Dissertation

Abstract

In this essay I will defend a version of Kripke’s necessity of origin thesis. Firstly I will exposit Kripke’s n.56, and lay out his argument. Following that I will detail Salmon’s response to it. Salmon purports to show the extra premise Kripke needs to complete his argument. I will then show Cameron’s response to Salmon, which points out that this premise is unacceptable for those with anti-essentialist intuitions. I will then respond to Cameron with a thesis for the essentiality of origin that uses identity, rigid designation and Leibniz’ law. I will show how that this solves Cameron’s belief that his W3* cannot be shown to be an impossible world without assuming essentiality of origin. I will make an attempt to further extend my argument by arguing that tables that are not identical to their hunks can be shown to have their origin essentially by this principle.

Introduction to Kripke

In lecture III of Naming and Necessity Kripke puts forth an argument for necessary connections between distinct existents contra Hume. Particularly, he makes a case for some object having an essentiality of origin. Some objects, according to Kripke, essentially have the origin that they actually have. The general principle seems to be: for certain types of x, if x’s origin is actually y, then x’s origin is essentially y.

Kripke gives two examples of this purported necessity of origin. Case 1: the Queen necessarily has the parents she has, or is necessarily derived from the zygote that she is actually derived from. Case 2: if a table that is actually derived from a certain hunk of wood, then it is necessarily derived from that hunk of wood which. I will focus on the essentiality of origin for tables throughout this essay, though I think that with a certain amount of tweaking, I can demonstrate show how my thesis can also apply to the Queen/zygote case.

In footnote 56, Kripke gives ‘something like a proof’ (Kripke, 1981, p. 114 n.56) of the principle ‘if a material object has its origin from a certain hunk of matter, it could not have had it its origin in any other matter’ (Kripke, 1981, p. p114 n.56). This is, of course equivalent to the principle – If a material object’s actual origin is a certain hunk of matter, then its origin is necessarily from that hunk of matter and no other. In logical form, using Salmon’s notation:

(x)(y)[T (x, y) (z)(T (x, z) → z = y)]

Where x is a material object, T is the origin relation and y is derived object. In clumsy English, for all x and for all y, if x’s origin is actually y then necessary that for all z such that x is derived from z then z is identical to y.

Background to the argument

I will undertake an exegesis of Kripke’s argument. I’ll go through lecture III leading up to n.56. It is particularly important to examine the genesis of the argument because footnote 56. is very bare. From reading the text we may be able to determine the possible suppressed premises that Kripke uses. From my reading of Kripke, it seems that he puts the cart before the horse in his belief of the essentiality of origin. He has strong intuitions for origin essentiality, and the argument is used to justify these intuitions, rather than the other way round. He writes of the Queen ‘it seems to me that anything coming from a different origin would not be this object’ (Kripke, 1981, p. 113). This intuition about objects and their origins come well before footnote 56.

Kripke first establishes that identity is the necessary relation between the thing and itself (Kripke, 1981, p. 108). We then consider a situation where Hesperus and Phosphorus are 2 distinct objects. He claims that this is not a situation where Hesperus is not Phosphorus - a denial of the necessity of identity. In fact, it is a situation where one, the other or both of those objects is not the object it actually is. This hints at the first of the essential properties that objects must have. The object that is Hesperus is necessarily Phosphorus. He then introduces the arguments by the essentialist Sprigge who asks if we can conceive of this very object (the Queen) being possibly a swan (Kripke, 1981, p. 111). These rhetorical devices are understandable because of the lecture format of these essays. However, should we really be allowed to motivate belief in essentiality because of the limits of our conceivability1?

Kripke’s argument

Kripke seems to utilise various intuition pumps2 to motivate one’s belief in the essentiality of origin. These intuitions pumps soften us up for the ensuing footnote argument. Questions about the Queen possibly being a swan linked to questions about whether she could be derived from different parent’s structure our intuitions in an unhelpful way. Firstly, asking whether we could imagine the Queen to be a swan is a sortally essentialist question – not a question about the essentiality of origin. Any intuition produced by examining whether the Queen could have different parents can be matched by equally compelling intuitions from an anti-essentialist position. If we transfer my gametes into another possible world and they grow, by a series of odd happenstances into an exact model of the adult Queen who is the head of state in that world while simultaneously the Queen’s gametes evolve into an exact adult replica of me it seems odd to identify me with the Queen, or vice versa.

Another way of structuring our intuitions in the opposite direction is to suppose that 2 of the Queen’s ancestors might be different. Let’s suppose that her great-great Grandmother on her mother’s side and her great-great Grandfather on her father’s side were not who they actually are. I think it’s perfectly possible to imagine this very Queen having partially different ancestors. However, according to Kripke, this would not be our Queen – because with different ancestors, one has different parents. I don’t think intuitions are particularly helpful when discussing cases of metaphysical necessity.

