A formulation of Leibniz’s Law / the Indiscernibility of Identicals

Well, I should have said, “Dale, do you agree or disagree with the last three sentences?” 🙂

I have what I hope is a clearer question: Do you conjecture that the human soul is nothing but non-physical mental substance or do you conjecture that the human soul also has hyperdimensional parts?

I’m asking: what sort of particular properties do you believe in?

My answer would be that this is an obviously ill-formed question as it stands. What counts as a property depends on the context. Sometimes one will want to distinguish between properties and accidents, sometimes between properties and subjects; sometimes the terms will be isomorphic to predicates (properties just are what predicates refer to), sometimes will include modalities and sometimes won’t, etc. So the question can’t be made sense of without specification to a context. You can ask, in other words, what kinds of properties I think really exist if we use ‘properties’ to indicate propria, or if we use it to indicate non-essential qualities, or if we use it in a sense in which parts of the definition of the essence are the properties of the thing, or if we use it in a sense in which properties are what identifies the possible world, etc.; but asking what kinds of properties I think exists makes the same error as asking what kinds of intuitions I think people can have, namely, the error of thinking that I would use such a historically malleable term in a single univocal sense. In the broadest sense, properties are just whatever we can reasonably attribute to something as belonging to it; what we can reasonably attribute to things will depend on what we are doing, because reasonable attribution is not invariant across contexts. For some things being to the right of something will be something reasonably attributable to it as belonging to it somehow, and thus could be called a property of it; for some things it won’t. If I were proposing as self-evident a principle that involved properties, I would have to define what I meant by ‘property’ relative to a context; there would be no way for anyone to know what I meant without it. But I’m not, and there are too many to make it reasonable for me to go around playing blindman’s bluff trying to figure out what you have in mind, particularly since, to know that the principle is even a candidate for being universal, necessary, and self-evident, you must already know what it means, and, assuming it’s not an ineffable truth, should be able to convey it.

I don’t really care how abstract or concrete the discussion is; but I do want definitions. Definitions and definitions alone are the test of whether a claim genuinely fits the bill of a “universal, necessary, and self-evident”. They don’t need to be rigorous accounts of the natures of things (nominal or operational definitions would be fine), but I do need to know how you are using the words, or I don’t know the limits, conditions, or boundaries of the terms, and thus don’t actually know what the principle is.

So, God-as-subject just is God-as-object. I assume you’re assuming that, because the counterexample must make the antecedent true and consequent false. But you think they can differ? What would be a mode of one which is not a mode of the other?

That God as subject is subject and God as object is object. After all, it’s at least enough to distinguish them that we can put God, under the intension of ‘subject’, into x, and God, under the intension of ‘object, into y, and keep the two distinct all the way through. If this kind of intensional distinction is or can be a distinction in intrinsic modes of subjects as opposed to those of objects, then the consequent equivalence is broken without breaking the antecedent identity. If extensionally identical values of variables can under any circumstances have intensionally distinct intrinsic modes, the conditional doesn’t hold for those.

All identity statements have to assume that some intensional distinctions don’t matter. In x=y, we obviously are intensionally treating x and y differently in some sense — they get different letters to indicate that they are different variables and they have different locations in the equation (to the left and the right of the equality sign, for instance). We simply assume that these can be ignored to make sense of the statement as an identity statement; this allows us to focus on purely extensional matters. It’s when we get into the sorts of intensions that are typically handled by things like modal operators that things get tricky. It’s precisely this that causes problems for the standard version of the Indiscernibility of Identicals — it fails in certain kinds of plausible temporal logics, epistemic logics, etc. (because it fails to take the quirks of the relevant intensions into account), which is equivalent to saying that you can propose temporal, epistemic, etc. scenarios that are plausible counterexamples.

