Necessarily coextensive, yet distinct?

So here’s an Aristotelian puzzle that I do not know how to sort out. It has apparently been reinstated, or a version of it, by Fine. I believe he did not even present it as a puzzle. Anyway, take a look at it, and help me solve it. Otherwise, I’m lost (and so is my paper).

Suppose you believe that properties are the set of their instances. Suppose, furthermore, that you are a modal realist. Aristotle was not, but he does believe in potential and actual bearers of properties, and he does think these are within the extension of a property [Meta, V.26].

In any case, there is a familiar problem with this view: coextensive properties. ‘renate’ and ‘chordate’ have the same actual extension, yet they are different properties. The solution is easy and well known: ‘renate’ and ‘chordate’ are not coextensive because they have different extensions in other possible worlds. Aristotle’s reply would be similar: ‘renate’ and ‘chordate’ are not coextensive because they have different potential instances.

The problem comes with a twisted version of this objection. Suppose you have necessarily coextensive properties, and yet distinct ones. (This is what Fine presents in his ‘famous’ paper against modal accounts of ‘essence’, where he claims ‘essential property’ is not synoymous with ‘necessary property’, I think, however, that Aristotle’s example is better). Aristotle talks about ‘Grammarian’ and ‘Human’. According to Aristotle, this much is true:x is human iff x is a grammarian (or has knowledge of grammar). Yet, ‘Human’ reveals the essence of its instances, and ‘grammarian’ does not.

My question is this: is there any way in which one can sort this case out, and still be extensionalist about properties? Do you know of any extensionalist reply to this? Or should we simply claim that ‘grammarian’ and ‘human’ have the same meaning?

Advertisements

25 Responses to Necessarily coextensive, yet distinct?

  1. Steve C. says:

    Hey Edu, isn’t the grammarian/human example a very bad one once we move to the possible worlds framework? Surely there are possible worlds with Martians who have knowledge of grammar. or maybe I’m missing something

  2. edu says:

    Steve,

    Well, yeah! I guess I was not clear enough. Aristotle is assuming that ‘being a grammarian’ is the same as ‘having knowledge of a human language’ or ‘speaking a human language’.

    Does that help?

    I guess the idea is to interpret ‘grammarian’ in such a way that is consistent with Aristotle’s claim that x is a grammarian iff x is human. If, on the one hand, your martian is distinct enough not to be considered human, then it is not grammarian (perhaps a speaker of a ‘martian-non-human-language’?) If, on the other hand, your martian is similar enough to speak human languages, then it seems good enough to be human. Isn’t it?

  3. Steve C. says:

    Well, it feels like a stretch to me. It’s not evident to me that one needs to be a human to have knowledge of, or to speak, a human language. Arguably, other sorts of beings (perhaps even computers) could achieve this. (But I’m not acquainted with Fine’s article either)

  4. Alex S. says:

    Let’s just grant that Aristotle is right that necessarily, x is a human iff x is a grammarian. (Although I agree with Steve that this assumption is wildly implausible. But perhaps there is some other pair of properties that will do.) One strategy is for the property extensionalist to first argue for the following principle, and then argue that the above pair violate it:

    (P) Necessarily, having property E is what is to have the property P only if P is not a constituent of E.

    I’m not sure how to spell out the notion of `a property’s being a constituent of another property’ more precisely and in a way that will not offend the property extensionalist’s scruples. But the intuition is clear: my being a grammarian cannot ‘reveal the essence’ of my being a human, since one cannot reveal the essence of the former property without ultimately having to ‘reveal the essence’ of the latter. Another strategy is for the property extensionalist to first argue for the following principle, and then argue that the above pair violate it:

    (C) Necessarily, having property E is what is to have the property P only if E and P are substitutable salva veritate in intentional contexts of such-and-such type.

    This principle seems to work for the pair of properties under consideration in causal, nomological, and explanatory contexts. The following biconditional, for instance, strikes me as false:

    (C1) My parents are disposed in circumstances C to having human children iff my parents are disposed in circumstances C to have grammarian children.