Footnote 56

I’m now examine footnote 56, and provide Salmon’s reinterpretation. Argument 1:

Let ‘B’ be a name (rigid designator) of a table, let 'A' name the piece of wood from which it actually came. Let 'C' name another piece of wood. Then suppose B were made from A, as in the actual world, but also another table D were simultaneously made from C. (We assume that there is no relation between A and C which makes the possibility of making a table from one dependent on the possibility of making a table from the other.) Now in this situation B ≠D; hence, even if D were made by itself, and no table were made from A, D would not be B. Strictly speaking, the 'proof' uses the necessity of distinctness, not of identity.

(Kripke, 1981) Emphasis my own.

This argument purports to use a rigid designation theory of reference, coupled with necessity of distinctness and an independence thesis to prove an instance of the essentiality of origin. If B and D name two separate tables as in the actual world, and they have their origin in two separate hunks of

1 This was meant to be ironic. I hope that’s acceptable for a dissertation.2 As described by Daniel Dennet in consciousness explained (Dennet, 1991, p. 12)

wood A and C and producing a table from one does not prevent the possibility of producing a table from another, they are not identical, and by necessity of distinctness, they are necessarily distinct. So by this principle, even if D was made by itself, and no table were made from A, D would not be B. The desired conclusion is that it is not possible for table B to be made from C.

At first reading, in an unreconstructed version of the argument, all Kripke has shown is not that it is that it is not possible that table B comes from hunk C. Rather, Kripke has shown is that even if D were made by itself, it would not be B.

Salmon’s Reply

Salmon frames Kripke’s arguments clearly in terms of possible worlds. He strengthens the argument to show that if we frame B as being a possible table, rather than an actual one we can show that not only is it the case that if the origin of an object is actual it is necessary but additionally if a table’s origin is possible, then its origin is necessary. The argument begins as follows:

We begin by letting 'B' be a name of an arbitrary possible table in an arbitrary possible world W1. We also let 'A' name the hunk of matter from which table B is originally constructed in W1, and we let 'C' name some distinct hunk of matter that also exists in W1. [...] [We] must assume at this point that there is a possible world, call it 'W2', in which B is still a table originally constructed from hunk A, but now a second table, which he names 'D', is constructed from hunk C in such a way that it follows from the fact that their original component materials, A and C, are distinct that the tables B and D are distinct.

(Salmon, 1979, p. 708)

Salmon extends the argument by adding two additional premises in attempt to derive the desired conclusion. Firstly he adds P1:

P1: For any table x and any hunks of matter y and y', if it is possible for table x to be originally constructed entirely from hunk y while hunk y' does not overlap with hunk y, then it is also possible for table x to be originally constructed entirely from hunk y while some other table x' distinct from x is simultaneously originally constructed entirely from hunk y'.

(Salmon, 1979, p. 708)

This is the compossibility thesis. One can derive from this that for any table produced from hunk C, it is also possible to produce a distinct table from hunk A. Salmon’s rebuttal follows:

“The immediate conclusion that Kripke intends to derive is the assertion that table B could not originate from hunk C, i.e., that there is no possible world in which table B is originally constructed from hunk C. B is an arbitrary table in an arbitrary possible world W1, and C is an arbitrary hunk of matter that does not overlap with hunk A, B's original component material in W1. If B cannot originate from any arbitrary hunk, then it necessarily originates from is its actual hunk. It follows from this that if it is possible for a given table to originate from a certain hunk of matter, then it is necessary that the given table originate from that very hunk of matter, or at least from no entirely distinct hunk of matter.”

(Salmon, 1979, p. 709)

In W2, B and D are distinct physical objects, hence B≠D. By necessity of distinctness B≠D. If D were made from C by itself, in any possible world, it would not be identical to B. To illustrate the connections between this and the necessity of origin I’ll extend Salmon’s argument to hopefully shed light on Kripke’s intuitions. We can take another possible world W3. In W3 a table is made from C. Is it B? Kripke would say no. We go back to W2, the world where C & A are made into tables. The table made from A in W2 is B, as in the actual world, and the table made from C is D. Because the table

made from C is distinct from B, by necessity of distinctness it is distinct in W3 therefore C cannot be the origin of B.

Sadly, this extension fails. To presume that because D or that because some non-B table is derived from C in W2m it must be the case that some non-B table must be derived from C in W3 is already to assume some sort of essentiality of origin thesis.

According to Salmon’s reconstruction, without my (failed) extension what Kripke shows is not that ¬T(B,C) – that any possible table constructed from C would not be B. All he has shown is that table D, when derived from C, even in a world where B does not exist, would not be B, by necessity of distinctness. This is not essentiality of origin. Salmon suggests an extra premise to move from [T(D,C)B≠D] to (x)[T(x,C)x≠D] – a thesis that implies essentiality of origin.

From here on I will discuss the reconstructions by Salmon, Cameron and others.

Reconstructions Of Kripke’s Argument

Kripke’s argument is incredibly bare. The bulk of it is under 100 words. Because of this there have many attempts to reconstruct the argument to make it formally valid. I will explore a few of them here.