In essence, the issue here is that, assuming that the principle is true and that this is not a counterexample, we seem to face a choice among the following:

(1) We can deny that, in a being that necessarily knows itself and thus is necessarily both an object and a subject of its knowing, being an object or a subject is not an intrinsic mode. In effect, this means that, whatever intrinsic modes, the fact that a property, feature, or quality is necessary to a thing is not on its own a sufficient reason for thinking it is an intrinsic mode.
(2) We can deny that there is any such thing as self-knowledge in a strict sense: subjects and objects of knowledge are always non-identical. In effect, we are saying that being a subject and being an object is a difference in intrinsic modes and therefore rules out identity between subject and object. Knower and known are always different, although, of course, they could be related somehow.
(3) We can hold that being a subject and being an object are both intrinsic modes, but that in self-knowledge they are not different intrinsic modes. This is equivalent to saying that self-knowledge does not require a distinction between subject and object; you can have self-knowledge without a subject or object in the distinguishable senses that we usually think of actions having subjects and objects.

Possibly there are others; if so the list can be extended. But since each of these gives us a very different conception of what an intrinsic mode is, then, since the point was that the modified LL has to be self-evident, (assuming it actually is self-evident) at least one of these must be self-evident for the sense of intrinsic mode that is relevant here (or the necessary self-knowledge case is a counterexample). Keep in mind that I’m not here proposing a counterexample: I don’t know what you mean by intrinsic modes so as to be able to say whether it’s a counterexample or not. I am instead trying to figure out what you mean by intrinsic modes from the behavior of the principle in unusual situations. You can take your pick of any of the choices, or add any others, and that’s fine; this is not an attempt at refutation, but an attempt at figuring out what you mean by intrinsic modes by looking at what about your conception of intrinsic modes would rule this out as a refutation.

On the possible worlds case, I take it that it would follow that what something could be or have is never an intrinsic mode of it in the sense relevant to the principle here. (I don’t really care what other people might do, but only what you are doing; for one thing the others are not the ones actually proposing the principle, and for another, as far as I know they might very well do very different things; if we get into hypotheticals we will never have an end, because we can take any non-self-contradictory principle about intrinsic modes and propose hypothetical answers for what somebody could assume, ad hoc, that intrinsic modes are in order to keep the principle from having counterexamples. What matters is whether, maintaining the same meaning of the same terms, the principle in fact does have counterexamples. If it doesn’t, one can see how far that applies to analogous examples in alternative metaphysics. But if we let the meaning of the terms jump around from the beginning, we aren’t finding principles that are irrefutable because they are self-evident but principles that are irrefutable because they are understood equivocally.) In other words, we are to assume, for seeing how you understand this principle, that only what is actually the case is even a candidate for being an intrinsic mode?

I notice that the nonrelational sense of ‘intrinsic property’ came up above; obviously this is relevant to the self-knowledge case. In the sense you are using the term, do you think that all intrinsic modes are nonrelational, or are there at least some relational intrinsic modes (e.g., necessary ones)?

I suppose that anybody believing in soul sleep would reject the existence of a hyperdimensional spirit, so that would be a different model.

Dale, I was thinking of that a person’s properties consist of their biological body and hyperdimensional spirit. I suppose I am unsure how to identify the intrinsic properties of a person going from fetus to childhood to adulthood to postmortem. How do you identity a person’s intrinsic properties? Also, there are no intrinsic properties in creation from God’s perspective.

Hi Dale,

I’ve enjoyed reading this blog for a while, but this is my first post. 🙂

I’m still learning formal logic, so I want to make sure I follow. You’re just saying that x = y only if x and y are the same way at the same time, right?

If so, I agree that this is perfectly self-evident. However, I think adding the extra variable for time is only necessary if our concept of a “thing” is too vague. We live in dimensions of space and time, and as such what constitues any thing (say, me) ought to be considered to include both my extent in space and my extent in time. It makes no sense, then, to speak of a different “me” today and yesterday; at both times you merely get a snapshot from my whole temporal existence (much like examining one of my cells under a microscope is one snapshot of my physical existence). With this understanding it seems you can use Leibniz’s Law without any trouble arising from the apparent “change of an object over time”–the object is actually (to put it poorly) the sum of its states through time. Any “property” of that object may then be its state at a given time, its state over an interval of time, etc. So I don’t really disagree with you, but I think confusion over identity can be clarified without complicating the formula.