    The reason why (C1) should strike you as false, too, is that a pair of properties might be necessarily coextensional even if the circumstances in which (instances of) these properties bear certain causal, nomological, or explanatory relations to (instances of) other properties differ. And perhaps this must be the case if one of the pair ‘reveals the essence’ of the other.

  5. Edú says:

    Well, unlike you guys, I do not think that the human-grammarian example is implausible, even less wildly. But I will not get into a defense of this here. Aristotle has other examples (see Joan Kung “Aristotle on Essence and Explanation”): ‘naturally civilized animal’ and ‘animal capable of having knowledge’ with ‘human’; ‘being colored’ and ‘being surfaced’. Kit Fine has another example: ‘being a member of the singleton SOCRATES’ and ‘being Socrates’. I hope that, at least the latter, works.
    I am not sure exactly of what to say about Alex’s arguments. It seems to me that the extensionalist has only two ways to argue: (i) show that they are not really coextensive, and accept they are distinct; or (ii) show that they are not two different properties, and accept they are coextensive. I don’t know exactly what Alex’s strategy is. Sometimes it seems as if he follows (i), but then again, he starts by accepting that ‘x is human iff x is a grammarian’, which is tantamount to accepting that ‘human’ and ‘grammarian’ are coextensive.
    Alex presents two principles of property-identity, and claims that ‘human’ and ‘grammarian’ fail to meet them. That seems like saying that they are not really the same, or in Alex’s own words, what it is to be a Grammarian is NOT what it is to be Human.
    As a matter of fact, Aristotle seems to agree with Alex’s principles. His claim is that ‘Human’ is essential and ‘grammarian’ is not, because the former is needed in order to explain what a man is, whereas the latter is not. Hence, revealing the essence of a man requires ‘human’ to be used, and not ‘grammarian’; but one cannot reveal the essence of what a ‘grammarian’ is without revealing the essence of what a human is. That is what Aristotle thinks, and that seems to be what Alex grants at the beginning of his comment.
    Aristotle also seems to assume that ‘Grammarian’ and ‘Human’ are not substitutable salva veritate in all contexts. At least this one seems obvious: ‘x reveals the essence of Socrates’. Aristotle says that, even though every grammarian is human and every human is a grammarian, only HUMAN reveals the essence of Socrates, not GRAMMARIAN. That seems to meet Alex’s criterion. So they are different properties.
    But that does not solve the problem for the extensionalist. All that Alex shows is that they are different properties. If the extensionalist accepts this, then she MUST show that they are NOT coextensive. We must show that the reason why the terms are not substitutable salva veritate is owed to its not being coextensive. We cannot simply show they are not substitutable and infer that they are not coextensive. That would be begging the question. The anti-extensionalist can simply say: well they are not substitutable because they are not the same property, even though they are coextensive.
    Our opponent could even reply, contra Alex, that C1 is actually true. In so far as your parents are disposed to have human children, and all human children are grammarians, you parents are disposed to have grammarian children. The fact that they do not consciously consider this does not make it less true that having human children is having grammarian children. After all, that is what makes it true that ‘x is human iff x is a grammarian’, which is what we have, for the sake of the argument, agreed on.
    It might be, however, that I am mistaken and Alex is not trying to defend the extensionalist but, rather, argue against that view.

  6. Alex S. says:

    Suppose that someone where to say that properties F and G are necessarily coextensive, yet intuitively F and G are distinct. Is this a difficulty for property extensionalism? Edu say that it is, and I thought that I disagreed. But now I’m concerned that the reason I disagree has to do with a (somewhat non-standard) understanding I have of ‘property extensionalism’.

    At its root, property extensionalism is ultimately a thesis about the individuation of properties. One way to understand this thesis is as saying that

    (PE1) Necessarily, F and G are distinct properties iff the set of F instances is not identical to the set of G instances.

    This is the most influential form of property extensionalism, and perhaps this is how Edu understand it as well. If so, then Edu is right. But (and here is my non-standard understanding of the thesis at issue) this seems like a very restrictive version of property extensionalism. Here is how I understand ‘property extensionalism’:

    (PE2) Necessarily, the facts in virtue of which F and G are distinct properties hold solely in virtue of the extensions of the sets of property instances (and perhaps, Boolean operations upon them).

