There have been several challenges to the multiple realizability framework (MR). Kim (1992) argues by analogy that 'pain' is like 'jade', the latter being a non-projectible term since the property expressed just is the disjunction jadeite or nephrite. In the case of 'pain', assuming causal closure of the physical and causal inheritance, pain just is the disjunction of its realizers. Since disjunctions of heterogeneous properties are unfit for inclusion in laws, 'pain' is unfit for inclusion in laws.
Recently, a colleague of mine, Ted Poston, and I have been developing a paper (presented at the Alabama Philosophical Society's 2008 meeting under the title, "Alethic Functionalism and the Metaphysics of Reduction") arguing that Kim's argument applies to alethic functionalism, a view developed by Michael Lynch (UConn) which holds that truth is a higher-order, multiply realizable property. In this post I don't want to consider that argument; rather I want to consider something tangentially related, namely the issue of translation.
Assumptions:
(1) Genuine MR properties are autonomous (non-reducible).
(2) Truth is a genuine MR property.
From this it follows that
(3) Truth is non-reducible.
What sense of autonomy are we working with here? Although several commentators have sought to avoid Kim's conclusion in different ways (see Antony (2003), Antony and Levine (1997), David (1997), I want to focus on Fodor's (1997) "Special Sciences: Still Autonomous after All These Years." In that piece Fodor argues that the disjunction of a higher-order property's realizers must be "metaphysically open" in order to avoid the identification of the higher-order property with the disjunction for the reason that disjunctions are unfit for inclusion in laws while higher-order, genuine MR properties are fit for inclusion in laws.
(4) A disjunction of realizers for a property P is metaphysically open when there exist metaphysically possible but non-actual realizers for P.
Jade is not a genuine MR property because it just is either jadeite or nephrite. Pain, on the other hand, is a genuine MR property because there exist metaphysically possible but non-actual realizers for pain (a state of a computer, say).
Enough by way of summary. In this post I want to argue that this view has a surprising implication. Let me note that for Lynch discourses are not contexts (in the semanticists sense). Discourses can be thought of as sets of sentences (or propositions, if you like) such that all members of a set have the same "near perfect" realizer, where a discourse's near perfect realizer will be the property playing the "truth role" for that discourse. For my purposes, it does not matter how they are determined (whether a priori, etc.). Let me add a few more assumptions.
(5) If a sentence S of L translates a sentence R of L2 then S and R have the same realizer property, that is, S and R belong to the same discourse.
I am not going to argue for a specific view of translation, but suffice it to say that many anti-reductionists argue by way of failure of regimentation of recalcitrant sentences into a less problematic idiom to the non-reducibility of the former (or its metaphysical commitments) to the latter (to its metaphysical commitments). If translation ensures reduction one way or the other then sentences standing in the translation relation to one another must have the same metaphysical commitments and hence must belong to the same discourse.
Now, (6) If x is a genuine MR property then x has a metaphysically open disjunction of realizers. [Fodor's claim]
So, (7) truth has a metaphysically open disjunction of realizers. [from (1), (2), (6)]
But then (8) there exist metaphysically possible but non-actual realizers for truth (or non-actual discourses) [from (7) and (4)]
Let's call one such non-actual discourse NA.
(9) NA contains a sentence S (or proposition S) belonging to a non-actual discourse with a non-actual realizer for truth. [from (8) and definition of discourse]
(10) If S were translatable into a sentence of an actual language then it would belong to an actual discourse. [from (5)]
But (11) S doesn't belong to an actual discourse. [from (9)]
Hence, (12) there exists a discourse with a sentence (or proposition) untranslatable (or unexpressible) by any sentence belonging to a language in the actual world. [from (10), (11), (9)].
Long story short, if one thinks that truth is a genuine MR property and that such properties have metaphysically open disjunctions of realizers, then one is committed to the existence of in principle untranslatable but metaphysically possible languages (or language fragments).
Recently, a colleague of mine, Ted Poston, and I have been developing a paper (presented at the Alabama Philosophical Society's 2008 meeting under the title, "Alethic Functionalism and the Metaphysics of Reduction") arguing that Kim's argument applies to alethic functionalism, a view developed by Michael Lynch (UConn) which holds that truth is a higher-order, multiply realizable property. In this post I don't want to consider that argument; rather I want to consider something tangentially related, namely the issue of translation.
Assumptions:
(1) Genuine MR properties are autonomous (non-reducible).
(2) Truth is a genuine MR property.
From this it follows that
(3) Truth is non-reducible.
What sense of autonomy are we working with here? Although several commentators have sought to avoid Kim's conclusion in different ways (see Antony (2003), Antony and Levine (1997), David (1997), I want to focus on Fodor's (1997) "Special Sciences: Still Autonomous after All These Years." In that piece Fodor argues that the disjunction of a higher-order property's realizers must be "metaphysically open" in order to avoid the identification of the higher-order property with the disjunction for the reason that disjunctions are unfit for inclusion in laws while higher-order, genuine MR properties are fit for inclusion in laws.
(4) A disjunction of realizers for a property P is metaphysically open when there exist metaphysically possible but non-actual realizers for P.
Jade is not a genuine MR property because it just is either jadeite or nephrite. Pain, on the other hand, is a genuine MR property because there exist metaphysically possible but non-actual realizers for pain (a state of a computer, say).
Enough by way of summary. In this post I want to argue that this view has a surprising implication. Let me note that for Lynch discourses are not contexts (in the semanticists sense). Discourses can be thought of as sets of sentences (or propositions, if you like) such that all members of a set have the same "near perfect" realizer, where a discourse's near perfect realizer will be the property playing the "truth role" for that discourse. For my purposes, it does not matter how they are determined (whether a priori, etc.). Let me add a few more assumptions.
(5) If a sentence S of L translates a sentence R of L2 then S and R have the same realizer property, that is, S and R belong to the same discourse.
I am not going to argue for a specific view of translation, but suffice it to say that many anti-reductionists argue by way of failure of regimentation of recalcitrant sentences into a less problematic idiom to the non-reducibility of the former (or its metaphysical commitments) to the latter (to its metaphysical commitments). If translation ensures reduction one way or the other then sentences standing in the translation relation to one another must have the same metaphysical commitments and hence must belong to the same discourse.
Now, (6) If x is a genuine MR property then x has a metaphysically open disjunction of realizers. [Fodor's claim]
So, (7) truth has a metaphysically open disjunction of realizers. [from (1), (2), (6)]
But then (8) there exist metaphysically possible but non-actual realizers for truth (or non-actual discourses) [from (7) and (4)]
Let's call one such non-actual discourse NA.
(9) NA contains a sentence S (or proposition S) belonging to a non-actual discourse with a non-actual realizer for truth. [from (8) and definition of discourse]
(10) If S were translatable into a sentence of an actual language then it would belong to an actual discourse. [from (5)]
But (11) S doesn't belong to an actual discourse. [from (9)]
Hence, (12) there exists a discourse with a sentence (or proposition) untranslatable (or unexpressible) by any sentence belonging to a language in the actual world. [from (10), (11), (9)].
Long story short, if one thinks that truth is a genuine MR property and that such properties have metaphysically open disjunctions of realizers, then one is committed to the existence of in principle untranslatable but metaphysically possible languages (or language fragments).