Why the hostility? My principle is much like, e.g. Cartwright’s. Why think it strange that someone tries to refine a formula to get around counterexamples, rather than hand-waving about “contexts” on necessary restrictions? And why think it strange that I want to make a point in my preferred lingo, while being as neutral as possible about property-theories?

But this is not what you’ve been doing. You’ve been deliberately refusing to clarify your “preferred lingo” in a discussion where the precise question at issue is whether the principle in question is so universal, necessary, and self-evident any adult could see that it is on knowing the meaning of the terms. Having made that strong claim, you seem to be deliberately dancing, and indeed doing some surprisingly high-handed dancing that refuses to take any concerns seriously, in order to avoid having to do what would be required to back that up: namely, letting us know what the actual meanings of the terms are.

There are so many things about what you are doing here that I simply don’t understand at present. To take just one example, if you’re going to pack everything into predicate W, there’s no need to go up to three variables. Simply take the original LL and qualify the predicate in the consequent so that it, too, deals with intrinsic modes under a quasi-temporal condition. All problems solved, and it is clear what is going on, even though we would still need a precise definition of intrinsic modes: the scope of the law is being restricted to those domains where the modal problems don’t arise. So why the juggling with the variables? The variables themselves don’t change the fundamental problem, which as I noted in my first argument (which still stands as far as it goes), remains for any expression analogous to LL except for number of variables. And your response confirms this: all the weight actually falls under W, which you keep gesturing at vaguely. But, again we could have a predicate analogous to W at the simpler LL stage. So why the extra layer of complexity? I don’t know. If I knew how intrinsic modes were supposed to be working here, conceivably it might make sense, but I don’t. But, apparently, no matter how much I tell you that I don’t, you’re just going to assume that I really do and am lying, and just tell me to use whatever terms I usually use to talk about what you’re talking about. Let’s not operate on the assumption I really already know what you’re talking about, so far as even to have a preferred terminology for it, but am just being stubbornly obtuse, and let’s just go, for the sake of the argument, with the idea that I really do need actual explanations.

On your explanations here about intensions of intentionality, we’re still at the level of examples, and therefore guessing at what could be a counterexample on the basis of vague analogies, but here’s a question that may help: if there is any entity that necessarily knows itself completely, its being both a subject of self-knowledge and an object of self-knowledge would seem like an intrinsic property. Now, if its complete self-knowledge is genuine, itself as known by itself just is itself as knowing itself. But itself as object can’t have all intrinsic modes in common with itself as subject, because the intrinsic properties of objecthood and subjecthood themselves are different: objecthood and subjecthood are intensionally different and this is essential to what they are. Thus it would seem that itself as subject and itself as object are intensionally different, that this intensional difference is intrinsic. So it seems at first glance that we have itself as subject just being itself as object, and yet itself as subject being distinct as to intrinsic modes from itself as object. I assume you’ve considered cases like this, so the question is, why isn’t this a counterexample?

Or take another alternative. Assume counterpart theories of modality are false, and that your counterparts in possible worlds are, in fact, just you. This is at least a common way of thinking. But we can still talk about what you would do in other possible worlds. And this means that the you in possible world w1 has features that the you in possible world w0 don’t, and vice versa. But the you in possible world w1 has all its features intrinsically — that’s what locates it in w1, and so also with the you in possible world w0, or in any other. But this would generate counterexamples to your principle. So your general criteria for what counts as an intrinsic mode or property must rule this kind of reasoning out as self-evidently false (for those criteria). How?

I don’t follow you. If DTL just is DTR, why would anyone think they have those differences?

DTL is a split second or perhaps 10^35 Plank units older than DTR.