    Clearly, (PE1) entails (PE2): the sets of property instances mentioned in (PE2) are just the sets of F and G instances mentioned in (PE1). But (PE2) does not obviously entail (PE1). For F and G might be partially individuated by sets of property instances other than those of F and G. For example, F and G might be partially individuated by their relations to other properties. And as long as those relations hold solely in virtue of the extensions of the sets of their instances, then (PE2) would be satisfied but (PE1) might not.

    So my question now is: is it (PE1) or (PE2) that I’m supposed to defend? If it’s (PE1), then I concede that necessarily coextensive yet intuitively distinct properties are a counterexample to property extensionalism. But if it’s (PE2), then I think I can defend what I wrote in my previous post.

  7. Edú says:

    I like the thrust of Alex’s non-standard proposal. I did, as he suspects, assume a starndard view on property-extensionalism. I now understand better what the initial point was, and I think I agree. But I am still not convinced, perhaps because I have not properly understood, that it will work.

    If I understand it, Alex aims at giving us more resources for property individuation. Not only can we take the set of all instances, but also the relations that those instances stand in; i.e., relations that belong to the properties in virtue of its extension. This, in principle, seems to solve the problem since, as Alex points out, the set of these relations most probably will not be identical with the set instances of the properties. Therefore, you can partially define, say, ‘Grammarian’ by means of the relations that hold in virtue of its extension. This set of relation will certainly be different from the set of instances of, say, ‘human’. Hence, we do have a satisfactory extensional account of ‘Grammarian’ and ‘Human’ that distinguishes among them.

    So far, so good. I am still worried, however, that an anti-extensionalist my reply in the following way. So the set of relations that a property has in virtue of the relations of its instances is not coextensive with the set of its instances. But that is not only true of, say, Grammarian, but also of Human. Furthermore, if the set of instances of ‘Grammarian’ is coextensive with the set of instances of ‘Human’, then it must be that all the relations in which the instances of the former stand are exactly those in which the instances of the latter stand. After all, they have exactly the same instances. If so, then the set of relations that partially defined ‘Grammarian’ above may also partially define ‘Human’. We still do not know why that set of relations is more a definition of one than a definition of the other. Furthermore, if we take the difference between the set of instances of ‘Human’ and the set of relations of instances of ‘Grammarian’ to prove that they are different properties, then we are in big trouble. For exactly the same difference holds between the instances of ‘Human’ and the set of relations of instances of ‘Human’. Thus, we should admit that the property HUMAN is importantly distinct from itself.

    I do not know how to avoid this objection. I do think, however, that Alex’s response, or something pretty close to it, should solve the problem.

  8. Edú says:

    I’m very puzzled now. I have been considering Alex’s proposal a bit further. I think the following is an example of his, but I want to present it in a different way, so that we can test it better.

    Suppose there are only two humans and, therefore, two grammarians. Thus, whatever is true of humans is true of grammarians, and vice versa. Now, suppose that one (i.e., Pierre Menard) is a scrivener while the other (i.e., Funes) is an architect. They both do whay they do in virtue of their humanity, but not in virtue of their knowledge of grammar. The scrivener, however, writes down very good copies of Aristotle’s Metaphysics and Cervante’s Don Quijote. He does so in virtue of his being a grammarian.

    Now suppose we Follow Alex’s PE2, individuate GRAMMARIAN as the set of objects, pairs of objects, triples, etc. that hold in virtue of {Pierre, Funes} being the extension of GRAMMARIAN. This will, allegedly, include the extension of the relation ‘x copied y’, which is defined as

    {, }

    So a partial definition of ‘Grammarian’ would include this:

    GRAMMARIAN {(Pierre, Funes),(,)}

    Then the objection comes: as a matter of fact the set of pairs {, } also hold in virtue of [Pierre, Funes} being the extension of HUMAN. How can we distinguish between this? The only thing that comes to my mind is to say that the set of pairs above is part of the definition of GRAMMARIAN because it holds of the extension IN VIRTUE OF the knowledge of grammar that the subjects have. An alternative definition for HUMAN would be :

    HUMAN {(Pierre, Funes),(,), (,)}

    where {,} stands for the ‘x built y’ relation. Strictly speaking, we should have a third property.

