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

For instance, there are no physical features by which anIn 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,

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.

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∘!=!,Operation ∘ can be summarised as

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=!, !∘!=!.

x∘y=! if x=! or y=!,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?

x∘y=x+y if x+y<8,

x∘y=! otherwise.

(*) 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)

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