I need to be clearer about DTR. DTR is not the reflection but the person being reflected in the mirror, which is a split second before the person looking into the mirror. We could also call DTR DT1 and DTL DT2 while DT1 is a mere split second before DT2 instead of the first scenario with DT1 being years several years before DT2.

Dale, I have some clearer ideas on this:

We agree that DT1 and DT2 are identical to each other. But do we also agree that DT1 and DT2 have some different properties due to years of biological changes such as your example of weight difference?

Also, at the micro level, we agree that DT reflected in the mirror (DTR) is identical to DT looking in the mirror (DTL). But do we also agree that DTL and DTR have some different properties at the quantum level and micro different respiration properties?

Before I press the issue further. I’d like to hear a little bit more as to why (2) would be false if the argument used the names to refer to the same self.

That is, But God judges me as if I were [the same person].

Dale,

I don’t follow. It seems to me that your principle very well could let me infer that you are not numerically the same as your slimmer, younger self just because t1 and t2 are not identical.

Hi Dale. I am thinking about your version of LL and I think I get it. But I get lost when thinking about how we persist through time. It seems to imply that I am not numerically the same person I was last year–or at least it is compatible with the idea I am not the same person as last year. It seems to just say things are identical with themselves at some time t. At a later time t2 I am the same as I am at t2, but who cares? Aren’t we interested in whether we are the same at t1 and t2?

I believe, Christ is a full representation of God, in the same sense as an infinite sequence of digits is a representation of a real number. But the question whether an infinite sequence of digits is the same as a real number is meaningless. The answer depends on our definition of a real number which may vary. In the same way the question whether Christ is God is meaningless. Every property of God is represented as a property of Christ, but these two properties (of God and of Christ) are sometimes different. That God has a son is property of God which is represented as some other (I’m not sure which) property of Christ. There are no contradiction in my theology.

Well, should I write a detailed blog post on this issue? But why, is this philosophy useful for people at all? It is just true.

Yes, the first time I heard about the monothelite controversy, I couldn’t get my head around how anything with two wills could possibly be one person. The actual text of the council doesn’t address this, but it’s pretty clear from other theological writings that they mean two faculties or capacities of willing, and this I can make some sense of. In fact, it does seem to me to follow from Chalcedon, for if Christ is really to be human, he must move his arm the same way I move my arm, and not by an exercise of omnipotent power. Without a human will, it seems that we would end up conceiving of Jesus as like a remote-control robot being operated by God, rather than as a human (and divine) person.

BTW, I’m starting dissertation work on Berkeley this fall, supervised by Van Cleve.

Your Gethsemene example is a little complicated. According to the orthodox (conciliar) Christology, as far as I can understand it, Christ both wanted and did not Christ to be crucified. Specifically, it is held (again, if I understand correctly) that the single person, Christ, has two volitional faculties, the single divine volitional faculty which he shares with the Father and the Holy Spirit, and an ordinary human volitional faculty just like ours. It seems that with the former he wanted the crucifixion, and with the latter he wanted to avoid it (though the claim of moral perfection is supposed to mean in part that the human will always ultimately submitted to the divine will rather than clashing with it, so we are talking about mere wants as opposed to decisions here).

Anyway, having a human volitional faculty and wanting, according to his humanity, to avoid the cross, and even becoming incarnate can all be truly predicated of the Son, but not of the Father or the Holy Spirit or, for that matter, the Trinity, and none of them seems to be able to be dealt with by complications about time or about opaque referential contexts. (Besides, it seems to me that trying to deal with such things by means of opaque referential contexts would amount to Sabellianism.) So we clearly can’t say ‘the Father is God’ and ‘the Son is God’ both with the ‘is’ of (numerical) identity. Fortunately, there seems to me to be very little evidence that historical Trinitarianism was intended this way, except perhaps by the (rather confused) author of the ‘Athanasian’ Creed. Leibniz wasn’t the first to discover Leibniz’s Law.