    ARCHITECT {(Funes),(,)}

    Thus, one can say that GRAMMARIAN and ARCHITECT are proper subsets of HUMAN, and so, distinct from them. If this is correct, then my only worry is the following. Is it, or is it not, a bit ad hoc, or even circular, to appeal to ‘what is done in virtue of being a grammarian’ to distinguish between GRAMMARIAN and HUMAN?

    [p.s. excuse my lousy use of set theoretic devices, and my boolean ignorance, if it shows]

  9. Dustin says:

    Hi Edu,

    I don’t see the puzzle. Perhaps it would be best to start by laying out a clear statement of the view for which the case presented is supposed to be a problem. You start with that “extensionalist” view, according to which a property JUST IS the set of its instances. Notice that this is a stronger view than the view that property P1 = property P2 if and only if P1 and P2 are coextensive. The former entails the latter, but not the other way around, because we could hold that P1 and P2 are indentical if and only if P1 and P2 are coextensive, and yet still not IDENTIFY a property with its extension–we might claim that the property is something else, maybe something in Plato’s heaven. A silly view, but a view.

    You then say that the extensionalist must modify his view to account for the chordate/renate case. But now what is the view? You suggest something along these lines: property P1 and property P2 are identical if and only if P1 and P2 are NECESSARILY coextensive. But notice that this is NOT actually (yet) an extensionalist view. Recall above that an extensionalist view doesn’t just tell us that P1 and P2 are identical when they are coextensive, it also IDENTIFIES the property with its extension: it says that the property JUST IS the extension. So the analogy here is that a view according to which P1 and P2 are identical if and only if they are necessarily coextensive is not yet an extensionalist view: it must go further and IDENTIFY a property with some sort of extension.

    This is exactly what Lewis does. For Lewis, a property P JUST IS the set consisting of all and only the members of its actual extension and the members of all its possible extensions. But this is a move not obviously open to us actualists. Because Lewis is a modal realist, there actually ARE these possibilia lying around to be included as members of the set identified with the property. Not so for the actualist.

    So my question is this: what, for an actualist and extensionalist, would be the set identified with a property?

  10. Edú says:

    Hi Dustin,

    This is my second reply, for some reason the former got lost. Briefly put, the problem is about an extensionalist reading of Aristotle. There are two things that make me think that Aristotle’s universals are extensions, like Lewis’ properties. First, Aristotle accepts the real existence of both, actual and possible things. Thus, he also accepts that two universals (e.g., chordate and renate) may have the same actual extensions and yet different potential extensions, and thus, not the same TOTAL extension. Second, Aristotle talks about Universals as if they are collections: they contain the things that they are true of, they cease to exist if they things they are true of cease to exist, and they are causally inefficacious.

    The problem is this: Aristotle also accepst that HUMAN and GRAMMARIAN are both necessarilly coextensive and distinct. The former reveals the essence of Socrates, the latter does not.

    So the problem is that, if both Lewis and ARistotle are correct, then we must admit (1)-(2):

    (1) Identify Universals as extensions (of both potential and actual instances).
    (2) If P1 and P2 are necessarily coextensive, then P1 = P2.

    But then, if the HUMAN-GRAMMARIAN or the SOCRATES-MEMBER OF SINGLETON cases hold, then we must accept also (3):

    (3) necessarily coextensive properties might still be distinct.

    (3) seems to contradict (2) and (2) follows from (1). (1) just is the extensionalist position. So there’s the problem.

  11. dtlocke says:

    Thanks for the clarification.

    Just so I’m clear, the assumption underlying your argument seems to be:

    A) If for some X the essence of X is to be P1 but it is not the essence of X to be P2, then P1 is distinct from P2.

    Is that right? Seems pretty plausible to me.

    But if so, why not just say: well, Aristotle was wrong, then, to hold that the property of being human and the property of being a grammarian are necessarily coextensive. Not only was that claim just flat out false (as evidenced by the examples produced by the commentors above), but it was also inconsistent with his own extensionalist position.

