting your feelings. That's the sense in which it is "just something they say." But not only can you not conclude from someone saying something that it must not have a truth-value, in this case the effect is only produced if you assume that it does, and they assume that you will assume that it does. If they know you will discount what they say as being just mean-girl noise, or just noise period, there's no reason for them to say it. The conventionalist can retreat again and say that the hurt feelings are known inductively to follow utterances of "loser," and that's all the mean girls need. That might actually be true! But you have to show that such an account really will extend to cover all language use. This situation is so simple than I think what we're really seeing is not exactly language at all but something more like dominance signaling that happens to use language because, well, there it is; we tend to use words even when what we're doing is really nothing more than growling articulately.
  • Andrew M
    1.6k
    This situation is so simple than I think what we're really seeing is not exactly language at all but something more like dominance signaling that happens to use language because, well, there it is; we tend to use words even when what we're doing is really nothing more than growling articulately.Srap Tasmaner

    Nice post!

    A good survey of the options in there. As I see it, in the end we're doing things with words. The relevant context reveals what we're doing, not just the words or sentences themselves.

    Which, in turn, would seem to relate identity and convention to purpose. Keeping in mind Ryle's regress - we don't necessarily need to have articulated a purpose in order to have one.
  • Metaphysician Undercover
    10.9k
    So now we're back to Isaac's teapot and the missing screw. In that discussion, the question was only about successfully referring to a particular that (might or) might not possess a property you believe (or don't believe) it does. I think it's plain that you can; for some cases, I'm leaning on the causal theory of names, and for others on how demonstratives work: you can clearly demand someone get "that" off your kitchen table even when you know very little about what "that" is. Exactly how that works may be unclear; that it works, I believe, is not. (We may come back to the double-bind theory of reference eventually.)Srap Tasmaner

    I have no problem with referring to particular things, and this is because I accept the law of identity. The real problem is with change to a thing. How can the same thing at one time have a property which it does not have at a later time? Shouldn't this make it not the same thing? So Aristotle proposed the law of identity to say that a thing has an identity proper to itself, regardless of changes to it. It's just an assumption which we must make to allow for the observed temporal continuity of existence. There is said to be a relationship between what a thing actually is (provided for by form) and what it potentially is (provided for by matter). The thing itself is understood as a temporal continuity of this relationship. So issues like Theseus' ship become irrelevant because they propose a problem which is created by failing to properly respect the difference.

    Also, I think that we need to respect the difference between an object and a subject. Predication is of a subject, not an object. So when you speak of an object for the purpose of predication, like "my kitchen table", you represent a perceived object as a subject "my kitchen table", and you proceed in predication. We talk as if we are referring directly to the object, but for the purpose of logical clarity it is best to maintain a separation between the subject with predications, and the object which is supposed to be represented. Then if problems arise, with temporal continuity for example, we can always inquire as to how well the name (subject) represents the object.

    Here, we might start with the question of whether "being on my kitchen table" is a property of the object in question. It can be expressed as a predicate, as I've just done, but we could just as well express the situation as my kitchen table having the property of "having that on it," assuming again that "that" will manage to refer to the object. Or we could define a two-place predicate "on" such that "on" is true of an ordered pair <that, my kitchen table>. For either of the one-place predicates (of that, or of the table), I would be asking you to make something that is true of one of them false; for the two-place predicate, I would be asking you to make something that is true of the two of them false.Srap Tasmaner

    I would say that logically, you have two subjects, "my kitchen table", and "that", each assumed to be representing an object. And, you are not predicating anything of either of these two, but describing a relationship between them. The relationship you call "an order".

    Do we say that "on" takes three objects, the two from before and a third that specifies the order? If so, the third would look something like this: "1 = thing, 2 = table". Such a list can be presented in any order, so we don't have a regress, only a rule about each natural number up to the arity of the predicate being used, so this is a genuine option. But our new on/3 takes two concrete objects and a third which, whatever it is, is not like that. I say "whatever it is," because the semantics of the ordering list are unclear at this point: are those objects in the list, or expressions referring to objects? I guess either would do, but we're still building in a lot of other stuff, some of which looks suspiciously abstract, so we could just give in and have "on" take a single abstract object which is the ordered pair <thing, table>.Srap Tasmaner

    I would say that the "order", or relationship is definitely not a type of object, being completely different from an object, as something inferred through logic and definiions rather than perceived through sensation. "On" is not used to refer to an object, so if we make a subject called "on", this subject does not represent an object, it represents a relationship between objects. And that relationship is defined in spatial terms, or mathematics, or something like that.

