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

Baynesr at comcast.net Baynesr at comcast.net
Mon Sep 26 11:43:57 EDT 2011


 It might help if I give you the formulation of mind body supervenience which is most well known, although it is an evolving conception. 

Here is Kim's 'indiscernibility' definiton: 

"Mental properties *supervene* on physical properties in that necessarily any two things...indiscernible in all physical properties are indiscernible in mental properties." 

On this definition we can infer that if mental properties are changed then physical properties are changed. When I say "If the limits are changed so, too, is the area" I mean to say that the limits supervene on the area. My last point as I recall was that supervenience no more entails identity or reduction (a major controversy is how "reductionist" is supervenience) than supervenience of limits entails identify of limits on area. This in a nutshell is all that I'm really claiming. Now to address some of your points I do need some idea of which df. of 'supervenience' you have in mind and how this relates to your discussion of the functional relations; supervenience is a special kind of functional relation. Another point I make which I believe important is the matter of "realizers," and here I mean the term in Putnam's sense in his discussion of functionalism. 



----- Original Message -----

From: Baynesr at comcast.net 
To: "Scott Holbrook" <scott.holbrook at gmail.com> 
Cc: "hist-analytic" <hist-analytic at simplelists.co.uk> 
Sent: Monday, September 26, 2011 9:25:56 AM 
Subject: Re: A Mathematical Analogy to Mind/Body Supervenience 




What do you take supervenience to be and how does this relate to your remarks on functions? I need to know this before I can understand your point(s) here. If the limits supervene that is all I need on the definition of 'supervenience' I'm using, the "indiscernibility" definition. (Kim Mind in the Physical World, p. 10.) 






----- Original Message -----

From: "Scott Holbrook" <scott.holbrook at gmail.com> 
To: Baynesr at comcast.net 
Cc: "hist-analytic" <hist-analytic at simplelists.co.uk> 
Sent: Monday, September 26, 2011 6:28:02 AM 
Subject: Re: A Mathematical Analogy to Mind/Body Supervenience 

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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