  12. Patrick says:

    I think the whole argument hinges on the choice of properties.

    “human” and “grammarian” are absolutely *not* necessarily coextensive; there could be Vulcan grammarians, Homo erectus grammarians, or even chimp grammarians in all manners of other possible worlds; and there are plenty of human beings that are not grammarians even in the broad sense of understanding syntax—e.g. infants.

    Indeed, I don’t think it’s at all problematic to say that any two properties that would be necessarily coextensive would also be identical; indeed, set-theoretically this is the ZF axiom of comprehension.

    I mean, try proposing a counterexample! The only necessarily coextensive properties I can come up with are all definitions or follow tautologically from definitions, and so the identification doesn’t seem at all problematic.

    E.g., “Is a bijection” and “is an injective and surjective functional mapping between sets” are necessarily coextensive, but they are also identical!

    The only reason this seems puzzling is that we have adopted a choice of “necessarily coextensive properties” that are nothing of the sort.

  13. Edú says:

    Dustin and Patrick,

    Thanks for your comments. Here are some brief replies.

    I think none of the exit strategies you propose work out. One goal of Aristotelian scholarship, as of any other historical figure, is to come up with the best interpretation of his text. The claim that Aristotelian universals are extensions is an interpretation that, I think, has some very good evidence on its side. But it is not the only interpretation. Some think they are non-unit classes intensionally understood, some think they are inherent properties. Hence, if other interpretation is such that it does not ‘just’ claim that Aristotle’s claim about Grammarians and Humans is flatly false and/or inconsistent with the rest of his claims, those are better interpretations. Briefly put: when interpreting any historical figure to claim that your philosopher is ‘flatly false’ or ‘plainly inconsistent’ is just NOT an available move.

    As for the choice of properties. I am not still not convinced by Patrick’s argument. I don’t see why Humans cannot come from Vulcan, especially if we assume that Vulcan has such an environment that it allows for grammarian beings to evolve. And I am pretty sure that by definition there cannot be chimp grammarians. Research in cognitive science has shown the limits of chimp cognition as far away from being capable of using/parsing linguistic information. Everyone (i.e., Spelke, Bloom, Shatz, etc.) agrees, even Chomsky, that grammar is a human-specific cognitive capacity. The latter even argues that it ‘evolved’ with humans. So, I think the claims that there could be chimp grammarians is quite controversial and, judging by the evidence, almost flatly false.

    But, forget about the properties. As I said above, there are other important examples that allow us to take the worry out of the historical context. As I said above, Kit Fine argues (explicitly following Aristotle) that there is a distinction between necessary and essential properties. So, Patrick, here are the properties that you need to scuffle against:

    ‘being Socrates’ and ‘being a member of the singleton SOCRATES’.

    They are necessarily coextensive, yet distinct.

  14. Patrick says:

    I stand by everything I’ve said.

    “humans” from Vulcan are not human in the ordinary definition; indeed, I can imagine all sorts of aliens who differ from the human race in profound ways, but still use grammar. Not to mention the fact that you didn’t refute my point that many humans are not grammarians, e.g. infants.

    The whole problem IS the choice of properties; that’s the only reason there seems to be any difficulty.

    Yes, I am perfectly comfortable saying that “being Socrates” and “being a member of the singleton SOCRATES” are one and the same property. Indeed, it seems ontologically parsimonious in a way that asserting these to be distinct properties does not.

  15. Edú says:

    Patrick,

    Just a few comments.

    1) your claim that many humans are not grammarians, as I said before, is controversial. Many linguists and psycholinguists debate on this. A powerful line of thought, initially presented by Chomsky, claims that universal grammar is genetically encoded. If so, then all humans, in so far as they belon to the same species and share the relevant DNA, have such grammar. Hence, even infants are grammarians. Others think otherwise. I agree. But unless you have arguments or evidence that sorts out this conundrum, I think your claim is not well supported. As for the vulcans case, I tend to think that ‘being human’ is a natural property. So I guess I cannot agree with you until you find a way, common to natural sciences, to show that your vulcans are different enough in the relevant biological ways from what natural sciences tell us about humans.