    Can we do something similar with other cases? For instance, if my bike tire is flat, is it a different object once it's inflated, or is it just a different arrangement of tire and air, the tire itself never changing? (In this case, we may or may not have any specific batch of air in mind.) But then what would we say about the shape of the tire, that surely changes when it's inflated? If anything is a property of an object, surely its shape is. But I make different shapes when I sit and when I stand — does that make me a different person? What all of these examples have in common is that there are at least two different times considered: the tire is never flat and inflated at the same time, I am never sitting and standing at the same time, and so on. So a first attempt at distinguishing what is essential to an object from what is accidental is, naturally, distinguishing what is constant or invariant about it, what does not change from one time to another, and what does or can change from one time to another. Essential is what is time-less, and accidental is what is time-dependent. The same dog barks at one time and not at another.Srap Tasmaner

    i think you've touched on a completely different issue here, a more complex issue. This is the relation of parts to a whole. When we name an object it is composed of parts, and the object is considered to be a whole, consisting of parts. However, as Aristotle described, we speak of privations, and perfection in respect to the whole. So this is a sort of ideal which we impose, on the object. Your bike is more perfect when the tire is filled with air, even though it is still the same object, as having the same identity, regardless.

    One solution offered, in a sort of conventionalist spirit, is that this is all a collective fiction: there are no things with identities that we come along afterward and refer to; rather, our various acts of reference, intended and accepted by us as such, and our deeming these acts successful, is all there really is here.Srap Tasmaner

    Yes, I think I see this in the same way. The law of identity is a useful fiction, like mathematical axioms are. It allows us to talk about a thing's temporal extension, as a thing, thus making it into a subject. We could say that everything changes from one moment to the next, as time passes, therefore there is no such thing as an object with temporal extension. However, we notice that certain aspects appear to remain unchanged for durations, so we want to be able to talk about these things with duration as existent things. So we posit a law of identity which allows that there is something real which remains unchanged as time passes, this provides us with the basis for accounting for the reality of consistency, which is what scientific laws are built on.

    That means there are two overlapping arguments here: one the one hand, the conventionalist can keep poking holes in whatever theory of object identity the other side comes up, because he needs no such theory anyway, and may even think no such theory is possible; on the other hand, the object-identitarian has to come up with a theory that works and show that it is needed, which means he also has to find some flaw in the conventionalist account of our referential speech acts — not for the sake of his theory but to show that some theory is even needed. What's not clear in any of this is how the evidence is to be handled: I'll venture that most people's pre-theoretical intuition is that we talk the way we do because things are the way they are, and that our talking the way we do is in fact evidence that things are the way we say they are.

    But we have those pesky scientific refutations of how we talk: sunrise, solidity, and so on. That doesn't show that how we talk is never evidence of how things are, but it does show that it isn't always such evidence. On the other hand, the conventionalist can shift from the claim that how we talk is only evidence of how we talk, and nothing more only for methodological reasons, to a claim that how we talk is only we how talk — now meaning our agreement is precisely evidence that there is nothing more.
    Srap Tasmaner

    The way we talk is really not reflective of the way things are, that should be obvious. Talking is purpose driven, like a tool which conforms itself to what we are doing, so it's really more reflective of our intentions. That's why "meaning" might commonly be defined as "what is meant". But intention stands before us as a dark philosophical unknown, so people are often not inclined to look that way. This is why it takes a special way of talking, the scientific method, based in a special intention, to move toward an understanding of the way things really are, rather than simply following where natural language leads us. In other words, language needs to be disciplined if we desire to develop an understanding of reality.

