1 of 1- DanielCC
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Chandler Against S5 and the Necessity of Possibility
In his article 'Plantinga and the Contingently Possible' Hugh Chandler offers an argument against Axiom S5, the thesis that whatever is possible is necessarily possible (◊A⊃□◊A). This axiom is important in many modal systems and arguably central to the possible worlds enterprise as a whole as intended to convey the fullest sweep of the possible. I offer a brief summary of Chandler's animadversion below in the interests of seeing what criticisms people will come back with.
To start he asks us to take these two premises as intuitively true:
Premise I: A particular entity, Y, could not have come into existence with a completely different set of parts
Premise II: Said entity, Y, could have come into existence with (at least) one of its parts different from those it actually has.
Through his essay Chandler uses a bicycle as his choice example. Armed with these two premises and his trusty transworld cycle he goes on to make the following argument. Suppose it is possible for Y to have half of its parts replaced whilst still remaining Y. Now imagine a world, W*, where Y came into existence with half of its parts different from those it has in the actual world. In W* it is possible for Y to undergo the 'tolerable' change of up to half of its parts- yet if this is the case then there is a world relative to the actual world where Y has a completely different set of parts and yet is still Y, a conclusion directly contra to our Premise I. Due to this our Premise I thesis that ‘it is not possible Y should have come into existence with a completely different set of parts’ cannot be interpreted to range across all worlds – instead it must mean any worlds where this occurs are not accessible to the actual world. This then disproves the S5 thesis that what is possible is necessarily possible.
I won't attempt a direct answer to this argument but the here are a few thoughts worth keeping in mind: first of all what non-ad hoc way to do we have of determining the cut-off point up to which an entity can tolerate change? This issue is lurking behind puzzles like the Ship of Theseus and the Sorites Paradox. One’s stance in mereology will go a long way to informing one’s answer to all these.
Secondly it does not escape notice that a lot of the entities used in example are artefacts as opposed to proper substances. I would argue that entities such as ships, watches, bicycles and bronze statues do not appear in the fundamental inventory of the world - their names are not denotative of natural kinds but say something of human interest e.g. whatever fulfils a given role relative to our desires. They are what Husserl conveniently term 'Use-Object' terms.
So, with all this in mind, discuss!
Last edited by DanielCC (4/25/2016 9:42 am)
- John West
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Re: Chandler Against S5 and the Necessity of Possibility
You may be missing a premise, Daniel. I've changed some of the symbols, but kept my rendition of the argument faithful to the way you wrote it in your post:
(1) A particular entity, a, could not have come into existence with a completely different set of parts.
(2) a could have come into existence with at least one different part.
(3) It is possible for a to have half its parts replaced whilst remaining a.
(4) Imagine world v, where a came into existence with half of its parts different from a in w.
(5) By axiom S5, since (3) is true in w it's true in v.
(6) Hence, there is a world—call it u—relative to the actual world w where a came into existence with completely different parts than in w.
By stipulating that the half replaced in the move from v to u is partially identical with the half added in the move from w to v, I can keep every premise in this part of the argument true without getting (6).
- John West
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Re: Chandler Against S5 and the Necessity of Possibility
You also don't need both (2) and (3). You can add a general version of (5*) to block my counterexample, drop (3), use (2), and rerun your argument until you've replaced all actual world a's parts:
(1) A particular entity, a, could not have come into existence with a completely different set of parts.
(2) a could have come into existence with at least one different part.
(3*) Hence, there is a world v, where a came into existence with one part different from a in w.
(4) By axiom S5, since (2) is true in w it's true in v.
(5*) Possibly, the part replaced in the move from v to another world, u, is identical to part of a in w.
(6) Hence, there is a world, u, relative to the actual world w where a came into existence with two different parts than in w
You can use S5, (2), a general version of (5*), and (6) to run the argument until you get (7):
(7) Thus, there is a world t relative to the actual world w where a came into existence with completely different parts than in w.
So you have the aporetic tetrad:
(8) A particular entity, a, could not have come into existence with a completely different set of parts.
(9) a could have come into existence with at least one different part.
(10) Axiom S5.
(11) Possibly, the part of a replaced in the move from world x to world y, where x≠y, is identical with part of a in w.
At least one of the four limbs must be wrong.
