Second Order Logic or Set Theory?
نویسندگان
چکیده
منابع مشابه
Second order logic or set theory?
We try to answer the question which is the “right” foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first order theory, we have to rephrase the question. We formulate what we call the second order view and a competing set theory view, and then discuss the merits of both views. On the surface these two vi...
متن کاملSecond order logic and set theory
Both second order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved. We take it upon ourselves in this paper to compare the two approaches, second order logic on one hand and set theory on the other hand, evaluating their merits and weaknesses. We argue that we should think of first or...
متن کاملSet Theory, Higher Order Logic or Both?
The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for speciication, the beneets of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Fu...
متن کاملSecond Order Logic, Set Theory and Foundations of Mathematics
The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the power sets. It is argued that in many ways this difference is illusory. More importantly, it is arg...
متن کاملModal Deduction in Second-Order Logic and Set Theory - I
In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in 11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We rst extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Bulletin of Symbolic Logic
سال: 2012
ISSN: 1079-8986,1943-5894
DOI: 10.2178/bsl/1327328440