    If that were true, it would not only deny the object-identitarian what was counted pre-theoretically as evidence but change the character of what's to be explained by any such theory. If the mean girls call you a loser, that's just a thing they say: the truth-value of their statement matters to you, but not to them; what matters to them is producing some effect, of hurting your feelings. That's the sense in which it is "just something they say." But not only can you not conclude from someone saying something that it must not have a truth-value, in this case the effect is only produced if you assume that it does, and they assume that you will assume that it does. If they know you will discount what they say as being just mean-girl noise, or just noise period, there's no reason for them to say it. The conventionalist can retreat again and say that the hurt feelings are known inductively to follow utterances of "loser," and that's all the mean girls need. That might actually be true! But you have to show that such an account really will extend to cover all language use. This situation is so simple than I think what we're really seeing is not exactly language at all but something more like dominance signaling that happens to use language because, well, there it is; we tend to use words even when what we're doing is really nothing more than growling articulately.Srap Tasmaner

    Now, it should become clear that the concept of "truth" needs to be based in honesty, the use of language to honestly reflect one's intentions, rather than the notion of an objective truth value. There is no objective truth value, just like there is no thing with its own identity, even though I believe in that law of identity. I believe in it because it has proved very useful in helping us to communicate, and ultimately to help us understand the nature of reality, but I do not believe that it is very accurate, or a perfect representation, or 'true' in the sense of correspondence.
  • Srap Tasmaner
    4.1k
    in the end we're doing things with words. The relevant context reveals what we're doing, not just the words or sentences themselves.Andrew M

    I just can't get around the idea that in most, but not all, cases we use the words we do because they're the right ones. I don't think a linguistics that is all pragmatics with no syntax or semantics is a real option.

    Which, in turn, would seem to relate identity and convention to purpose.Andrew M

    I wouldn't deny that there are choices we make, sometimes implicitly, which enable us to enact our purpose; I just don't think that makes our purpose constitutive of the objects we interact with. I think they have to be there, as they are, for us to have the options we do, among which we select the one that aligns with our purpose. If you can sometimes sort papers by author and sometimes by keyword, depending on your purpose at the moment, it's because they have authors and keywords. If they didn't, these wouldn't be options for you.
  • Andrew M
    1.6k
    I just can't get around the idea that in most, but not all, cases we use the words we do because they're the right ones. I don't think a linguistics that is all pragmatics with no syntax or semantics is a real option.Srap Tasmaner

    I agree. But which are the right words also depends on context (which seems apropos a thread on truth).

    I wouldn't deny that there are choices we make, sometimes implicitly, which enable us to enact our purpose; I just don't think that makes our purpose constitutive of the objects we interact with. I think they have to be there, as they are, for us to have the options we do, among which we select the one that aligns with our purpose. If you can sometimes sort papers by author and sometimes by keyword, depending on your purpose at the moment, it's because they have authors and keywords. If they didn't, these wouldn't be options for you.Srap Tasmaner

    All good. But I don't think we can successfully take a view from nowhere on this. We perceive the world in a particular way that is, in part, dependent on the kind of creature that we are.
  • Metaphysician Undercover
    10.9k
    Anyway, I thought your argument was about accidental properties, not essential properties; that we might be wrong about the ball being red, not that we might be wrong about the ball being a ball. I don't see how the community could be wrong about what we call a "ball". Then again, I don't see how the community could be wrong about what we call "red".Luke

    I was talking about the reasons why we say that the ball is a "red ball", and we assume that it cannot not be red. because it is a red ball I think this is analogous to the reasons why we used to say that Pluto is a planet, and we would have been inclined, at that time, to say that it cannot not be a planet.

    What object are you talking about here?Luke

    I don't see the relevance.

    Yes, there is reasoning involved in teaching language. My point was that in teaching the meaning of the word "red" to someone, the teacher doesn't arrive at the meaning through "reasoning". The teacher knows how to use the word; they must, otherwise they couldn't teach it to someone. Recall that this was in response to your statement:Luke

    I don't see the relevance.

    The teacher does not "impose on the ball that it cannot not be red, just because our reasoning says so." The teacher and other English speakers call it "red" because that's what we call it.Luke

    That's not what the issue was though. The issue was whether this particular ball which we classified as "red ball", because we thought it was that type of ball which could not be other than red, would still be the same object, this ball, if somehow it became apprehended as not red. We called it "red ball" because we thought it is necessarily red. But if it is demonstrated not to be a red ball, like Pluto was demonstrated not to be a planet, then we ought to accept that the reasoning by which we identified it that way was wrong, and not try to impose on the ball that it must be a red ball.