Last edited by John West (4/25/2016 2:22 pm)
- Due_Kindheartedness
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Re: Chandler Against S5 and the Necessity of Possibility
Premise (I) is false. Things can come into existence with a different set of parts.
- Due_Kindheartedness
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Re: Chandler Against S5 and the Necessity of Possibility
Here's my proof: a positron is the same as an electron, except for charge and pairity, and an antiproton is the same as a proton, except for charge and parity. Two antihydrogen atoms and one antioxygen atoms form an antiwater molecule, which is exactly like water except that if it means a real water molecule it will explode violently. But if you don't have any real water nearby, anti-water is the exact same thing as water and completely indistinguishable.
- DanielCC
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Re: Chandler Against S5 and the Necessity of Possibility
Tomislav Ostojich wrote:
Here's my proof: a positron is the same as an electron, except for charge and pairity, and an antiproton is the same as a proton, except for charge and parity. Two antihydrogen atoms and one antioxygen atoms form an antiwater molecule, which is exactly like water except that if it means a real water molecule it will explode violently. But if you don't have any real water nearby, anti-water is the exact same thing as water and completely indistinguishable.
Unfortunately there's a slight confusion here. Chandler's argument was talking of individual things (so when he uses the term 'same' he means that same individual) - Premise I draws on certainly widely shared Kripkean thesis about the necessity of origin and origins essentialism - whereas you appear to be arguing about things being of the same kind.
I would follow Alexander denying that Water and Anti-Water are identical in kind. Both are differing natural in virtue of their having different casual powers and dispositions, as well as their being differing powers pointing to their existence e.g. Anti-Hydrogen and Anti-Oxygen having the capacity to form Anti-Water under X conditions.
Last edited by DanielCC (4/26/2016 4:29 am)
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Thread Starter- John West
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Re: Chandler Against S5 and the Necessity of Possibility
To add some degree of description and argument to Daniel's first paragraph:
Unfortunately there's a slight confusion here. Chandler's argument was talking of individual things (so when he uses the term 'same' he means that same individual) - Premise I draws on certainly widely shared Kripkean thesis about the necessity of origin and origins essentialism - whereas you appear to be arguing about things being of the same kind.
Necessity of origins is pretty much what it says on the can: it's the thesis that if an object (e.g. a tree) originated from a certain source (e.g. an acorn) in our world, the actual world, then the object also originates from that same source in any other possible world in which that object exists.
Here's Lowe's four-worlds argument for necessity of origins (with a paragraph break that he doesn't, but should, include):
We are given T which originates from acorn A in this, the actual world, which we may call w0. Suppose, then, that there is another possible world, w1, in which A does not exist and a tree, T1, originates from a different acorn, B. And suppose we maintain, contrary to the thesis of necessity of origin, that T1 is identical with T.
Then the following problem seems to arise. There is, it seems, yet another possible world, w2, in which both acorn A and acorn B exist and grow into exactly similar trees—let us call them T2a and T2b respectively. If we ask which of these two trees is identical with T, it seems that we should say that it is T2a, rather than T2b, that is identical with T—because T2a and T2b being otherwise similar to one another, T2a more closely resembles T in virtue of having grown from the same acorn, A. So far, then, we have claimed that T1 is identical with T2a. But now consider a fourth possible world, w3, which is just like w2 except that acorn A does not exist and so does not grow into a tree. Since w3 is just like w2 except that acorn A does not exist, the tree which originates from acorn B in w3, which we may call T3, is identical with T2b—and T2b, we know, is not identical with T2a. So it follows that T3 is not identical with T2a. But if T3 is not identical with T2a and yet, as we have just concluded, T2a is identical with T1, it follows that T3 that is not identical with T1. However, for all that we have said so far, world w1 and world w3 are indistinguishable from one another, both being worlds in which acorn A does not exist and a certain tree grows from acorn B. Yet we have been compelled to conclude that those worlds do differ, in that numerically different trees grow from B in the two worlds. That seems absurd, for two worlds surely cannot differ merely in respect of the identity of a certain object. The only way to avoid this absurdity, it seems, is to reject the supposition that T is identical with T1 and so uphold the thesis of necessity of origin.
Incidentally, I'm not sure rejecting the supposition that T is identical with T1 is the only way to avoid the absurdity.
Last edited by John West (4/26/2016 7:00 pm)