Salmon

According to Salmon, Kripke has shown that:

(1) T(B,A) Assumption(2) T(D,C) Assumption(3) B≠D Assumption(4) B≠D By necessity of distinctness axiom & (3)(5) [T(D,C)B≠D] introduction

What he has not shown is

N1. (x)[T(x,C)x≠B]

which is equivalent to

N2 ¬T(B,C).

This is the principle that Kripke is aiming for if he wants the basis for a proof of the necessity of origin. Can Kripke move from (5) to a necessity of origin principle using solely uncontroversial premises, or those derived from a theory of reference?

Salmon suggests that another premise needs to do the work to move from (5) to N1. The first suggestion is that ‘if it is possible for table D to originate from hunk C, then it is necessary that D must originate from hunk C’ (Salmon, 1979, p. 711). This would do the brunt of the work of the argument. One would almost immediately be able to move from this to N2, the only additional premise being needed would be the antecedent of the conditional – that it is actually possible that T(D,C).This is a question begging premise – it is a statement of the essentiality of origin. In Salmon’s words – it’d be a howler if it were Kripke’s missing premise (Salmon, 1979, p. 711). Additionally, it does not fit Kripke’s footnote argument. One does not need necessity of distinctness to prove necessity of origin if one has this premise. If Kripke had had this premise would render much of his footnote discussion redundant.

Salmon’s second proposal to rescue Kripke’s argument is P2 or P2’. According to Salmon, Kripke assumes P2 as a tacit premise, though as this may be too strongly essentialist, he further weakens it to P2’.

P2: If it is possible for a table x to originate from a hunk of matter y, then necessarily, any table originating from hunk y is the very table x and no other.

(Salmon, 1979, p. 711)

P2': If it is possible for a given table x to originate from a certain hunk of matter y according to a certain plan P, then necessarily any table originating from hunk y according to precisely the same plan P is the very table x and no other.

(Salmon, 1979, p. 716)

P2 will get you straight to the essentiality of origin if we add the compossibility premise P1; there is no need to appeal to (5). Again, it doesn’t fit the structure of the footnote argument. Additionally, anyone with anti-essentialist intuitions would reject this argument, because P2 is an essentialist premise. For anti-essentialists, a premise like P2 would only justify indulging in confusion – it wouldn’t motivate any new believers in essentiality. Salmon finds P2 very intuitive but others may not, and he doesn’t provide an independent motivation for it. I will now explore Cameron’s reconstruction.

Cameron

Another approach to reconstructing Kripke’s argument involve taking D to not be a rigid designator. There is textual support for this, as I’ve indicated in the Kripke block quote above. In n.56 Kripke specifies that all the other hunks and tables are named. When invoking table D he writes ‘...another table D’ and does not encase it with quotation marks. Cameron suggests that D is a table variable and does is not a rigid designator for a particular table. Instead, it is merely the table that is derived from C.

Though Salmon finds P2 or P2’ very convincing, Cameron does not. Intuitive appeals to essentialism to justify a particular essentialist thesis guarantees that many will not sympathise with that argument. Cameron argues that if he were given a block of wood he ‘could make a table that was four-legged or three-legged, tall or short, round or square, thin or wide’ (Cameron, 2005, p. 264) – why would they all be identical tables? Additionally, what’s so special about a table – One man’s footstool is another man’s table – does their identity depend on which it is? Obviously these intuitions will not wash against the weakened premise P2’ as it implies extra sortal conditions on table identity. However, those with anti-essentialist intuitions can reject this too.

Kripke’s project is to derive necessity of origin from his theory of reference coupled with uncontroversial premises. We should see if we can finish the project with this design, rather than jumping to premises that Kripke may not have used.

Cameron tries to construct essentiality of origin it using strictly Kripkean premises. He focuses on the independence assumption, ‘there is no relation between A and C which makes the possibility of making a table from one dependent on the possibility of making a table from the other’ (Cameron, 2005, p. 262). It proceeds as follows. Let’s take a case where in the actual world B is made from A and C is made from D. In this world, it is clear that A and C are distinct as distinct physical objects are distinct. Because they are distinct, they are necessarily distinct – by the necessity of distinctness. If we take a world where B is made from C but no table is made from A this seems to violate the

independence principle, as then B would not be able to be made from A as distinct tables are distinct. It seems that the table made from C cannot be B – it is not a genuine possibility because for it to do so, it would prevent B being made from A – violating the independence principle.

This argument preserves validity. However, if we read the independence principle as implying that the table that is derived from a hunk restricts necessarily the possibility of particular tables being derived from other hunks this doesn’t seem to be a principle we should accept. Why would an anti-essentialist accept this strong reading of the essentialist principle? It seems that the only justification for a principle would be rooted in intuitions for the essentiality of origin.

