Feser is now saying that this indeterminacy (or is it a different form of indeterminacy?) can be resolved (well, sort of) by taking into consideration the intentions of the calculator's designers and users. Ross nowhere says anything like this. How are we to understand Feser? He gives us the puppet metaphor. Ross merely says

*The machine adds the way puppets walk,*and develops the idea no further. Maybe Feser means that the puppet 'goes through the motions of walking', but isn't really walking. Likewise the calculator 'goes through the motions of adding', making analogous steps to those that we do when we add two numbers on paper, but this isn't really adding. Real adding has to involve the

*understanding*of number and addition that we humans have. This, I guess, is the

*intentional*component that has to be added (!) to mechanical addition to get genuine addition (sort of).

I think this is stipulative to the point of begging the question. We can't deny that there is a very broad concept we can label

*addition*---perhaps

*augmentation*would be better---that we apply outside of strictly numerical circumstances.

*Add a pinch of salt*, say. Within this concept we find a narrower and harder-edged concept of strictly numerical addition, and within this the concept of addition of numerals to base ten. I find this concept completely determinate. It's still abstract because it depends on the idea of a

*digit*, which itself is abstract. Almost any ten distinct physical objects, marks, or material patterns suffice for a concrete realisation. Likewise, we need the idea of a

*sequence*of digits, and this can be realised by physical adjacency and direction---beads on wires, marks on paper running left to right, say, or charge-bearing capacitative cells with order determined by linking conductors. The concept of addition within this symbolic system is purely syntactical. It's just a matter of juggling the symbols around according to rules, and syntactic devices like gear-wheeled mechanical calculators or like electronic calculators and computers can realise it. Determinately. Any putative meanings of the symbol sequences, any intentions of the machine's designers and users, have no bearing on this.

This is my objection to Ross/Feser. I'm not really interested in the larger argument as to the immateriality of thought. I just concentrate on Ross's premise regarding physical indeterminacy of function. I think Ross is quite wrong on this. It's almost as if, for Ross, the notion of

*function*is intrinsically intentional. For a mathematician or physicist it's just an abstract descriptive term, part of his tool-kit for dealing with the world, and no more intentional than any other term. Note, though, that it's of higher order than ordinary relational terms like

*less than*, say, being descriptive of relations themselves. A function is a non-one-many relation, so

*less than*is not functional.

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