Archive for the ‘Physicalism’ Category

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Clarity In Talking About The Status Of Attributes

October 13, 2010

When the ontological status of a property or attribute is in question, the central issue is the ontological status of an object’s possessing or exemplifying a property.  When the ideological status of a property or attribute is in question, the central issue are the kinds of predicates that express the property.  The following example brings this out starkly:  A property can be mental, but not physical (ideologically), but can be ontologically physical, but not mental.

If a mental predicate \textup{A}(x) \in \Psi is not lawlike coextensive with a physical predicate \textup{B}(x) \in \Phi, where \Psi and \Phi are appropriate vocabularies, the attribute expressed by \textup{A}(x) is mental, but not physical.  Nevertheless, by the principle of physical exhaustion (PE), the attribute is physical, but not mental (ontologically), as it is possessed solely by physical objects.

Entity-wise, every attribute is mathematical-physical, but only those attributes are mathematical-physical that are expressible by mathematical-physical predicates.  So, if physical reductionism is false (which is likely the case), there are attributes which are mathematical-physical entities, but are not mathematical physical attributes.

The confusion arises when terms like “mental” or “material” are used to call out properties or attributes without clearly setting out whether one is talking about the ontological or ideological status of the attribute.  This is an important point by Hellman, and we will see how this distinction and physicalist materialism in general are useful in clarifying questions of reductionism and materialism in the philosophy of mind when we turn to an analysis of Chalmers’ anti-materialist claims.

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The Ontological and Ideological Status of Attributes

October 12, 2010

With the principle of Physical Exhaustion (PE: (\forall x)(\exists \alpha)(x \in \textup{R}(\alpha)) where \textup{R}(\alpha) is a rank in the hierarchy of the physical), which allows us to say that everything is exhausted by the physical, every attribute is mathematical-physical (i.e., existing somewhere (possibly high-up) on the set-theoretic hierarchy; see this and this). Thus the ontological status of attributes is mathematical-physical.  Now, for a given vocabulary \psi, and for any attribute that expressed by a predicate that makes essential use of members of \psi, call that attribute a \psi-attribute. So, for example, attributes expressed by physical predicates are physical attributes and those expressed by psychological predicates are psychological. This is their ideological status.

The ontological status of a thing has to do with which extensions of predicates (of ontological kind) under which the thing falls. The most encompassing of such predicates is “is mathematical physical’.  But there are other, narrower ways to distinguish the ontological status of things.  For example, some metaphysical predicates, “is abstract”, “is concrete”, or some scientific ones, “is an elementary particle”, “is an event”, “is a person”, “is a social process”, “is a physical magnitude”, etc. Some other ontological kind predicates have empty extensions: “is a soul”, “is a phenomenally raw feel not identifiable with any entity in the hierarchy of the physical”.  But if something were to satisfy these predicates, the predicates would indicate the ontological kind of these things.  So the important semantic relationship here is satisfaction of ontological kind predicates.

This is different than in the case of the ideological status of attributes, where the important semantic relationship is expression of an attribute by a predicate –i.e., the relationship between the argument and value of a universalizing function. Every entity has an ontological status, but only universals have ideological status determined by the types of predicates for which the universal under consideration is the value of the universalizing function.

So the ideological status of an attribute, is given by the predicates that express it.  These predicates themselves can be classified, for instance, according to scientific discipline, psychological-predicates, physical-predicates, Economic/Sociological-predicates, etc.  These classifications are historical and are subject to change due to a variety of factors –not all of them scientific.  Hellman explains that attributes themselves may have more than one ideological status: for the predicate ‘is in pain at t‘ is coextensive in a law-like fashion with a complex physical predicate then ‘being in pain’ is both a psychological and a physical attribute since it is expressed by both psychological and physical predicates.

In the next update I’ll go into Hellman’s discussion of the confusion that results when the ideological and ideological status of attributes is not clearly stated in debates concerning materialism and the mental.

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Hellman’s Physicalist Materialism

September 8, 2010

I’m moving onto Hellman’s “Physicalist Materialism”, a paper whose aim is to apply the physicalist materialist position he developed in “Physicalism” to problems in philosophy and philosophy of science.  I want to focus on just three parts of this paper. The first is the examples Hellman gives of determination without reduction. The second is the distinction he clarifies between the ontological and ideological status of attributes, properties and relations.  The third is the section on the mental.  I really want to get into the section on theoretical equivalence, but I will only do so if I can somehow fit it into the evaluation of the anti-materialism of Chalmers.

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“Physicalism” Concluding Summary

September 7, 2010

It took me a good while to get through this paper –more than I expected –but here we are.

What has Hellman accomplished?