    2) If you are pretty comfortable saying that ‘being Socrates’ and ‘being a member of the singleton Socrates’ are one and the same property, then I think we just don’t share enough background to have a proper discussion. I think there are several reasons to think that these are different properties, and that the parsimony criterion is rather immaterial here. First, because it is essential of Socrates that it is a human being, but it is not essential of Socrates that it is the member of any set. Being human defines Socrates. Being the member of the singleton Socrates, does not define Socrates. Second, if the parsimony criterion where enough to defend your claims, then we could just simply say that ‘human’ and ‘grammarian’ are one and the same property. After all, it seems ontologically parsimonious in a way that asserting these to be distinct properties does not.

    I think that if you want to stand by everything you’ve said you need to say a few more things.

  16. Patrick says:

    1) I don’t know enough linguistics to seriously debate this. What I do know is that Japanese grammar is almost completely different from Latin grammar (I know both, after all; Latin, for instance, lacks adnouns and has a future-perfect tense), and it seems highly unlikely that this would be the case if grammar were something encoded at birth. For now, let’s just say that the claim that “human” and “grammarian” are necessarily coextensive is at best controversial, and so it can’t be our paradigmatic example. The Socrates example is much better.

    2) Hm. All right then. We need to get on a better mutual foundation. I don’t think I should begin, however, since what I hold is basically that a given property can be fairly equated to sets comprising all entities for which a given proposition is true. I don’t know that this is even the best way to characterize properties; I just don’t see it as especially problematic.

    So I turn the question to you: what, if not this, *are* properties? How are they distinct from sets, and how can this be discerned?

    As for the question of whether “being a member of the singleton SOCRATES” is essential to Socrates, I offer a possible-worlds-semantic argument that in fact it is.

    A property P is essential to an entity E iff it is “de re” necessary, i.e. iff, for all possible worlds W_r, if E exists in W_r, then E has P.

    Socrates, if he exists in a given world, necessarily has the property of being in the singleton SOCRATES; therefore this property is essential. It didn’t seem essential intuitively, but in fact it is.

    (Note, by the way, if you deny that Socrates necessarily is a member of SOCRATES, you must also deny that the two properties are *necessarily* coextensive.)

  17. Patrick says:

    (The above needs corrected slightly; it should say:
    … if E exists in W_r, then E necessarily has P.

    Sorry if that added any confusion.)

  18. Alex S. says:

    To take the attention off the human/grammarian and the Socrates/singleton SOCRATES examples, how about these two necessarily co-extensive (higher-order) properties?

    Def: x is F iff x is the property of being a vector magnitude.
    Def: x is G iff x is the property of being a vector direction.

    Argument: Suppose that vectors (e.g. electric field magnitudes) are genuine properties of the objects which possess them. Necessarily, every vector has a magnitude and a direction. So necessarily, every vector has the (higher-order) properties F and G defined above. But F and G are distinct properties: for example, the magnitude and direction of a vector have distinct causal and modal profiles. Yet no other properties have F and G. So F and G are properties that are necessarily coextensive, yet distinct.

  19. Lei says:

    I suspect that Alex’s principle (C) is overly restrictive for property identity. (“Necessarily, having property E is what is to have the property P only if E and P are substitutable salva veritate in intentional (intensional?) contexts of such-and-such type.”) Probably only analytic identities that result from synonymy (“the property of being a bachelor = the property of being an unmarried man”) can pass the test of C.

    First, synthetic identity cannot pass the test of C. It is widely agreed that the property of being water is identical with the property of being H2O, but obviously someone may believe, for example, that the stuff in the bottle is water without believing that the stuff in the bottle is H2O. Second, even some kinds of analytic identity cannot pass the test of C either. For example, the property of being 1000/125 is identical with the property of being 8. But it is quite conceivable that someone doesn’t believe that 1000/125 equals 8.

  20. Edú says:

    I suspect the problem Lei raises is not insurmountable. Briefly put, it is Frege’s old puzzle concerning the substitution of coreferential terms within belief reports. Frege (and Fregeans) like to sort out this problem by semantic means; i.e., claiming that the coreferential terms in question are not in fact synonymous. It seems as though there are other ways around this problem. Here is one that, I think, makes more sense: blame it on the ascribee’s ignorance.