This reconstruction differs from both Salmon’s and Kripke’s. It differs from Salmon as Cameron’s conclusion is mostly derived from Kripkean premises while Salmon’s argument can discard requirements of the necessity of distinctness and independence. However, though it largely matches the text of Kripke – there is clearly some value added material. Kripke relies on the necessity of distinctness between B & D to reach his conclusion that B≠D even if B does not exist. If we treat D as a variable, this collapses as it is not longer a rigid designator.

P.T.O

A Modest Proposal

I want to make a modest proposal to derive what I see as some value in Kripke’s argument. It is slightly different to the other versions I have read. It relies heavily on the necessity of identity & Leibniz’s law to justify another premise in the chain of Kripke’s reasoning. It’ll be restricted in its application but may provide some justification for some instances of purported necessity of origin. Briefly, I’m firstly going to claim that by Leibniz’ law & the necessity of identity the hunk from which a table is derived is identical to it. Because they are identical, they are necessarily identical, and by this construction their origin being the hunk is essential to it.

Salmon writes:

“We may assume, for the sake of simplicity, that when Kripke says that a table x was originally made from a hunk of matter y, he means that table x was originally constructed entirely from all of hunk y, i.e., that no (original) part of table x did not come from hunk y, and furthermore that no part of hunk y did not contribute to forming part of table x. It follows from this, presumably, that it is impossible for the same table x to be originally constructed from a hunk of matter y and at the same time to be originally constructed from a distinct hunk’ of matter y'”

(Salmon, 1979, p. 707 n. 4)Diagrams like Cameron’s3 are misleading from the perspective that they appear to show the hunk and the table from which it is made as being two distinct objects – they are different sizes and shapes and appear to coexist. Taking Salmon’s footnote into account, I envisage it more like this:

When we refer to the hunk, there are nominally two hunks that we may be referring to. Firstly there is the hunk (Hunk O) that is the totality of the wood that surrounds and includes hunk X. Secondly there is the hunk (Hunk X) which consists of the entirety of the material that constitutes table Y and no extra. It seems clear that if we are going to follow Salmon’s footnote, when we say that table are essentially derived from hunks, we are talking about hunk X, not hunk O.

If we were talking about hunk O, it is likely we would prove too much when arguing for essentially of origin. If we could prove that tables not only essentially have their origin in the wood from which they were actually made but also in the wood surrounding the wood of which they were actually made –

3 For example, see this image:

Diagram 2.

Hunk O

Diagram 1.

Hunk XTable Y

what’s to stop the argument running on and proving that the workshop in which the table was created, or the particular space-time location of the object are essential to it. This doesn’t seem to be something that modern supporters of the essentiality of origin are willing to accept4.

If we have an unrestricted composition then, the spatial coordinates that mark out Hunk X are an object. While hunk O and table Y are, by Leibniz’ law not identical, hunk X and table Y seem to follow the principle ∀F(Fx ↔ Fy)→x=y. They both consist in the same material, the only thing that differs from the two is that hunk x is sheathed by a wooden cladding and table y is not. It seems that hunk X and hunk y are numerically identical. Firstly, I will run through my argument and then in the next section I will discuss some criticisms that Leibniz’ law does not indicate that hunk X = table Y.

Following the above, let’s assume that hunk X and table Y are identical objects. When we form table Y out of hunk X we are not so much as forming a new object out of distinct, old one we are revealing a pre-existing object. From this principle there are an almost infinite amount of tables contained within Hunk O, each one is its own individual ‘hunk’, and each one is necessarily connected to the material from which it would have came if it had been revealed. The traced lines in Diagram 1 represent a possible table. Each time Hunk O is destroyed to reveal an individual table, that table is identical to the ‘hunk’ from which it actually came, in the case of table y it is hunk x. If the hunk were different then the tables that are revealed from it will be different. Table Y=X, so if table Y were derived from hunk X in the actual world, it is necessarily identical to hunk X - (X=Y)

This seems like a long way from footnote 56. but I shall attempt to show that principles that are invoked here are similar to n.56. I’m going to argue by reduction ad absurdum that if it’s the case that in the actual world X is the origin of Y, it is the case that it is not possible that any other Z could be the origin of Y. This models the proof in n.56 for the necessity of identity. To do this I claim that X=Y, and by necessity of identity, (X=Y). From here onwards, I will show that because of this there is no other object such that it can be the origin of Y.

Let’s posit some arbitrary distinct hunk Z which is the origin of Y, that is, it is distinct from X, such that it could be the origin of Y, while @T(Y,X). So ZX and T(Y,Z). By the intuition above Z=Y. However, if Z=Y and Y=X then X=Z. If Z is identical to table X then by S5, or the symmetry of the accessibility relation between possible worlds, or the transitivity of identity then Z is identical to Y. However, we have already specified that Z≠Y so either ¬ (Z=X) or ¬(Y=X). If it’s the case in the actual world that Y originates from X, we determine that Y=X, thus we can discard the case where ¬(Y=X). So it must be the case that ZY. By necessity of distinctness (ZY). Because we are talking about arbitrary tables and arbitrary hunks, it seems that from this we can derive the essentially of origin for table Y – i.e. (X)(Y)[T(X,Y) (Z)(T(X, Z) → Z=Y)].

