By Wolfgang Balzer;C.U. Moulines;J.D. Sneed
This booklet has grown out of 8 years of shut collaboration between its authors. From the very starting we determined that its content material may still pop out because the results of a really universal attempt. that's, we didn't "distribute" elements of the textual content deliberate to every considered one of us. to the contrary, we made some degree that every unmarried paragraph be the manufactured from a standard mirrored image. real team-work isn't as ordinary in philosophy because it is in different educational disciplines. we predict, even though, that this can be extra as a result of idiosyncrasy of philosophers than to the character in their topic. shut collaboration with confident effects is as profitable as something could be, however it can also end up to be really tricky to enforce. In our case, a part of the problems got here from in simple terms geographic separation. This prompted unsuspected delays in coordinating the paintings. yet greater than this, as time handed, the buildup of specific effects and ideas outran our skill to slot them into an natural solidarity. assorted varieties of exposition, other ways of formalization, assorted degrees of complexity have been concurrently found in a voluminous manuscript that had turn into thoroughly unmanageable. particularly, a section of the textual content have been conceived within the language of type conception and hired rules of a slightly summary nature, whereas one other half was once expounded within the extra traditional set-theoretic variety, stressing intui tivity and concreteness.
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Extra info for An Architectonic for Science: The Structuralist Program
E. of potential models of an empirical theory. If we were interested in establishing a criterion for drawing a sharp boundary between pure mathematics and empirical science we would use this idea: The first discipline would consist of theories not putting any (semantic) constraint on the content of the base sets of their models; empirical science consists of theories which do put such constraints - which differentiate between "plausible" and "implausible" potential models on some pre-theoretic grounds.
Now with symbols for sets and with the usual symbols from set theory and logic we can build formulas. Let A denote such a formula. We write A(u) in order to denote that the symbol "u" (which is to denote a set) occurs in A, and similarly A(u l , ... , un) if the symbols "u l", ... , "un" occur in A. We write A[u l , ... , unl in order to denote that at most "u l", ... , "un" occur in A as symbols denoting sets (except bound variables). Then we can say that a formula A applies to structure (D I' .
We have not yet defined general notions of actual and potential models. Although in all examples of theories we shall analyze and also in the general considerations connected with them the distinction between potential and actual models turns out to be very helpful and natural, the question of how to draw this distinction in general is more difficult than it appears at first glance. The difficulty in principle arises from the well-known difficulty with the concept of lawlikeness which has been discussed in classical philosophy of science for decades.
An Architectonic for Science: The Structuralist Program by Wolfgang Balzer;C.U. Moulines;J.D. Sneed