Definition 2.23: Stalnaker’s uniqueness assumption: for every world ? and antecedent ?, that is entertainable at ?, there is a smallest ?–admitting sphere around ? containing exactly one
3.1 The extended argument from admissible paraphrase – a defense.
In the context of investigating the nature of the truth of subjunctives asserted by way of reductio, where he considers them as being instances of non-trivially true counterpossibles, Lewis (1973, p.24) for the sake of argument accurately envisages the overview character of
110 Routley (1980,n p.89).
such an extension, which would proceed by positing impossible worlds, before quickly dismissing it, on grounds of it being founded on a ‘confused fantasy’.111
[O]ne sometimes asserts counterfactuals by way of reductio in philosophy, mathematics, and even logic. These counterfactuals are asserted in argument, and must therefore be thought true; but their antecedents deny what are thought to be philosophical, mathematical, or even logical truths, and must therefore be thought not only false but impossible. These asserted counterphilosophicals, countermathematicals, and counterlogicals look like examples of vacuously true counterfactuals.
There are other things they might be, however. They might not really be counterfactuals, but subjunctive conditionals of some other kind. More interesting, they might be non-vacuously true counterfactuals, understood in the way I have proposed; but so understood under the pretense that along with the possible possible worlds that differ from our world only in matters of contingent, empirical fact, there also are some impossible possible worlds that differ from our world in matters of philosophical, mathematical, and even logical truth. (The pretense need not be taken very seriously to explain what happens in conversation; it just might be that this part of our conversational practice is founded upon a confused fantasy.) (Lewis 1973, p.24)
What is contained in the phrase ‘a confused fantasy’? It refers to the claim, which Lewis labels ‘a pretense’, that posits the existence of impossible worlds that differ from the actual one in matters of philosophical, mathematical and logical truth. Does Lewis label such an extension of his analysis a fantasy because there are no ways the world could not have turned out? But then we could use Lewis’ own justification for possible worlds given in the form of his argument from admissible paraphrase, by merely extending it in support of impossible worlds, whilst maintaining its form.112 So, if Lewis’ argument from admissible paraphrase for possible worlds is sound, then the soundness of the extended justification is only conditioned
111 I take that what Lewis means by subjunctives asserted by way of reductio, are subjunctives of the form where the antecedent is the hypothesis of the reductio argument and the consequent the absurd conclusion derived. That is given the reductio ‘HYP… ⊥,’ Lewis has in mind the subjunctive ‘HYP > ⊥’.
112 The argument appears throughout Lewis’ work. The versions of the argument I’m primarily relying on are taken from Lewis (1973, p.84) and Lewis (1986, p.2). Vander Laan (1997, §3) refers to it as ‘the argument from ways’.
on whether one accepts the rather uncontroversial premise that not everything is possible.113
Here is the original version of Lewis’ argument:
Ordinary language permits the paraphrase: there are many ways things could have been besides the way they actually are. On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit ‘ways things could have been’. I believe that things could have been different in countless ways; I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called ‘ways things could have been’. I prefer to call them ‘possible worlds’. (Lewis 1973, p.84)
To reiterate, if we accept this argument, then why should we not accept the following
argument that there are impossible worlds?114 The extended argument is a conditional thesis:
if the paraphrase argument justifies belief in possible worlds, as ways things could have been, then by parity of reasoning, the same form of the argument justifies belief in impossible worlds, as ways things could not have been.115 Being a conditional thesis, the full parity of reasoning argument can also be viewed as a reductio of genuine realism, directed to those who commit to concrete possible worlds only.116
The conditional argument first appears in Naylor (1986, pp.28-29) where it is presented in a way that could be interpreted as a direct reductio of genuine realism. It has also been taken up by Yagisawa (1988, p.183) where it serves as a lynchpin thesis in the conditional
endorsement of extended modal realism. However, Yagisawa leaves it up to the reader whether the conditional thesis is to be taken as serving the modus ponens argument endorsing concrete impossible worlds, or the modus tollens arguments that would effectively echo Naylor’s (1986) intended reductio of Lewis’s justification of possible worlds, the soundness of which is premised on a consensus that impossible worlds do indeed lead to trouble. In Naylor’ (1986) note to Lewis, the implication seems to be that a conclusion to the effect that the argument can be shown to speak equally in favour of impossible worlds is trouble enough. This is implicit since Naylor appears to expect the extended conclusion to speak for
113 Mortenson (1989), is the rare exception to that view. 114 Naylor (1986, p.29)
115 Divers (2002, p.68)
116 In fact the extended argument can be viewed as a reductio of Lewis’s theory of genuine possible worlds (Yagisawa 1988), (Divers 2002).
itself without any further comment, since he doesn’t bother to make one. But this is not really enough without an independent reason as to what is troublesome about positing impossible worlds. Moreover, Skyrms (1976, p.326) had already warned against caricaturizing Lewis’s argument in a way that ignores the included proviso that taking the paraphrase at face value is only justified insofar as it doesn’t lead to trouble.
I do not make it an inviolable principle to take seeming existential quantifications in ordinary language at their face value. But I do recognize a presumption in favor of taking sentences at their face value, unless (1) taking them at face value is known to lead to trouble, and (2) taking them some other way is known not to. Lewis (1973, p.84)
But naturally there is no consensus as to what ‘trouble’ exactly amounts to. There is however a predicament that a classicist would wish to avoid, which would be taken as sufficient grounds to reject the extended argument, without abandoning the original one – namely, theoretical inconsistency. As it will be shown, Lewis gives an argument precisely to that effect, albeit a bad one. For him this is reason enough to reject the parity of reasoning
argument, but it is a reason premised on a misunderstanding highlighted in the fragment from Routley, which I demonstrate in the sext section. Consequently, I conclude that the extended argument from admissible paraphrase in favour of impossible worlds is safe from the charge of running into the kind of trouble that Lewis believes it does.
To appreciate Lewis’s reasons for banishing impossibilia from his ontology, it is necessary to give at least a rudimentary outline of those key elements of his metaphysics that are the primary suspects in being responsible for this “impossibilia phobia”.