    Teachers, and other English speakers called Pluto a planet, because that's what we called it. When the reasoning was demonstrated as faulty, these English speakers had to adjust. They did not insist that Pluto must be a planet because that's what we call it.

    I just don't think that makes our purpose constitutive of the objects we interact with. I think they have to be there, as they are, for us to have the options we do, among which we select the one that aligns with our purpose. If you can sometimes sort papers by author and sometimes by keyword, depending on your purpose at the moment, it's because they have authors and keywords. If they didn't, these wouldn't be options for you.Srap Tasmaner

    It might be useful for you to reconsider this to some degree. We, as living human beings, have sensory systems which have evolved from nothing. That means that over the millions or billions of years of evolution which have produced our sensory systems, the sensory systems have been shaped and formed by what has proven to be useful. So the way that we perceive things, as objects, is a product of that usefulness. The important thing to note, is that unlike your example, alternative options for how we perceive things, are not there for us.

    We have been forced into this mode of perceiving because it served some evolutionary purpose, and now it is a fixed part of our being, which we cannot opt out of. And as you mentioned in the other post, we just keep getting pesky scientific refutations. Science has provided us the means to get beyond the limitations of our sensory equipment. Plato's principal message was that the senses deceive us in our quest for truth, follow the intellect not the senses. And I suppose, through the presupposition of free will, we've managed to develop the intellect as an alternative option, under the notion that it can operate independently from the senses. In Aristotle's ethics, contemplation is the highest virtue.
  • TonesInDeepFreeze
    1.8k
    "No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the car". If I was looking for the book, then I would not appreciate my friend being coy that way, but he would not be logically incorrect." - TonesInDeepFreeze

    The crank replied to that I refute myself by admitting that I would not appreciate the coyness and that the issue is a moral one.

    That's the kind of reply made by someone who doesn't know how to discuss philosophy.

    (1) The bit about coyness was merely for flavor. We can leave it off:

    The speaker might know that the book is in the car but still be literally honest and correct, in saying "The book might be in the car".

    If your friend asks, "Where is the book?" and you don't know and answer, "I don't know, but it might be in the car", or if you don't know and answer just, "It might be in the car", then you don't think your friend is a liar for that!

    That is tremendously obvious not just philosophically but in everyday communication.

    Not knowing whether proposition Q is true does not preclude that Q might be true.

    I can't believe this even needs to be belabored.

    (2) Consider another example even including the coyness bit:

    Your birthday is soon. You ask your friend whether there will be a party. He says, "There might be, and I'm not saying more". Then there is a party, and you find out that your friend knew about it all along, and you do appreciate his coyness because it preserved a welcome suspense and surprise. And, by the way, what he said is true in both instances, and in both instances, he did not lie.

    It's ridiculous that one should even have to explain such things to the crank, but I do in the interest of an abundance of refuting his utterly wrongheaded thinking.

    (3) And, obviously, we don't refute a basic understanding of the mere modality of 'possibly' with regard to epistemic considerations by going completely out of the ballpark by saying the modal notion is refuted on ethical grounds!

    /

    One more time:

    "I don't know Q" is not inconsistent with "Possibly Q".

    No rational person thinks otherwise.

    and

    "Necessarily Q" is not inconsistent with "Possibily Q"

    No rational person thinks otherwise. Or at least, no rational person informed about modal logic thinks otherwise.

    /

    Somehow, contrary to both basic philosophy and everyday language, some people have jumped to the conclusion that 'Possibly' is the negation of 'Necessary'. There is no rational reason to jump to that conclusion. Jumping to that conclusion seems to me to be a function of people not stopping to think that negation is not the only differing relation between concepts. The relation here is not negation but rather of duals.

    Let q, Q, R be any sentences:

    (1) 'necessary' ('N') is primitive, not defined. 'possibly' ('P') is defined, not primitive.

    * The modal operators are duals, not negations, of each other.

    df. Pq <-> ~N~q

    thm. Nq <-> ~P~q

    That is NOT equivalent with:

    Pq <->~Nq

    That is NOT a definition used in basic modal logic.