    That is to say, if ‘H2O’ and ‘Water’ always refer to the same thing, then it is the case that whoever believes that some container has water that person ipso facto believes that such container has H2O. If you reply that such a belief report is false I will say you beg the question. If you say it is not fellicitous, I will agree. And then say that it is true, even though it does not represent the subject’s state of mind according to the traditional rules of Folk Psychology. When interpreting others sometimes we are not suppossed to find out what the subject is really committed to (e.g., the bottle contains H2O) but what the subject thinks she is committed to. That way we’ll be able to predict her behavior.

    It could be added that the subject ignores what the meaning of ‘Water’ is. What we are dealing with here is the problem of ignorance and false belief, and not with the invention of a second realm of meaning beyond that of reference.

    Mutatis mutandis for our concerns. Unlike beliefs, properties are non-psychological entities. It better not be that Folk Psychology rules over them. I think Alex’s principle can still stand after Lei’s criticism. There are other (apparently non-extensional) contexts where it seems to work out well (e.g. ‘F reveals the essence of Socrates better than G´).

  21. Lei says:

    Edu, thanks for your reply. :)

    “Frege (and Fregeans) like to sort out this problem by semantic means; i.e., claiming that the coreferential terms in question are not in fact synonymous.”
    Yes, I agree that “H2O” and “water” are not synonymous, but the crucial question is: Does it follow from the fact that two terms are not synonymous that the two objects the two terms denote respectively are not identical?

    “That is to say, if ‘H2O’ and ‘Water’ always refer to the same thing, then it is the case that whoever believes that some container has water that person ipso facto believes that such container has H2O.”
    I should clarify something. In order to be an intensional context, the belief ascription should, of course, be understood in a de dicto sense. Then, do you still think, on a de dicto reading, “whoever believes that some container has water that person ipso facto believes that such container has H2O”?

    “It could be added that the subject ignores what the meaning of ‘Water’ is. What we are dealing with here is the problem of ignorance and false belief, and not with the invention of a second realm of meaning beyond that of reference.”
    I’m not sure I understand this passage right. Do you mean that if someone who believes the bottle has water doesn’t believe that the bottle has H2O, it is only because she ignores the meaning of ‘water’? Do you mean that the meaning (sense) of a term is just its reference? If you think that the meaning of a term is distinct from its reference, it is quite possible that someone knows the meanings of two terms but doesn’t believe they denote the same object. If you think that the meaning of a term is just its reference, it seems to me that it makes no sense to say “F reveals the essence of Socrates better than G” (given that F and G necessarily co-refer to the same object).

  22. Edú says:

    Lei, thanks for the questions,

    I’ll try to be brief. I do not consider myself a Fregean. I do think that if ‘F’ and ‘G’ happen to be referential terms AND coreferential, then they do have the same semantic content. I guess my answer to your subsequent questions just follows from this.

    I think there was perhaps a confusion. I do not take all intensional contexts, or all opaque contexts, to be reduced to belief ascriptions. I do not think, of course, that if we limit ourselves to de dicto ascriptions the subject still believes the bottle has H2O. That’s granted. What I am arguing for here is that we should not limit ourselves to de dicto ascriptions when dealing with belief reports. Sometimes it is better to make de re ascriptions, especially when you want to know what is the case, and not just what the subject believes.

    “Do you mean that if someone who believes the bottle has water doesn’t believe that the bottle has H2O, it is only because she ignores the meaning of ‘water’? Do you mean that the meaning of a term is just its reference?”

    No, I do not mean to say that it is ‘only’ because of that. But I am quite sure that, as I said, it should be added that the subject in question does not know the meaning of ‘Water’ if she does not know that Water is H2O. Just like I do not know the meaning of ‘Electron’ if I have no idea of what its essential properties are. I take it that professors of Physics are the authorities concerning the meaning of ‘Electron’.

