Reduction and Elimination in Philosophy and the Sciences

pled way to demonstrate the success or failure of reductions.
What is more, it seems to me that Chalmers’s and
Jackson’s account fails to ground the metaphysical necessity
that, according to physicalism, connects physical to
mental states, on relations between concepts, propositions,
or whatever else can become objects of knowledge,
whether that be a priori or a posteriori. This is because, by
construing the relation of a priori entailment as one between
functions from possible worlds to extensions, their
account seems to reverse the required order of explanation,
analysing a supposedly logical - conceptual relation in
metaphysical terms, whereas what was being advertised
originally was exactly the opposite. To say that knowledge
of the complete physical description of the world would
allow us to have a priori knowledge of all macroscopic
facts, which is what the original thesis about a priori entailment
included, is to say that our understanding of the
terms that we use in order to describe the world in physical
terms, allows us to deduce, without looking at the world
any further, its complete description in macroscopic terms.
But, an essential component of this thesis seems to be
that it is our a priori understanding of the concepts involved
that grounds the derivation, not the objects that are
referred to by these concepts. In Chalmers’s and Jackson’s
account, the burden of the derivation is transferred to
the level of extensions, not the way that these extensions
are represented by us. This, in my view, renders the account
unsuitable to be used in explicating the way metaphysically
necessary relations are grounded on logical -
conceptual relations such as that of entailment.
In later work, Jackson tries to accommodate similar
criticisms, by attempting to reconcile the metaphysical
nature of his proposed relation of entailment with the
apriority that supposedly characterizes it. Thus, he calls
the relation of a priori entailment that he endorses de re,
claiming that it is a type of metaphysical necessitation
between properties, not necessitation between sentences
or concepts. Here is the relevant definition that he appeals
to, quoted directly from his paper:
132
P1 a priori necessitates P2 iff one’s grasp of what it
is to be a P1 and what it is to be a P2 allows one to
see that if P1 is instantiated then so is P2.
(Jackson 2005, pp. 252-3).
However, I do not think that this move can serve Jackson’s
argument. It is obvious that, contrary to his pronouncements,
his characterisation of de re a priori necessitation,
by appealing to our ‘grasp of what it is to be’ a given property,
proceeds via concepts; given this, Jackson clearly
has to suggest a way in which these concepts are related.
Since he repudiates explicit conceptual analyses, he has
to represent the relation between them as a relation between
functions, i.e. a priori intensions. But, as has been
argued above, lacking explicit analyses, the relation between
these intensions can never be cognitively obvious,
since it operates at the limit, i.e. as a relation between the
concepts’ extensions across possible worlds. This cannot
be reasonably thought of as a relation between mental or
linguistic representations; rather, it seems to be closer to
what he and Chalmers would call a metaphysically ‘brute’
one.
But, if the commitment of physicalism to a priori
entailment is to be rejected, so that our true high-level
descriptions of the world cannot be derived from the
complete physical story, then how can the thesis ever be
vindicated? If physical properties fail to account
completely, in a fully reductive account, for the successful
Physicalism Without the A Priori Passage — Harris Hatziioannou
explanations that we give in macroscopic terms, in what
sense can they be considered superior in the explanatory
scheme of things? A full answer to these questions
certainly needs a systematic investigation into the relation
between properties that pertain to different levels of
explanation. However, I think that the key for accepting
physicalism without an a priori passage is to realize that,
even within the domain of physics, the descriptions of
complex systems can very rarely be derived in an a priori
way from the descriptions of their constituents. The
derivation must necessarily involve idealizations,
simplifying assumptions, approximations, and brute
numerical methods, all techniques that rupture the smooth
mathematical derivation of properties that pertain to more
complex systems, thus rendering impossible the a priori
passage from one level of description to another. The
failure is already apparent in the classical three-body
problem, which has exact solutions only in some restricted
forms. And, of course, it is patently obvious in more
complex systems: even knowing the momentary positions
and momenta of all the fundamental particles that
comprise an iron atom, say, we have no hope at all of a
priori deducing, on the basis of our best laws of quantum
theory, their dynamical evolution in time. To arrive at the
physics of such complex systems from the physics of more
simple ones, we simply have to resort to methods which
are, at least in part, justified by appeal to empirical data.
Physics simply does not have an analytically solvable
equation that describes the behaviour of every system that
falls within its scope. In fact it has such equations only for
unrealistic, highly idealized systems, which are
encountered in tightly controlled experimental situations
(see Cartwright 1999).
I think that the important point to keep here is the
following: If the passage from simple to complex systems
is not a priori guaranteed even within physics, then we
should not expect that the passage from each
neurophysiological to its corresponding mental state will be
thus guaranteed either. I am aware that this point raises
doubts concerning the way in which an antireductionist
account such as this could support physicalism: if no
smooth reductions are forthcoming, not even within the
domain of physical theory, how can we ever be confident
that it is the physical properties that account for the causal
and other characteristics of mental states? I believe that,
just like in the cases of the classical three-body problem
and the iron atom we have reason to believe that the
features of the world that are responsible for the dynamical
evolution of these systems are physical (albeit ones that
cannot be precisely quantified), so in the case of a
psychological state we have reason to expect that the
features that are responsible for its causal outcomes are
also physical, even if there is no way to move from the
physical description to the psychological one, except by
appealing to ‘brute’ a posteriori knowable necessitation.
Thus, we may view the psychological description as
capturing, vaguely and imprecisely, the salient features of
the physical system, while at the same time expecting that
it will be the description of the underlying complex physical
state that will ultimately fully account for mental
phenomena, in the sense of providing the exact sufficient
causes for them, the effective mechanisms that are
present in the world. It is true that we need independent
arguments to warrant this expectation, but, of course,
plenty of these have already been given in the literature,
and there is no space to discuss them here. I hope at least
that these sketchy suggestions point towards a viable
understanding of a posteriori physicalism.