Changes

Because it was necessary to begin informally, I started out speaking of things called “variables” as if there really were such things, taking it for granted that a consistent concept of their existence could be formed that would substantiate the ordinary usages carried out in their name, and contemplating judgments of their worth as if it were a matter of judging existing objects rather than the very ideas of their existence, whereas it is precisely the whole question at issue whether any of these presumptions are justified.  As concessions to common usage, encounters with these assumptions are probably unavoidable, but a formal approach requires one to backtrack a bit, to treat the descriptive term “variable” as nothing more substantial than a general name in common use, and to examine whether its uses can be maintained in a purely formal system.  Further, each of the “variables” that is taken to fall under this term has to allow its various indications to be reconsidered in the guise of mere signs and to permit the question of their objective reference to be examined anew.

Because it was necessary to begin informally, I started out speaking of things called “variables” as if there really were such things, taking it for granted that a consistent concept of their existence could be formed that would substantiate the ordinary usages carried out in their name, and contemplating judgments of their worth as if it were a matter of judging existing objects rather than the very ideas of their existence, whereas it is precisely the whole question at issue whether any of these presumptions are justified.  As concessions to common usage, encounters with these assumptions are probably unavoidable, but a formal approach requires one to backtrack a bit, to treat the descriptive term “variable” as nothing more substantial than a general name in common use, and to examine whether its uses can be maintained in a purely formal system.  Further, each of the “variables” that is taken to fall under this term has to allow its various indications to be reconsidered in the guise of mere signs and to permit the question of their objective reference to be examined anew.

At this point, it is worth trying to apply the insights of nominalism to these questions, if only to see where they lead.

At this point, it is worth trying to apply the insights of nominalism to these questions, if only to see where they lead.

It is the general advice of nominalism not to confuse a general name with the name of a general.  To this, pragmatism adds the distinct recommendation not to confuse an individual name with the name of an individual, because a particular that seems perfectly determinate for some purposes may not be determinate enough for other purposes.

It is the general advice of nominalism not to confuse a general name with the name of a general, that is, a ''universal'', or a property possessed in common by many individual things.  To this, pragmatism adds the distinct recommendation not to confuse an individual name with the name of an individual, because a particular that seems perfectly determinate for some purposes may not be determinate enough for other purposes.

In the perspective that results from combining these two points of view, general properties and individual instances, alike, can take on from the start an equally provisional status as objects of discussion and thought, in the meantime treated as interpretive fictions, as mere potentials for meaning, awaiting the settlement of their reality at the end of inquiry.  Meanwhile, the individual can be exactly as tentative as the general, and ultimately, the general can be precisely as real as the individual.  Still, their provisional treatment as hypothetical objects of reasoning does not affect their yet to be determined status as realities.  This is so because it is possible that a hypothesis hits the mark, and it remains so as long as a provenient fiction, something called a likely story on account of its origin, can still succeed in guessing the truth aright.

In the perspective that results from combining these two points of view, general properties and individual instances alike can take on from the start an equally provisional status as objects of discussion and thought, in the meantime treated as interpretive fictions, as mere potentials for meaning, awaiting the settlement of their reality at the end of inquiry.  Meanwhile, the individual can be exactly as tentative as the general, and ultimately, the general can be precisely as real as the individual.  Still, their provisional treatment as hypothetical objects of reasoning does not affect their yet to be determined status as realities.  This is so because it is possible that a hypothesis hits the mark, and it remains so as long as a provisional fiction, something called a likely story on account of its origin, can still succeed in guessing the truth aright.

Unlike generals, individuals, and numerous other forms of logical and mathematical objects, whose treatment as fictions does not affect their status as realities, one way or the other, there does not seem to be any consistent way of treating variables as objects.  Although each one of the elemental and the functional construals appears to work well enough when taken by itself in the appropriate context, trying to combine these two notions into a single concept of the variable can lead to the mistake of confusing a function with one of its values.

Unlike generals, individuals, and numerous other forms of logical and mathematical objects, whose treatment as fictions does not affect their status as realities, one way or the other, there does not seem to be any consistent way of treating variables as objects.  Although each one of the elemental and the functional construals appears to work well enough when taken by itself in the appropriate context, trying to combine these two notions into a single concept of the variable can lead to the mistake of confusing a function with one of its values.

Whether one tries to account for variables or chooses to explain them away, it is still necessary to say what kinds of entities are really involved when one is using this form of speech and trying to reason with or about its terms, whether one is speaking about things described as "variables" or merely about their terms of description, whether there are really objects to be dealt with or merely signs to be dispensed with.

Whether one tries to account for variables or chooses to explain them away, it is still necessary to say what kinds of entities are really involved when one is using this form of speech and trying to reason with or about its terms, whether one is speaking about things described as “variables” or merely about their terms of description, whether there are really objects to be dealt with or merely signs to be dispensed with.

According to one way of understanding the term, there is no object called a "variable" unless that object is a sign, and so the name "variable name" is redundant.  Variables, if they are anything at all, are analogous to numerals, not numbers, and thus they fall within the broad class of signs called "identifiers", more specifically, as "indices".  In the case of variables, the advice of nominalism, not to confuse a variable name with the name of a variable, seems to be well taken.

According to one way of understanding the term, there is no object called a “variable” unless that object is a sign, and so the name “variable name” is redundant.  Variables, if they are anything at all, are analogous to numerals, not numbers, and thus they fall within the broad class of signs called ''identifiers'', more specifically, ''indices''.  In the case of variables, the advice of nominalism, not to confuse a variable name with the name of a variable, seems to be well taken.

If the world of elements appropriate to this discussion is organized into objective and syntactic domains, then there are fundamentally just two different ways of regarding variables, as objects or as signs.  One can say that a variable is a fictional object that is contrived to provide a variable name with a form of objective referent, or one can say that a variable is a sign itself, the same thing as a variable name.  In the present setting, it is convenient to arrange these broad approaches to variables under the NOSs where one finds them most often pursued.

If the world of elements appropriate to this discussion is organized into objective and syntactic domains, then there are fundamentally just two different ways of regarding variables, as objects or as signs.  One can say that a variable is a fictional object that is contrived to provide a variable name with a form of objective referent, or one can say that a variable is a sign itself, the same thing as a variable name.  In the present setting, it is convenient to arrange these broad approaches to variables under the NOSs where one finds them most often pursued.