    And NOT equivalent with:

    Nq <-> ~Pq

    That is NOT a theorem of basic modal logic.

    The relation is not of negation but of duals.

    P is the dual of N. And N is the dual of P.

    * Just as the the quantifiers are duals, not negations, of each other:

    df. ExQ <-> ~Ax~Q

    thm. AxQ <-> ~Ex~Q

    That is NOT equivalent with:

    ExQ <-> ~AxQ

    That is NOT a definition used in quantifier logic.

    And NOT equivalent with:

    AxQ <-> ~ExQ

    That is NOT a theorem of quantifier logic.

    The relation is not of negation but of duals.

    The existential quantifier is the dual of the universal quantifier. And the universal quantifier is the dual of the existential quantifier.

    * And note how 'all' and 'some' correspond with 'necessary' and 'possible'. Roughly stated:

    "for all x, Q" is true if and only if Q is true for all x

    "for some x, Q" is true if and only if Q is true for at least one x

    and

    q is necessary if and only if q is true in all worlds

    q is possible if and only if q is true in at least one world

    * Just as 'and' and 'or' are duals, not negations, of each other:

    df. (Q or R ) <-> ~(~Q & ~R)

    thm. (Q & R) <-> ~(~Q or ~R)

    That is NOT equivalent with:

    (Q or R ) <-> ~(Q & R)

    That is NOT a definitions used in sentential logic.

    And NOT equivalent with:

    (Q & R) <-> ~(Q or R)

    That is NOT a theorem of sentential logic.

    The relation is not of negation but of duals.

    Disjunction is the dual of conjunction. And conjunction is the dual of disjunction.

    /

    And to refute a confusion of the crank:

    The crank mentions that we use the phrase 'possible worlds' in "q is necessary if and only if q is true in all possible worlds" and then we define 'possible' in terms of 'necessary'.

    But 'possible' in 'possible worlds' is merely for intuition and is not at all needed formally. The semantics for modal logics need only mention 'worlds' (for that matter, not even 'worlds' needs to be mentioned as indeed "worlds" are merely members of a certain set that is part of a structure).

    Moreover, we do not define 'necessary'. It is primitive. But we do go on to adopt semantics and axioms so that it is a theorem (not a definition) that, roughly put, Nq if and only if q is true in all worlds.

    Also, as mentioned, we define 'possible' in terms of the primitive 'necessary'. But we recognize that we could do it in reverse: we could take 'possible' as primitive and define 'necessary' in terms of 'possible':

    df. Nq <-> ~P~q

    But that is not circularity. In any given treatment of the subject, we commit to one or the other but not both: 'necessary' is primitive or 'possible' is primitive.
  • Banno
    19.9k
    Odd that it needed saying, but well said.
  • TonesInDeepFreeze
    1.8k


    No one who knows anything writes:

    p is true iff p.

    The formulation is:

    'p' is true iff p.
  • TonesInDeepFreeze
    1.8k
    As to 'impossible':

    Yes, 'impossible' is the negation of 'possible'.

    df. Pq <-> ~N~q

    df. q is impossible <-> ~Pq

    /

    q is is necessary if and only if q is true in all worlds

    q is possible if and only if q is true in at least one world

    q is impossible if and only if q is is true in no worlds

    q is contingent if and only if q is true in at least one world and false in at least one world
  • TonesInDeepFreeze
    1.8k
    The notion that necessary implies impossible is, as reiterated, daft.

    So, we would not expect to find this as an axiom:

    Nq -> ~Pq

    But what about?:

    Nq -> Pq

    It is an axiom or theorem of just about all of the working systems of modal logic. (I think perhaps it is left off the initial "starter kit" axioms because whether it is needed as an axiom depends on whether it is derivable anyway from the other axioms, which may be formulated in various ways.)
  • TonesInDeepFreeze
    1.8k
    The word 'opposite' has caused problems in this thread because it is not been defined. An undefined word that causes confusion is less than needed. We have defined terminolgy (adding 'compatible' here as analogous to consistent):

    * negation of necessary: "not necessary". the negation of Nq is ~Nq.

    * negation of possible ("impossible"): "not possible". the negation of Pq is ~Pq.

