>Can you define mathematically, the term 'epiphenomenon'? I hear this term
>bandied about by mechanists like design is bandied about by the ID group,
>but I don't see how one can give it an objective definition. It has all the
>smell of a subjective term to me.
I hope, Glenn, you are not implying that if a concept cannot be given a
definition in mathematical terms, then it is a subjective concept!
Traditionally, 'epiphenomenalism' was the doctrine that physical (brain)
states cause mental states, but that mental states do not cause physical
(brain) states. The one-way causation in epiphenomenalism accomodated the
causal theory of perception, where the physical event of, say, photons
striking the retina, firing neruons, processes in the visual center of the
brain, etc. all caused the mental event of perception.
Epiphenomenalism is generally in disfavor as a theory of mind, as it fails
to explain much of anything. It wants to retain certain mental entities,
but it robs those entities of any causal power. Hence, there is no agency
and no free will.
A more overtly reductionistic theory claims that the mental supervenes on
the physical: S (a supervenient property/entity) supervenes on B (base
properties/entities) if and only if (i) if A has S, then anything else
which has the same B as A also has S; and (ii) if A changes with respect to
S, then some B of A has changed. The wetness of water would be a
supervenient property. Social concepts like nations, and moral concepts
like justice, are sometimes analyzed in terms of supervenience.
Supervenience leads to a form of property dualism, but since supervenient
properties/entities generally are not regarded as having causal powers, if
supervenience is used to reduce the mental to the neurophysiological, then
there is again no mental causation, hence no agency or free will.
Sometimes the term 'emergent property' is used in distinction to
supervenient property in the following way: E is an emergent property of B
just in case (i) E supervenes on B; and (ii) E has causal powers. An
example would be a "virtual governor" in a power generation/transmission
grid, a putative entity which emerges with the increasing complexity of the
grid and has the causal power to hold the frequency of the current in the
grid much closer to 60 Hz than any single governor on any one generator.
This two-way causal feature is not always included when "emergent"
properties are discussed, and often 'emergent' simply means 'supervenient.'
IMHO, an excellent case can be made (pace Massimo) that mental entities are
sui generis first order things which have causal powers; that is, that no
reduction of the mental to the physical is or can be successful.