First he showed us how to build the ontological principle of physical exhaustion, PE, (\forall x)(\exists \alpha) (x \in \textup{R}(\alpha)). PE allows us to say that everything is exhausted by the physical without (embarrassingly) implying that everything is in the extension of a basic physical predicate.

Then he introduced the identity of physical indiscernables, IPI, and IPI’, (\forall u)(\forall v)((\forall \phi) (\phi u \leftrightarrow \phi v) \rightarrow (u = v) and (\forall \psi) (\forall u) (\forall v) (\exists \phi) (\psi u \wedge \lnot \psi v \rightarrow \phi u \wedge \lnot \phi v), respectively.  IPI says that if two objects have the same physical properties, then they are the same thing, while IPI’ says that no two objects are distinct with respect to a \psi property without being distinct with respect to a \phi property.

These three principles neither independently nor in conjunction imply or require reduction to the physical, but they are also too weak to express the physicalist thesis that physical phenomena determine all phenomena.  He then turns his attention to principles of determination. In addition to PE and IPI/IPI’ Hellman introduces the determination of truth, Det-T: in \alpha structures \phi truth determines \psi truth if, and only if, (\forall m)(\forall m')((m, m' \in \alpha \wedge m \vert \equiv m' \vert \phi) \rightarrow m \vert \psi \equiv m' \vert \psi), and Det-R: in \alpha structures \phi reference determines \psi reference if, and only if, (\forall m)(\forall m') ((m, m' \in \alpha \wedge m \vert \phi = m' \vert \phi) \rightarrow m \vert \psi = m' \vert \psi).

Det-T says that once you have given a complete description of things in \phi terms, there is only one correct way to describe them in \psi terms.  Det-R says that if two \alpha structures agree in what they assign to the \phi terms, then they agree on what they assign to the \psi terms.

Given a notion of definability, Hellman is able to state the thesis of physical reduction, PE: in \alpha structures, \phi reduces \psi, if, and only if, (\forall \textup{P}(\textup{P} \in \psi \rightarrow \textup{P} is definable in terms of \phi in \alpha structures).

Given that assumptions about the mathematical-physical determination of all truths and, maybe, reference, are regulative principles of scientific theory construction –the assumption in general that all terms and all theories are reducible to mathematical-physical terms is probably false. Hellman’s physicalist materialism is instead composed of PE, DET-T and DET-R, with PE independent of PR and the determination principles.

Because there are non-standard models of the laws of science, our formal systems do not model scientific possibility in a way that permits the move from physical determination to physical reduction –thus Beth’s definibility theorem poses no threat to physicalist materialism.  And any way you cut it, the link between theories as syntactic entities and reductionism doesn’t carry over to determination of reference, ruling out even accidental co-extensiveness between terms.

This sets up the theoretical background for an evaluation of the applications of physicalist materialism across disciplines and problems in philosophy of science, mind and social theory.  In the next updates I  will be covering Hellman’s 1977 “Physicalist Materialism” (Noûs) as well as giving a detailed, critical, evaluation of some of the anti-Materialist claims David Chamers makes in the early chapters of his book The Conscious Mind: In Search of a Fundamental Theory.

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Reduction in α-Structures and Physicalist Materialism

August 27, 2010

Equipped with a notion of definability, Hellman gives an account of reducibility.  Reducibility holds when all the terms of the vocabulary being reduced are definable in the reducing vocabulary.

Letting \phi be the vocabulary of mathematical physics, \psi the vocabulary by means of which all other truths may be stated and \alpha as the set of structures representing scientific possibility, we have:

Physical Reductionism (PR): In \alpha-structures, \phi reduces \psi if, and only if, (\forall \textup{P})(\textup{P} \in \psi \rightarrow \textup{P} is definable in terms of \phi in \alpha -structures). And \phi effectively reduces \psi if every term in \psi is definable in a recursively enumerable set of definitions.

An interesting thing to note here is Hellman’s footnote 17 regarding the extension of reduction beyond linguistic primitives to sentences and laws stated in the language reduced.  If in \alpha-structures, \phi reduces \psi, then each law containing \psi terms, even bridge laws, is definitionally equivalent to a law stated in purely \phi terms.  This, of course, shows the incompatibility of PR with views on emergence, like the view that while the theory of evolution does not increase the number of physical entities in the universe, it does introduce lawlike regularities not expressible in terms of physical law.  It will be interesting to see what the story will be about the compatibility of Physicalist Materialism (next paragraph) and emergence theses.