    “If you think that the meaning of a term is just its reference, it seems to me that it makes no sense to say “F reveals the essence of Socrates better than G” (given that F and G necessarily co-refer to the same object)”

    I think this last claim of yours only follows if you are some sort of meaning absolutist. That is to say, if you think that everything we say about F’s has to be cashed out in terms of the meaning of ‘F’. But there are other things we can do. Like keeping reference for the meaning, or better, semantic content of ‘F’, and placing other stuff as the relational properties of F’s. That’s the solution I think Alex offered (I am not sure about his positions on Frege and meaning though). I see no problem with it, just like I see no problem with not being the kind of meaning absolutist that Frege seems to have championed.

  23. Lei says:

    “I think there was perhaps a confusion. I do not take all intensional contexts, or all opaque contexts, to be reduced to belief ascriptions. I do not think, of course, that if we limit ourselves to de dicto ascriptions the subject still believes the bottle has H2O. That’s granted. What I am arguing for here is that we should not limit ourselves to de dicto ascriptions when dealing with belief reports. Sometimes it is better to make de re ascriptions, especially when you want to know what is the case, and not just what the subject believes.”

    I just said “In order to be an intensional context, the belief ascription should, of course, be understood in a de dicto sense”. It doesn’t follow that “I take all intensional contexts, or all opaque contexts, to be reduced to belief ascriptions”.
    According to Principle (C) suggested by Alex, we do the test of property identity in an intensional context. So we should ascribe belief reports in a de dicto way in order for the context to be an intensional context. The question of whether we should ascribe belief reports in other ways in some circumstances is irrelevant.

    By the way, in my last post, I hastily supposed that F and G are two terms in your sentence “F reveals the essence of Socrates better than G”. Sorry for the misinterpretation.
    But if F and G are two properties, I’m very curious. What do you mean by “essence”? Could you give me a good example in which F reveals the essence of an object better than G (given that F and G are necessarily coextensive). After reading your previous posts, I found that the only example regarding the issue you offered is the example of HUMAN and GRAMMARIAN. I agree with other guys that human and grammarian are not “necessarily” coextensive.

  24. Edú says:

    Hi Lei,

    A quick question, and a quick answer. First, the question.

    If you do not think that all intensional contexts involve belief ascriptions. Then why should it follow from Alex’s principle (C) that you should make any belief ascription whatsoever? The principle simply claims that both properties should be substitutable salva-veritate within intensional contexts that are yet to be determined. I simply don’t see where the belief ascription comes from.

    Now the quick answer as I gave it to others that, like you, are not convinced by the Human-Grammarian example. I haven’t seen any convincing support for your claim. I have argued that the claim that humans are necessarily grammarians IS empirical, and that pretty much all research in psycholinguistics points to that claim. Even in cases of abnormal linguistic development there IS knowledge of Grammar. So, I guess I am asking for some evidence on your behalf.

    As for the other side of the coin. I guess it is difficult to have experiments with non-human grammarians. But I do presuppose (perhaps I am mistaken) that Darwin’s evolution and natural selection is applicable to life in other planets. I also suppose with Chomsky, and a ton of psycholinguists, that linguistic development is a biological, and genetically encoded, feature of the human species. So I guess there is a good chance that any other being from different planets that possesses such a biological feature may very well have evolved through very similar processes of natural selection. So similar that, I bet, for biological purposses it can count as a member of the same species. This, however, is especulation like that concerning the claim that humans and grammarians are not necessarily coextensive. Notice however, that it is only speculation halfway (i.e., that all grammarians are humans) for the other half (i.e. that all humans are grammarians) is well supported empirically.

    Still, I gave another example. I mentioned Kit Fine’s fairly recent paper where he claims that not all necessary properties are essential properties. One of his examples is concerned with being Socrates and being a member of the singleton Socrates. According to Fine they are both necessary properties of Socrates, but only the former is an essential property of his.

  25. Lei says:

    I don’t think that all intensional contexts (such as modal contexts) involve belief, not to mention belief ascription. What I’m saying is just that “some” intensional contexts do involve belief ascriptions. In my first post, I just give an example of intensional context, which is concerned with belief ascription.

    I have read Fine’s paper. He adopts a distinct usage of “essence”, which is not shared by some others. Actually, I’m very happy to regard being a member of the singleton Socrates as an essential property of Socrates. :)

%d bloggers like this: