[hist-analytic] A Mathematical Analogy to Mind/Body Supervenience

Scott Holbrook scott.holbrook at gmail.com
Mon Sep 26 07:28:02 EDT 2011

I think there's something funny going on with "the shape of the
curve."  For the FTC, the shape is more or less the function.  But,
one may be talking about e.g., parabolas in general.  Depending upon
whether I'm thinking of "shape" in one way the other, different things
may hold.  But I need to think more about this...

Or, maybe I just don't fully understand the analogy.  There are three
relevant considerations in the math example: the limits, the "shape"
and the area.  In the other case, we have mental properties and
physical properties (do we wish this to include the totality of
physical affairs or only some segment of interest?)...only two
relevant considerations.

You say the area supervenes on the limits...but this doesn't seem to
be entirely true.  Given a function, and given limits, then the area
is functionally determined.  Given an area and a function, then
perhaps there are more than one set of limits that would suffice, but
it still seems as if all the POSSIBLE limits are functionally
determined (which is not the same as absolutely...but the limits are
subvenient, so it shouldn't matter...certainly being determined need
not be a two-way street in this case).

But, why do we care that the limits aren't uniquely determined?  If
the area is analogous to the mental, then I should think the limits
are analogous to physical states of affairs (i.e., they are
subvenient).  So, given a particular curve (i.e., a function), then
the area IS determined by the limits...which is what Kim said (if
indeed limits --> physical and area--> mental).

Which still leaves me wondering about the role of the curve in all
this.  Is the curve to be the totality of physical affairs and the
limits some circumscribes section of the totality (e.g., a particular
human in a particular mental state)?

If this is the case, then I still don't see what's all that surprising
here.  Different limits yielding identical areas seems to be saying
nothing more than "different people can have the same mental states."
Granted, knowing that there is pain, somewhere, doesn't in anyway tell
me who is in pain, but, as I said above, I certainly know that types
of things that can be in pain (i.e., the possible limits are
determined).  But, once again, the individual is subvenient.

Now, given a particular human, I may or may not know what particular
mental state is subvenient (e.g., are those tears of joy or pain?).
But, in this case, it seems like the analogy would break down.  Since,
knowing the limits, given a particular curve, the area is determined.

Perhaps if you could just explain the analogy a little more clearly
I'll be able to clear up my own confusions.


P.S.  If mental properties are supervenient, but not absolutely
determined (or at the very least, severely limited in possibility),
then it seems as if strange things could happen.  Perhaps getting
punched in the face causes pain one day and pleasure the next (for the
same person)...or perhaps there could be alternating feelings of
pleasure and pain.  It seems to defeat the purpose of mental states if
they're just going to end up being cyclical in this on/off fashion.

Further, I don't see how we could ever, with any amount of
reliability, say that a given mental state obtains for an individual
as opposed to another (what criteria would I have for saying he's sad
as opposed to very happy?).  And the fact is, we do, with very
remarkable reliability, attribute mental states to others.

On 9/26/11, Baynesr at comcast.net <Baynesr at comcast.net> wrote:
> Here's another selection from my notebook. Again, I'm not firm on this; just
> taking notes.
> Kim says that the presence of the supervenient property is "absolutely
> determined by the subvenient property." Consider a mathematical analogy.
> Take the standard case of area under a curve between two limits of
> integration. If you change the shape of the curve you do not necessarily
> change the area lying underneath it between two limits.
> If you change the area of the curve you need not change the shape of the
> curve, even though the shape of the curve and the area are functionally
> related by the fundamental theorem of calculus. Note that the area of a
> curve can be "realized" (recall Putnam) in various ways, varying with the
> shape of the curve. The area of beneath the curve, however, "supervenes" on
> the limits (of integration): If the limits are changed so, too, is the area
> (ceteris paribus) under the curve. But what the limits ARE is not determined
> by the area. Similarly, although mental properties may supervene on physical
> properties they are not determined by the physical properties upon which
> they supervene. Or, at least, further argument is required.
> Regards
> Steve Bayne

"Conventional people are roused to fury by departures from convention,
largely because they regard such departures as a criticism of
-- Bertrand Russell

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