Related papers: Constructive truth and circularity
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
We define constructive truth for arithmetic and for intuitionistic analysis, and investigate its properties. We also prove that the set of constructively true (first order) arithmetical statements is Pi-1-2 and Sigma-1-2 hard, and we…
We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…
I outline a new theory of truth that resolves the classical and constructive versions of the liar paradox. The theory features a provably consistent axiomatization of a global self-applicative truth predicate. Truth is defined using…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation.…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a…
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
Infinity, in various guises, has been invoked recently in order to `explain' a number of important questions regarding observable phenomena in science, and in particular in cosmology. Such explanations are by their nature speculative. Here…
We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently…
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…
I discuss some connotations of mathematical notion of "truth" in the context of humanistic discourse
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a…