    * inconsistent (contradictories): "imply a statement and its negation". Q and R are contradictories iff together they imply a statement S and also ~S. Most starkly: Q and ~Q are contradictories, and R and ~R are contradictories. Also these are some contradictories:

    Nq and P~q

    Pq and N~q

    * consistent ("compatible"): "not contradictory". In particular, saliently, in this thread:

    Nq and Pq are consistent!

    The crank is just hard cold plain wrong about it.

    Why do I harp on that? Because:

    Don't Normalize The Cranks!
  • Agent Smith
    9.2k
    The word 'opposite' has caused problems in this thread because it is not been defined.TonesInDeepFreeze

    :cool:

    No one who knows anything writes:

    p is true iff p.

    The formulation is:

    'p' is true iff p.
    TonesInDeepFreeze

    I stand corrected!
  • Metaphysician Undercover
    10.9k
    Odd that it needed saying, but well said.Banno

    The speaker might know that the book is in the car but still be literally honest and correct, in saying "The book might be in the car".TonesInDeepFreeze

    If that's what you call "honest" communication, and "well said", then it's no wonder that I have an aversion toward communion with you two. Your principles for sharing with me are not up to the level of my principles for sharing with you. Sad but true. What a shame.
  • creativesoul
    10.9k
    Plato's principal message was that the senses deceive us in our quest for truth, follow the intellect not the senses.Metaphysician Undercover

    Plato's principal message amounts to setting an unattainable criterion. The intellect follows from the senses. The senses are primary. The intellect is secondary.

    Since you're speaking in evolutionary terms.

    Science has enabled us to increase our innate sensory capacities. One has no choice but to follow their senses even when it is the case that they're using tools.
  • creativesoul
    10.9k
    I've always wondered how anyone in their right mind would believe that logically possible worlds could tell us anything at all about the sort of truth that emerges long before we're able to talk about our own thoughts and beliefs. That's far more primary than extensive esoteric discussions with little or no practical value about some overly complex notion borne of metacognition.

    Logical possibility is a measure of consistency/coherency/validity. It is only by thinking about and discussing our own lives that we can arrive at a sensible discussion about logical possibility. Long before talking about how things could have been different, how things are different, how things could be different, long before all such discussions, we are humans living the set of experiences that all humans share... each set unique to one's own life. All those experiences are chock full of human thought and belief. Those thought and belief - that worldview - contained all sorts of thoughts and beliefs that are true and all sorts that were not.

    Some of those were not even able to be true or not. None of them were based upon making everything possible. Not everything is possible. Some things are impossible. No amount of argumentation will change events of the past. Yet we can easily stipulate a possible world in which we disregard that which is known to have happened, essentially replacing history(what happened and/or is happening) with falsehood. We can then further discuss what may or may not have been the case according to our stipulations. We can measure the consistency, coherence, and/or the validity against the current norms thereof.

    If it follows the conventional rules of logical inference, then it is deemed logical, reasonable, rational.

    A story can be perfectly meaningful, easy to read and understand, and otherwise intelligible to not only those with some mastery of language like us, but also to those still early on in the language use game. It could also follow all the rules of logical inference and still be false on its face... absurd even.

    This shows us that we we ought not place too much value upon those standards, particularly when the topic is truth.
  • Metaphysician Undercover
    10.9k
    Plato's principal message amounts to setting an unattainable criterion. The intellect follows from the senses. The senses are primary. The intellect is secondary.creativesoul

    For Plato it is not an unattainable criterion, it is a description of reality, what is the case. The soul necessarily precedes the body as the cause of order in the material parts which is what constitutes a living body, organized parts. So in Plato the mind is prior to the body, and must rule over it to maintain the order of the parts. That's a fundamental tenet of Plato's dualism, repeated many times. And he posits a third thing, passion or spirit, as intermediate between body and mind, and the means by which the mind rules the body. This third thing accounts for the supposed "problem of interaction" commonly charged against dualism. If the fundamental order gets reversed, and passion or spirit is allowed to ally itself with the body instead of the mind, and the intellect is allowed to follow the senses the result is irrational acts.

    Your claim, that the senses are primary, and intellect follows from the senses needs to be supported, justified. The problem is that sensation requires ordered material parts. And nothing but a mind or intellect is known to be capable of ordering parts.
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