Now, Hellman goes on to claim that while assumptions about the mathematical-physical determination of all truths and, possibly, reference are regulative principles of scientific theory construction –the assumption in general that all terms and all theories are reducible to mathematical-physical terms is without foundation and likely false.  The physicalism that he endorses instead is made up of PE ((\forall x)(\exists \alpha)(x\in \textup{R}(\alpha)), for \textup{R}(\alpha) a rank in the hierarchy), and principles of physical determination, Det-T and Det-R. This he calls Physicalist Materialism.  Like PE is independent of PR — PE is also independent from physical determination.

It’s important here to highlight just what physicalist materialism is:  Determination has traditionally been thought to imply reductionism.  Anti-reductionism has been traditionally held to be incompatible with determination theses. Physicalist materialism denies both of these claims; it is simultaneous support for principles of determination of truth and reference and anti-reductionism.

My next set of notes will be on Hellman’s evaluation of the effects of Beth’s definability theorem on physicalist materialism.

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A Note on Definability

August 26, 2010

Since we’re talking about definability I wanted to say that in general, for any language \textup{L}, any structure \mathfrak{A} in \textup{L} and any \textup{L}-formula \phi with n free variables, x_{0}, \dots, x_{n-1}, the n-ary relation (or predicate, since predicates represent relations) over the universe \textup{A} of \mathfrak{A}, \phi^{\mathfrak{A}} : = \{( a_{0}, \dots, a_{n-1}) \in \textup{A}^{n} : \models_\mathfrak{A}\phi [a_{0}, \dots, a_{n-1}\}, is the relation defined over \mathfrak{A} by \phi.

In Hellman’s terminology, \phi^{\mathfrak{A}} is \textup{A}, and he is saying that a predicate \textup{P} is definable in a family of structures \alpha if, and only if for every \mathfrak{A} in \alpha, \textup{P} = \phi^{\mathfrak{A}}.

With the next update I’ll move into Hellman’s account of reducibility.

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φ-Definability in α structures

August 25, 2010

At the start of §2.2 Reduction and Determination, Hellman introduces the notion of definability:

An n-place predicate \textup{P} is definable in terms of a vocabulary \phi in \alpha structures if, and only if, there is a finite sentence \textup{A} containing no nonlogical terms not in \phi and with occurrences of n distinct variables, x_{1},\dots, x_{n}, such that every structure in \alpha models (\forall x_{1})\dots (\forall x_{n}) (\textup{P}x_{1} \dots x_{n} \leftrightarrow \textup{A}).

\textup{P} is not just coextensive with a term in the \phi vocabulary.  What the claim of definability says is that there is a term, \textup{A}, in the \phi vocabulary such that the n-place predicate \textup{P} is coextensive with it in every structure in \alpha.

Hellman notes that to say that a term is definable in a given vocabulary is not to say that the term is synonymous with a term in that vocabulary.  While the notion of definability can be spelled out explicitly, the notion of synonymy cannot.  Also, the coextensiveness at issue here involves definability of terms in \phi terms over the structures in \alpha and since each structure \mathfrak{A} in \alpha is a model of the laws of science,  Hellman claims that definability is a kind of lawlike coextensiveness between terms terms.

From here, Hellman will go on to discuss reducibility that holds when all the terms in the vocabulary being reduced are definable in the reducing vocabulary.

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Determination of Reference

August 24, 2010

We’ve set out the determination of truth:

Det-T: In structures \alpha, \phi truth determines \psi truth iff (\forall m)(\forall m') ((m, m' \in \alpha \ \wedge \ m \vert \phi \equiv m' \vert \phi) \rightarrow m \vert \psi \equiv m' \vert \psi).

Now, the fact that two elementary equivalent structures are indiscernible in point of reference if each term has the same reference in each leads to a determination of reference principle similar to Det-T.

Det-R: In structures \alpha, \phi reference determines \psi reference iff (\forall m)(\forall m')((m, m' \in \alpha \ \wedge \ m \vert \phi = \ m' \vert \phi) \rightarrow m \vert \psi = m' \vert \psi)

Det-R says that if two \alpha structures agree in what they assign to the \phi terms, then they agree on what they assign to the \psi terms. In terms of the structure of the models we’re discussing, if the set \alpha is closed under automorphism, then Det-R is the condition that any bijection between the domain of m and m’ that is a \phi-isomorphism is a \psi-isomorphism.

And regarding the connection between Det-T and Det-R, Hellman points out that model-theoretically they are independent principles.  We have the set \alpha, the \phi and the \psi such that in \alpha structures, \phi reference determines \psi reference, but \phi truth does not determine \psi truth.