More formally:(1) ¬(X=Z) As hunks are actually distinct(2) @T(Y,X) Y is derived from X, as in the actual world(3) T(Y,X)X=Y Above thesis(4) X=Y elimination(5) T(Z,Y) Assumption for RAA(6) T(Z,Y)Z=Y Above thesis(7) Z=Y elimination (8) X=Z By S5 and (4) & (7)(9) (X=Z)&¬(X=Z) Contradiction(10)¬(T(Z,Y)) Conclusion5

4 Contra Leibniz, who under some readings believed that all things predicates of an object are essential to it.5 I’m aware that I’m moving between possible worlds here without notation. Howeverm as I’m constantly deriving identitym which is necessary, my logic remains valid, if a little sloppy.

The conclusion has not got the force of necessity. However, because I’ve made no specific assumptions about the table Y other than that it made from X and the origin relation in certain cases is a necessary identity relation – it seems that (10) is a necessary truth. For any Z, such that Z≠X, it is not possible for it to be origin of Y.

First I am going to dispute an argument that Cameron makes in his article – that his W3* cannot be shown to be an impossible world without assuming essentiality of origin. Kripke claims that W3 is an impossible world if B=D – as two distinct objects cannot be identical. Cameron claims that W3 is only impossible if the compossibility claim holds.

[Kripke claims] since it is possible to make B from A, if it is possible to make D from C then there exists a world where both D is made from C and B is made from A. [...] It is not clear why, if we are not essentialists about origin the table B(=D) cannot be made from the fusion of blocks of wood A and C. In which case W3 is better drawn as W3*. I cannot think of a reason why W3* is impossible that does not assume the essentiality of origin.

(Cameron, 2005, pp. 272-273)

The reductio only goes through if the possibility of W1 (where T(B,A)) and the possibility of W2 (where T(C,D)) entails the possibility of W3. But that entailment only succeeds, it seems, if the compossibility claim is true: that if it’s possible to make B from A and possible to make D from C then it is possible to make B from A and make D from C (Cameron, 2005, p. 273). But the compossibility claim does not look plausible unless one accepts the essentiality of origin. I dispute that to get to W3 one needs to hold compossibility. With my depiction of the mechanics of necessity of origin, it seems possible to dispute Cameron’s conclusion.

If table Y is made only and entirely out of hunk X, they are identical; by necessity of identity they are necessarily identical. If we take another hunk, hunk Z and construct table P out of it. Hunk Z and hunk X are such that they are distinct. By necessity of identity and necessity of distinctness, Y=X and Z=P and Z≠Y. It is possible now to construct W3 without going beyond S5 or assuming the compossibility claim (p&q)(p&q). Additionally, if Y=X and Z=P and Z≠Y then, by transitivity of identity X≠P. So W3* is an impossible world.

Possible criticisms

What is limiting about this proof is that it requires no manipulation on the part of the table for it to be sound. For the identity relation to hold between X and Y, nothing can be added to Y as it will no longer will satisfy the Leibniz law criterion for identity. If we were making foldable tables, or tables which change and include outside parts, it’s not clear that this proof will work. Additionally, other objects that change or lose their parts will not be necessarily identified with their origins using this argument. This argument needs heavy modification to ensure essentiality of origin for the Queen and her actual zygotes. I believe it is possible, though it would only be contingently necessary that the Queen is derived from her zygote as it requires some sameness of material and it may not be the case that we all retain the material from our zygotes throughout our lives.

In this section I’m going to that argue Leibniz’ law is applicable in this case. I will attempt to demonstrate that only internal properties are relevant in determining identity from Leibniz law. Secondly I’m going to attempt to extend the argument and argue that even though the table changes over time, it remains essentially connected to its origin. Thirdly I’m going to examine the egg, flour, cake case6 and examine the problems that it produces for my demonstration of the necessity of origin.

Applicability of Leibniz law.

The first claim against my depiction that actual origin entails necessity of origin because of necessity of identity in the above case is that Leibniz law is not applicable. Opponents may claim that ¬(hunk X= table Y) because it’s not the case that they share all and only the same properties. For example they may claim that hunk x might be located in a workshop, while table Y might be located in a house or they may claim that hunk x is sheathed by wood, while table y is not, or that hunk x has the relationship of parthood to hunk o, while table y does not. Because of these different properties, Leibniz’ law and thus identity does not apply, and my argument fails. I claim that the properties required for a valid implementation of Leibniz law are only intrinsic properties, as the properties listed above are relational properties, it does not matter if these change.

To illustrate why this is the case, let’s take the case of an arbitrary object p and change its environment. If we change its location, cover it or surround it by other objects (say to make a pile of objects such that p is part of the pile) its relational properties change7. If we accept Leibniz’ law applies to relational properties, as we change the relational properties around p it seems that p goes out of existence. If we reverse these changes p comes back. It seems very odd to say that by changing relational properties we can force objects out of existence. Additionally, it violates the uniqueness of composition thesis8. This is why I think my use of Leibniz’s law as applying to only intrinsic properties is acceptable.

