More on Ross and indeterminacy

James Ross argues that thinking cannot be a purely physical process because all physical processes lack a certain quality that is to be found in thinking.  Well, if I am performing an addition in my head or on paper and presumably thinking about addition, then I'm quite happy to admit that my thinking has qualities that a calculator doing addition lacks.  But my conviction of this is in no way reinforced by Ross's argument.  For Ross says that the distinguishing quality is determinateness (with respect to 'pure functions'), and I can't for the life of me see how a calculator doing such an addition lacks determinateness.

In section II of his JoP article(*) Ross says,

For instance, there are no physical features by which an
adding machine, whether it is an old mechanical "gear" machine or
a hand calculator or a full computer, can exclude its satisfying a
function incompatible with addition, say, quaddition (cf. Kripke's
definition (op. cit., p. 9) of the function to show the indeterminacy
of the single case: quus, symbolized by the plus sign in a circle, "is
defined by: x ⊕ y = x + y, if x, y < 57, =5 otherwise") modified so
that the differentiating outputs (not what constitutes the difference,
but what manifests it) lie beyond the lifetime of the machine.

In an earlier comment at Ed Feser's I noted that Ross's examples of these 'incompossible' functions were hard to understand, if not flawed, especially as time seems to play an important role in them. Time? In a 'pure' function? Nobody responded to that aspect of the comment.  Neither Ed nor any commenter has actually given us a proof by example that such functions exist.  So, here is a challenge. This is the operation table of a three bit wide adder circuit,

0∘0=0, 0∘1=1, 0∘2=2, 0∘3=3, 0∘4=4, 0∘5=5, 0∘6=6, 0∘7=7, 0∘!=!,
1∘0=1, 1∘1=2, 1∘2=3, 1∘3=4, 1∘4=5, 1∘5=6, 1∘6=7, 1∘7=!, 1∘!=!,
2∘0=2, 2∘1=3, 2∘2=4, 2∘3=5, 2∘4=6, 2∘5=7, 2∘6=!, 2∘7=!, 2∘!=!,
3∘0=3, 3∘1=4, 3∘2=5, 3∘3=6, 3∘4=7, 3∘5=!, 3∘6=!, 3∘7=!, 3∘!=!,
4∘0=4, 4∘1=5, 4∘2=6, 4∘3=7, 4∘4=!, 4∘5=!, 4∘6=!, 4∘7=!, 4∘!=!,
5∘0=5, 5∘1=6, 5∘2=7, 5∘3=!, 5∘4=!, 5∘5=!, 5∘6=!, 5∘7=!, 5∘!=!,
6∘0=6, 6∘1=7, 6∘2=!, 6∘3=!, 6∘4=!, 6∘5=!, 6∘6=!, 6∘7=!, 6∘!=!,
7∘0=7, 7∘1=!, 7∘2=!, 7∘3=!, 7∘4=!, 7∘5=!, 7∘6=!, 7∘7=!, 7∘!=!,
!∘0=!, !∘1=!, !∘2=!, !∘3=!, !∘4=!, !∘5=!, !∘6=!, !∘7=!, !∘!=!.

Operation ∘ can be summarised as

x∘y=!     if x=! or y=!,
x∘y=x+y     if x+y<8,
x∘y=!    otherwise.

I find it natural to say that ∘ agrees with + on the domain x>=0, y>=0, x+y<8.  This is math-speak. But Ross claims ∘ 'satisfies' a function incompatible with +.  Can we have an example of such a function please?




(*)  Immaterial Aspects of Thought, The Journal of Philosophy, Vol. 89, No. 3, (Mar., 1992), pp. 136-150 (available at http://www.jstor.org/stable/2026790)