Search results for "Intuitionism"
showing 10 items of 11 documents
Philosophy of Mathematics and Ontological Commitment
2000
This paper concerns Quine's classification of philosophies of mathematics as sketched in "On what there is" and offers a new reading of Quine's view. In his famous paper Quine defines three positions: Realism, Conceptualism, and Nominalism. Each of them, he says, has its modern expression, respectively, in Logicism, Intuitionism, and Formalism. According to Quine these foundational positions can be accepted or rejected on a clear and objective basis, according to their distinctive ontological commitments. Consistent with his own criterion for ontological commitment (buttressed by his view on impredicative definitions), Quine adopts the Realist (or the Platonist) position in mathematics. Lat…
Intuition Pumps and the Proper Use of Thought Experiments
2005
I begin with an explication of "thought experiment". I then clarify the role that intuitions play in thought experiments by addressing two important issues: (1) the informativeness of thought experiments and (2) the legitimacy of the method of thought experiments in philosophy and the natural sciences. I defend a naturalistic account of intuitions that provides a plausible explanation of the informativeness of thought experiments, which, in turn, allows thought experiments to be reconstructed as arguments. I also specify criteria for distinguishing bad "intuition pumps" from legitimate thought experiments. These criteria help us to avoid being seduced by the dangerous suggestive power of mi…
Relation between Social Conservatism, Moral Competence, Moral Orientations, and the Importance of Moral Foundations
2017
AbstractThis paper examines the relation between moral competence, moral orientations, importance of moral foundations, and political orientation, by combining two theoretical approaches in moral psychology--the cognitive perspective and social-intuitionist perspective. The participants (Study 1 N=348, aged 18 to 67, and Study 2 N = 361, aged 16 to 74) completed the Moral Competence Test (formerly Moral Judgment Test, Lind, 1978, 2008), the 30-Item Full Version of the Moral Foundations Questionnaire (Graham, Haidt & Nosek, 2008), and measurements of political orientation (a seven-point self-evaluation scale in study 1 and an 8-item social conservatism scale in Study 2). There was a nega…
Space-Time, Phenomenology, and the Picture Theory of Language
2010
To estimate Minkowski’s introduction of space-time in relativity, the case is made for the view that abstract language and mathematics carries meaning not only by its connections with observation but as pictures of facts. This view is contrasted to the more traditional intuitionism of Hume, Mach, and Husserl. Einstein’s attempt at a conceptual reconstruction of space and time as well as Husserl’s analysis of the loss of meaning in science through increasing abstraction is analysed. Wittgenstein’s picture theory of language is used to explain how meaning is conveyed by abstract expressions, with the Minkowski space as a case.
Introduction by the Editors
2015
Kohlberg’s approach to moral development and moral education continues to stimulate researchers and educators worldwide. His work still offers knowledge, methods and inspirations for understanding moral cognition and behavior, and how to foster it. This volume examines aspects of Kohlberg’s moral stage developmental theory and his theory of moral education to revisit their strengths and weaknesses in light of new questions and methods.
Quantum Mechanics as a Semantic Problem
2018
Physics, like all science, is grown out of a desire to understand the world. However, modern physics with its mathematical form has become increasingly removed from the world of everyday experience and visual imagination. In quantum mechanics it is impossible to visualize the reality represented by the theory. All we have is a consistent mathematical structure. Although the theory works perfectly well instrumentally, the question remains, how can the mathematics of the theory impart understanding? If we look at mathematics as a language, we are faced with the semantic problem: how does the language of mathematics acquire meaning? In an attempt to answer this question, I study Derrida’s earl…
Amount of Nonconstructivity in Finite Automata
2009
When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P.Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L. E. J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was "nonconstructive arguments have no value for mathematics". However, P. Erdos got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. R.Freivalds [7] showed that nonconstructive methods in coding theory are related to the notion of…
Amount of nonconstructivity in deterministic finite automata
2010
AbstractWhen D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P. Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L.E.J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was “nonconstructive arguments have no value for mathematics”. However, P. Erdös got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. The author (Freivalds, 2008) [10] showed that nonconstructive methods in coding theory are…
Bachelard, Enriques and Weyl: comparing some of their ideas
2012
Some aspects of Federigo Enriques mathematical philosophy thought are taken as central reference points for a critical historic-epistemological comparison between it and some of the main aspects of the thought of other his contemporary thinkers like Gaston Bachelard and Hermann Weyl. From what will be exposed, it will be also possible descry eventual educational implications of the historic-epistemological approach.
Evidence//Intuibility
2020
The concept of evidence is implied by distinct kinds of cognitive and reasoning processes carried out in ordinary experience or in specialized domains of knowledge, like science, philosophy, logic and mathematics. Theories have been developed along three orthogonal axes. Along the first axis, theories are located according to their view on evidence as a necessary and sufficient condition for knowledge. Along the second axis, theories are located according to the cognitive characterization of evidence. On the third axis, theories are distinguished by the individuation of the bearers of evidence.