Accounting for tables made from disparate parts.

In the argument I gave in the previous section I characterised the forming of table y from hunk x as the revealing, or unsheathing of a previously existing objects. It was easy to demonstrate that if we mapped out the connected spatial coordinates that contain object x that that object was identical to the spatial coordinates that constitute y. However, what happens when you have tables made from disparate objects? For example, if a table is made from separate planks? In forming the table one brings the planks together. Is it still the case that the y=x? I think so. In this case, one would map the spatial coordinates that mark out each of the planks. The table is identical to the sum of the planks. Each plank is marked out individually by spatial coordinates. These can be manipulated, rearranged

6 Kindly pointed out to me by Andrew McGonigal.7 Note that I’m modelling the things that happen to hunk x.8 Which is in turn implied by Leibniz’ Law and unrestricted composition, so to allow relational properties would contradict two relatively uncontroversial pillars of my thesis.

and brought together without changing any of the internal properties of the plank. Leibniz’ law still applies to cases where objects have disparate origins.

Accounting for Change

This depiction of essentiality still appears very limited. If I hammered a rusty nail into table y to better hold it together it seems that table y now has different internal properties to hunk x. If this is the case then it is not longer the case that hunk x = table y and because of this I can’t make a proof of the essentiality of origin. If my theory cannot withstand the slightest change in the properties of the table without losing its essentiality of origin, this seems like a pretty feeble theory. I’m going to now claim that if it’s the case that y is a part of y’ and y=x, then still (T(y,x’). So, if we hammer a nail into y such that y becomes y’, if it’s still the case that y=x then it’s the case that y’s origin is necessarily x. I think it’s a very plausible intuition to say that if the grouping concept of ‘table’ contain parts that have an essential origin, then the table as a whole has an essential origin. If a table is necessarily derived from a hunk, adding parts to that table doesn’t remove the essentiality of that origin9.

Egg + flour = cake.

Another purported counterexample is that of the cake. When we combine eggs and flour to create a cake it seems that the eggs and flour go out of existence, and the cake comes into existence. The origin (eggs & flour) are such that ≠ the later object – the cake. It is claimed here I can’t derive essentiality of origin because there is no identity relation between the origin and the object. My first pass response is to claim that though they may go out of existence but it’s still the case that the ingredients of the cake are identical to the cake. The concept ‘egg’, for example, is a grouping concept for a morass of microphysical particles arranged in a certain way. These physical particles remain intact when the eggs and flour are formed into a cake so it’s still the case that Leibniz’ law and thus identity holds. This case is better depicted thusly: the microphysical particles such they constitute egg and flour are identical to the microphysical particles that constitute the cake. Identity can still hold, it’s just the case that there is a very complicated rearrangement of the microphysical particles during the transformation from ingredients into cake. Each microphysical particle that constitutes the cake is identical to a microphysical particle that constitutes an ingredient. As all are identical, the ingredients=the cake, thus necessity of origin follows.

Andrew McGonigal has suggested10 that it might be the case that all the particles that were up spin in the eggs and flour and they might become down spin when formed into a cake. In this case it seems that identity would not hold between the cake and the eggs/flour, and thus the cake no longer has an essential origin in the eggs/flour because every particle that existed in the ingredients is no longer identical to any particle in the cake.

9 I’m thinking that this is entailed by the logical axiom weakening.10 In a personal conversation.

I think what Andrew has depicted is a limiting case of the necessity of origin. If every particle that constituted the origin ingredients of a cake has transmogrified into an entirely different particle I believe one has lost the link between the origin and the cake. The necessity of origin relationship that I’ve proposed is not something metaphysically fundamental; instead it is rooted in identity. My argument is slightly more limited that a universal theory for the essentiality of origin as it does not appear to include the cake example but it is deeply empirical, the things that have necessity of origin are the things that have a relationship of identity between the object and its origin. What follows from this is that we could factually determine which objects actually have an essential origin – this seems far better than relying on intuition, which is somewhat vague, and often liable to disagreement.

Conclusion

To conclude, in this essay I began expositing Kripke’s n.56. I then ran through Salmon’s and Cameron’s reconstructions of Kripke and showed why, in both cases they either wouldn’t convince the anti-essentialist, or how they failed. Cameron made assertion that the only way to show that W3* was an impossible world was to beggar the question. I then demonstrated that in some cases of table, W3* is an impossible world because of the necessity of identity and table/hunk identity relations. Finally, I examined some criticisms and gave them cursory responses to further clarify what I am proposing.

BibliographyCameron, R. (2005). A note on Kripke's footnote argument for the essentiality of origin. Ratio , 262-275.

Dennet, D. (1991). Consciousness Explained. Boston: Little, Brown and Co.

Kripke, S. (1981). Naming and Necessity. Oxford: Blackwell.