Hellman continues: if \alpha is the set of structures representing scientific possibility,  \phi the vocabulary of mathematical physics and \psi the (broader) vocabulary in which truths can be stated, then Det-T and Det-R are principles of physical determination.  Since we want \alpha to represent scientific possibility, every structure in \alpha must (at least) model all of the laws of science. But if having each member of \alpha model all of the laws of science is a sufficient condition for \alpha representing scientific possibility then, if T represents all scientific theory, the term ‘\alpha‘ could be uniformly replaced in every instance with ‘{m : m models T}’.

Hellman points out that since it seems possible to formulate T in language with only a finite number of non-logical symbols, T has models which go against the principles of physical determination.  Such models must be excluded if we are to hold onto these principles. In §2.2 Reduction and Determination, Hellman will set out ways to exclude these models while articulating more precisely the notion of scientific possibility.

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Evaluating PE and IPI

August 17, 2010

§1.2 is shorter but makes a very important point about PE and IPI, reductionism and dualism. Let physical reductionism be the claim that for the theory, formulated in a suitable language, that contains all the lawlike truths of science (including physical science), every scientific predicate is definable in physical terms.  That is to say, for every n-place predicate P, one can derive using only the laws of science, a formula of this form:

(\forall x_{1})\dots (\forall x_{n}) (\textup{P}x_{1} \dots x_{n} \leftrightarrow \textup{A})

Here, A is a finite sentence that contains only physical vocabulary as the nonlogical terms and n distinct variables, x_{1} \dots x_{n}. These equivalences are provable within scientific theory and are logical consequences of its laws. What may come as a shock to those who want to avoid mysterious dualism by adhering to such a strong form of reductionism is that even this reductionism is compatible with ontological dualism.

Hellman sets out the following basic theory to make this point. Let \Sigma be the theory that contains only two one-place predicates, P and Q and these non-logical axioms:

(\exists x)(\exists y) (x \not= y \wedge (\forall z) (z = x \vee z = y))
(\exists x) (\textup{P}x \wedge (\forall y) (\textup{P}y \rightarrow y = x))
(\exists x) (\textup{Q}x \wedge (\forall y) (\textup{Q}y \rightarrow y = x))
(\forall x) (\textup{P}x \vee \textup{Q}x)

All that \Sigma says is that there are just two objects and that just one of them is a P and just one of them is Q and everything else is either a P or a Q.  It follows from \Sigma that Q is definable in terms of P, but \Sigma gives no assurance that every object is exhausted by things that are P –as a matter of course, every interpretation where the axioms of \Sigma are true partitions the domain into disjoint subsets of P and Q type things.  And dualism here is a minimal case, since the reasoning can be carried over to any finite number of predicates.

This is a quick and elegant way of showing that reductionism is no shelter from dualism.

What Hellman concludes here is that while PE is necessary for physicalism, neither it nor IPI are sufficient for these reasons: PE does is silent about the scope and power of physical laws, while in IPI, quantification is restricted to the actual world and consequently neither can be used to voice the physicalist thesis that all phenomena are determined by physical phenomena.

We’ll see in §2 what the precise connection is between determination, definability and reduction.

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Wrapping up §1.1 of “Physicalist Materialism”

August 14, 2010

Now, before moving on to §1.2, we follow Hellman in noting that IPI an IPI’ don’t imply PE, but they do imply that there can be no more than one entity apart from the sum of all basic physicl entities.  IPI and IPI’ are stronger than PE, since everything may be exhausted by mathematic0-physical entities, but physical language may not be powerful enough to tell among nonidenticals.  In any case, like I said in the previous post, the upshot is that while IPI and IPI’ make use of the expressive power of the physical language, none of the principles, PE, IPI and IPI’ imply reductionism or even accidental extensional equivalence between the φ and the ψ. And, regardless of its complexity, no physical predicate covers the the extension of any biological or psychological predicate.

To summarize, in §1.1, Hellman has accomplished the following:

1. He has set out the physicalist thesis:”Everything is accounted for by mathematico-physical things satisfying predicates in Γ”.

2. He shows us how to build up a physicalist ontology using Γ.

3. Given the physicalist ontology, he defines the principle of Physical Exhaustion (PE): (∀x)(∃α) (x ∈ R(α)), where R(α) is a rank in the hierarchy.

4. Then he introduces the principle of the Identity of Physical Indiscernibles (IPI): (∀u)(∀v)((∀φ)(φu ↔ φv) → (u = v), where φ ranges over physical predicates and u and v range over arbitrary n-tuples of physical objects.

5.  And follows up by introducing IPI’: (∀ψ)(∀u)(∀v)(∃φ)(ψu & ¬ψv → φu & ¬φv), which says that for any non-physical predicate and any distinction that it makes, there is a physical predicate that makes that distinction as well.

6. He points out that PE, IPI and IPI’ do not imply reductionism or even accidental coextension between the physical and non-physical predicates.

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