@Richard: I think that’s a valid reduction. It explains non-negative integers reductively in terms of an isomorphism between two groups of things without appealing to numbers or number concepts.
@constant: regardless of the label, you still have 2 sets of things, those which it is possible to label fizzbin (following the rules) and those which it is not. Possibility is still there. So what does it mean that it is possible to label a node fizzbin? Does that mean that in order to understand the algorithm, which relies on possibility of labelling nodes “fizzbin” or not, we now must set up a different search space, make an preliminary assumption about which nodes in that space we think it is possible to label fizzbin (following the rules), and then start searching and changing labels? How does this process terminate? It terminates in something other than the search algorithm, a primitive sense of possibility that is more fundamental than the concept of “can label fizzbin”.
@Richard: I think that’s a valid reduction. It explains non-negative integers reductively in terms of an isomorphism between two groups of things without appealing to numbers or number concepts.
@constant: regardless of the label, you still have 2 sets of things, those which it is possible to label fizzbin (following the rules) and those which it is not. Possibility is still there. So what does it mean that it is possible to label a node fizzbin? Does that mean that in order to understand the algorithm, which relies on possibility of labelling nodes “fizzbin” or not, we now must set up a different search space, make an preliminary assumption about which nodes in that space we think it is possible to label fizzbin (following the rules), and then start searching and changing labels? How does this process terminate? It terminates in something other than the search algorithm, a primitive sense of possibility that is more fundamental than the concept of “can label fizzbin”.