Salmon, N. (1979). How not to derive essentialism from the theory of reference. The Journal Of Philosophy , 708-725.

I will then respond to Cameron with a thesis for the essentiality of origin that uses identity, rigid designation and Leibniz’ law. I will show how that this solves Cameron’s belief that his W3* cannot be shown to be an impossible world without assuming essentiality of origin. I will make an attempt to further extend my argument by arguing that tables that are not identical to their hunks can be shown to have their origin essentially by this principle.

However, the same types of considerations that can be used to establish the latter can be used to establish the former. (Suppose X ≠ Y; if X and Y were both identical to some object Z in another possible world, then X = Z, Y = Z, hence X = Y.) Alternatively, the principle follows from the necessity of identity plus the 'Brouwersche' axiom, or, equivalently, symmetry of the accessibility relation between possible worlds. In any event, the argument applies only if the making of D from C does not affect the possibility of making B from A, and vice-versa.

Reduction Cameron

It is possible to do a reduction on this suggestion

(x) (y) (y')[O (T(x, y) &- y does not overlap with y')D Li T(x, y')]

Example of a strongly essentialist premise: If it is possible for table D to originate from hun C, then it is necessary that D originate from hunk C. Salmon suggests that Kripke uses a third premise to get to his desired conclusion regarding the necessity of origin. He calls this P2 (If it possible for table X to originate from a hunk of matter y, then necessarily, any table originating from hunk u os tje very table x and no other). This does not beg the question, but it is still a strongly essentialist premise.

Suppose a table B, made from a hunk of matter A,,, inthe actual world, and another hunk of matter Cm—completelydifferent from Am—from which a table exactly like Bt could be made(the subscripts are merely a mnemonic device). Now consider apossible world W1( in which Cm is made into such atable, no table inthis world being made from Am. Is the table made from Cm in W(

the table Btl which in the actual world is made from A^,? No, Kripkeanswers, for there is another possible world, W2, in which both Am

and Cm are made into tables. Clearly the table made from Am in W2

is Bt, the table made from Am in the actual world, so the table madefrom Cm in W2, call it Dt , cannot be Bt in W2> and hence, by thenecessity of distinctness, cannot be B, anywhere at all. So the tablemade from Cm in W[, which is identical with Dt, the table madefrom Cm in W2, cannot be B, either. Thus Bt could not have beenmade from a hunk of matter completely distinct from that fromwhich it was actually made,1 for the supposition of this being so isthe supposition of just such a hunk Cm and possible world Wt as theargument has shown to be impossible. Note that the role of theexpression 'the actual world' in the argument could be filled by adesignation of an arbitrary possible world without detriment to itsvalidity. Thus, if valid the argument establishes also that B, couldnot have been made from a hunk of matter completely distinct fromany from which it could have been made.[T(D,C

Motivations for the hidden premiseBranching times

If we construct a branching times model of necessity. it explains why origin is important, in fact if the only essential properties were those

that were constructed out of a branching times scheme, origin would be the only thing necessary to an object.

Footnote 57

Salmon: the possibility od xonstructing the verytableIn one place he says that the argument assumes thatthe possibility of constructing table B from hunk A does not affectthe possibility of simultaneously constructing table D from hunkC, and vice-versa.

that the premiseKripke actually uses asserts that the possibility of constructingthe very table B from hunk A does not affect the possibility ofsimultaneously (i.e., in the same possible world) constructing adistinct table (meaning some table or other distinct from B) from hunk

C, and vice-versa.

What could motivate a proposal like P2? One proposal is the branching times model of necessity proposed by Mackie? He takes a belief based/etiology (why are we motivated to belief these premises). Mcginn philosopher suggests that these are truths de intellectu

In a branching times model of the necessityorigin the notion of possibility is characterised like this@We are identical with our gametes.Our gametes have a range of possible futuresthere are many possible ways our life could have gone.

Logical possibilites that involve different gametes don’t allow for the transitivity of identity between us and the gametes and are thus not identical to us. According to this model it is true

that it is possible that someone very similar to us has one or both different parents to us. However, what is not true is that that person is me. It doesn’t have the same identity as me.

The second point to justify is the idea that we are identical with out gametes.Another model of the argument’s (in)validity is to be found in Mcginn.

Salmon

Cameron

sTUFF

Non trivial TWI condsAs we can see here. For any such argument to be valid, there must be some non-trivial (criterion) identifier for transworld identification. What’s used here is This is the only way

Argument 2:That object in other worlds can be stipulated in such a way. This stipulation is equivalent to metaphysical essentialism

The table made from C, cannot be B, and hence by necessity of distinctness cannot be B anywhere at all. It cannot be B because, in the world where a table comes from Hunk A and a table comes from hunk C, if both are B then they would be the same table, but we have previously specified that they are distinct.

Cameron shows that P2 can completely circumvent Kripke’s argument for the essentiality of origin, one can get there only using P2 and (a≠b)¬(a=b).

