The conceptual framework of behaviorism is reconstructed in a logical scheme rather than along chronological lines. The resulting reconstruction is faithful to the history of behaviorism and yet meets the contemporary challenges arising from cognitive science, psycholinguistics, and philosophy. In this reconstruction, the fundamental premise is that psychology is to be a natural science, and the major corollaries are that psychology is to be objective and empirical. To a great extent, the reconstruction of behaviorism is an elaboration of behaviorist views (...) of what it is for a science to be objective and empirical. The reconstruction examines and evaluates behaviorist positions on observation and the rejection of introspection, the behavioral data language, theory construction, stimulus-response psychology, the organization of behavior, complex processes, agency, and the interpretation of mentalistic language. The resulting reconstruction shows behaviorism to be a pragmatic psychological version of positivism based on a behavioral epistemology. (shrink)

Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can explain the (...) consistency of T and suggest that an analogous explanation can be provided for the consistency of Peano arithmetic. (shrink)

Sebastian Grève interviews Felix Mühlhölzer on his work on the philosophy of mathematics.

The aim of the present paper is to offer a new analysis of the multifarious relations between mathematics and reality. We believe that the relation of mathematics to reality is, just like in the case of the natural sciences, mediated by instruments . Therefore the kind of realism we aim to develop for mathematics can be called instrumental realism. It is a kind of realism, because it is based on the thesis, that mathematics describes certain patterns of reality. And it (...) is instrumental realism, because it pays atten-tion to the role of instruments by means of which mathematics identifies these patterns. The article concludes by offering solutions to some famous semantic paradoxes based on the diagonal construction as corroboration for this claim. (shrink)

This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...) in his theory of axiomatics is presented. Specifically, it is shown that Carnap’s early model theory is based on a convention to simulate domain variation that is not identical but logically comparable to the modern account. (shrink)

Most empirical accounts of design suggest that designing is an activity where objects and representations are progressively constructed. Despite this fact, whether design is a constructive process or not is not a question directly addressed in the current design research. By contrast, in other fields such as Mathematics or Psychology, the notion of constructivism is seen as a foundational issue. The present paper defends the point of view that forms of constructivism in design need to be identified and integrated as (...) a founda- tional element in design research as well. In fact, a look at the literature reveals at least two types of constructive processes that are well embedded in design research: first, an interac- tive constructivism, where a designer engages a conversation with media, that allows changing the course of the activity as a result of this interaction; second, a social constructivism, where designers need to handle communication and nego- tiation aspects, that allows integrating individuals' expertise into the global design process. A key feature lacking these well-established paradigms is the explicit consideration of creativity as a central issue of design. To explore how cre- ative and constructivist aspects of design can be taken into account conjointly, the present paper pursues a theoretical approach. We consider the roots of constructivism in math- ematics, namely the Intuitionist Mathematics, in order to shed light on the original insights that led to the development of a notion of constructivism. Intuitionists describe mathe- matics as the process of mental mathematical constructions realized by a creative subject over time. One of the most original features of intuitionist constructivism is the intro- duction of incomplete objects into the heart of mathematics by means of lawless sequences and free choices. This allows the possibility to formulate undecided propositions and the consideration of creative acts within a formal constructive process. We provide an in-depth analysis of intuitionism from a design standpoint showing that the original notion is more than a pure constructivism where new objects are a mere bottom-up combination of already known objects. Rather, intuitionism describes an imaginative constructivist process that allows combining bottom-up and top-down processes and the expansion of both propositions and objects with free choices of a creative subject. We suggest that this new form of constructivism we identify is also relevant in interpreting conventional design processes and discuss its status with respect to other forms of constructivism in design. (shrink)

Cameron, Eklund, Hofweber, Linnebo, Russell and Sider have written critical essays on my book, The Construction of Logical Space (Oxford: Oxford University Press, 2013). Here I offer some replies.

This paper addresses John Burgess's answer to the ‘Benacerraf Problem’: How could we come justifiably to believe anything implying that there are numbers, given that it does not make sense to ascribe location or causal powers to numbers? Burgess responds that we should look at how mathematicians come to accept: There are prime numbers greater than 1010 That, according to Burgess, is how one can come justifiably to believe something implying that there are numbers. This paper investigates what lies behind (...) Burgess's answer and ends up as a rebuttal to Burgess's reasoning. (shrink)

This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...) a retraction, has been proved in Section 11.4. The last section gives a laconic answer to the question posed in the title of the paper. (shrink)

Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. It is the purpose of the present note to discuss a number of these issues, both from an historical, as well as a systematic point of view.