Ross went on to discuss Nathan Salmon’s discussion of Kripke’s argument in How Not to DeriveEssentialism from the Theory of Reference. Salmon notes the ambiguity in Kripke’s principle andsuggests that it should be read as asserting that “the possibility of constructing the very table Bform hunk A does not affect the possibility of simultaneously (i.e. in the same possible world)constructing a distinct table (meaning some table or other distinct from B) from hunk C, and viceversa.” But, says Salmon, while this gets Kripke to the conclusion that “in any possible world inwhich a table D is constructed, D . . . is not the same table as B” that is not the essentiality oforigin; for the essentiality of origin has nothing to do with the specific table D. What Kripke needsto show, says Salmon, is that any table constructed from C is not B. Let ‘T(x,y)’ denote that table xhas been made from hunk of wood y. Salmon’s claim is that although Kripke has proven

E1: □[T (D,C) → D = B], he needs to prove

E2: □∀x[T (x,C) → x = B] which is the essentiality of origin.

Salmon then seeks to find an extra premise that will take us from E1 to E2. The premise he choosesis

P2: ∀x∀y[♦T (x, y) → □∀z(T (z, y) → z = x)]

P2 tells us that in any possible world any table originating from hunk C must be D and not B; andso, says Salmon, we use “origin as a (necessarily) sufficient condition for being this very table inorder to prove that origin is also a (necessarily) necessary condition.”

If he were to use this premise he would have to independently verify it through some other intuitions (like branching times) which I will discuss later, or show how it can be derived from his theory of reference. It also does not fit into his argument. If he used this premise all he would have to show is that it is possible for a table to be derived from a hunk of matter – because then it would follow that it is necessary for it be derived from that hunk of matter. It would be needless to make the additional steps that Kripke actually makes

He would not need necessity of distinctness. These are all claims against this being a hidden premise that Kripke actually uses. However, it does have some independent force as an argument itself and I will examine the motivations later when discussing branching time models of necessity and deRosset’s paper.

Additionally, it also seems to prove too little as part of Kripke’s prject. It might prove that if one takes a particularly possible thing then it’s origin is necessary. However, it doesn’t show that the necessity of origin is nevessary.P2 Redux. What Ps actually says tha if any table y originating x then any table y that originates from x is y and no othter.

Box(D≠B)Box(T(D,C)->D≠B)

It makes the argument work how?

In addition, it does not seem the premise that Kripke is a assuming. He seems to sincerely believe that there is no additional premise that he needs to prove his argument.

Why? The things that can be [possibly] be predicated of an object are the things which may have happened to it after the thing itself was brought into existence?? The point at which an object is brought into existence is the object’s origin. This point cannot be altered as if we altered the origin of the object, we’d alter the object itself...

They are distinct, and by necessity of distinctness, they are necessarily distinct. In another possible world there exists.

Kripke asks how this very person could have originated from different parents (Kripke, 1981,p. 113). He says one can imagine that things in her life might have changed. We can imagine forward divergence, an open future, but we cannot imagine backward divergence. This is the branching times thesis of modality.

He suggests that though a full discussion of the problems of essential properties are impossible. When we ask what is possible of an object, we ask whether the universe could have gone on as it did from a certain time but diverge from its course to the actual world at a certain point. As an example, it would be possible for X to be have the properties Fx iff history could have diverged at point t, where X is in existence, and x is F at one divergence. This intuition supports essentiality of origin

Change over time,. Table no longer = hunk x. o Could argue for partial identity, such that table y is partially identical to hunk x

Could argue that because part of table is identical to hunk x then the whole table, when you take the table as a whole, it’s origin is necessarily that of hunk x

..point out that hunk o ¬= Y because of leibnizs law, but hunk x is. Egg cake case. All the up spin particles are now down spin. How does my solution propse

this. Is it an empirical oneo

When some of it’s properties change I want to still claim that it has that essential origin but let’s say a alrger obejct including the table a sub part of it originates from hunk x. Is the larger space tome coordinates have x essentially as it’s origin?

The principle I am using to claim that @T(X,Y)T(X,Y) is that@(T(X,Y) X=Y. I obtain identity via leibniz’ law ∀F(Fx ↔ Fy) → x=y. The spatial coordinates that carve out hunk x within hunk o are identical to the spatial coordinates that table y consists of. I envisage that some will disagreeThe problem with this version of the necessity of origin is that is solely seems to be a jazzed up version of necessity of identity and not really a example of necessity of origin at all. I am trying to derive metaphysical necessities from logical necessities. However, the only reason that X=Y holds for T(X,Y) is because of leibniz’ law - ∀F(Fx ↔ Fy) → x=y. Is it true that ∀F(Fx ↔ Fy) in the table/hunk example? Two possible differences in properties could be that hunk x does not have the property of a table and that hunk x is encased in wood while y is. To the latter I respond that leibniz’ law is only concerned with internal properties. To the former, I think this suffers from the fallacy of verbalism. Hunk x is table shaped, constructed out of the same material of as table y