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Whitehead and B.

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Russell, Principia Mathematica, Vol. I-III — Constructivity in Mathematics, Proceedings of the Colloquium held in Amsterdam in Hilbert and P. Bernays, Die Grundlagen der Mathematik, Vol. I ; Vol. I I Hilbert, loc. Carnap, Die logische Syntax der Sprache V II Carnap, Introduction to Semantics Russell, Introduction to Mathematical Philosophy Kleene, Introduction to Metamathematics, , p.

Church, Introduction to Mathematical Logic, Vol. I, p. X IV Thus, in some axiomatizations of set-theory, the concept of a self-containing set is meaningless whereas, in other axiomatizations, it has a meaning and can be shown to apply to some sets. Similarly, the set of all sets is meaningless in some axiomatic systems of set-theory although its existence is provable in other set-theoretical systems. Furthermore, in some systems of set-theory, a sharp line is drawn between sets and classes while other systems do without this distinction.

Fraenkel and J. BarHillel, Foundations of Set-Theory These views have been applied in his criticism of the computational model of artificial intelligence. In this hypothesis, building upon the aforementioned ideas, it is argued that the mind and the world form a kind of information feedback loop in which the mind is not just within the individual experiencing the world, but that it extends into the environment they are experiencing. Web resource: Andy Clark's Home Page. After earning two M. Craig is primarily a Christian theologian and apologist, as well as an analytic philosopher, and is recognized for his theological work and cosmological arguments.

Specifically, Craig is best known for his use of the Kalam cosmological argument, which has roots in medieval Islam, as proof of the existence of God. For Craig, in this argument if everything that begins to exist has a cause of existence, and the universe began to exist, then the universe must have a cause of existence, which he argues to be a divine, omniscient God. Craig's most famous book is Reasonable Faith: Christian Truth and Apologetics in which he discussed reformed epistemology, Christian apologetics, and the application of his ideas to evangelism.

Craig has been most influential as a major voice of contemporary theology.

Daniel Dennett received his Ph. Fletcher Professor of Philosophy at Tufts University. Dennett is a cognitive scientist in addition to being a philosopher, and his work considers philosophy of mind and science in relation to the fields of cognitive science and evolutionary biology. Though he has done significant work in philosophy of mind and cognitive science, such as arguing for consciousness the product of the interaction between physical and cognitive processes in the brain in his book Consciousness Explained , Dennett might be most well known for his criticism of religion. In his book Darwin's Dangerous Idea: Evolution and the Meanings of Life , Dennett has argued that the origin of morality can be found in evolution, and not from abstract sources.

Web resource: Daniel Dennett's Home Page. Edmund L.


Gettier is Professor Emeritus of the University of Massachusetts Amherst, and his work is focused in epistemology. Gettier stands out on this list because, unlike many of his counterparts, many of whom are best known for long, dense books, developed over the length of their careers, Gettier's fame and influence in the philosophy game comes from a three-page long essay written at the beginning of his career which, reportedly, he only wrote on a whim in order to pad his publication list.

Web resource: Edmund Gettier's Home Page. As an undergraduate, Allan Gibbard studied mathematics and physics, before earning a Ph. Gibbard's primary focus in in metaethics, and has been influential in arguing for a contemporary form of non-cognitivism, in which ethical sentences cannot be true or false because they do not express propositions.

This is opposed to the cognitivist view that claims ethical sentences are capable of being objectively true.

Logicism and Neologicism (Stanford Encyclopedia of Philosophy)

Like Christine Korsgaard, Gibbard is concerned with normativity. In his major book Wise Choices, Apt Feelings: A Theory of Normative Judgement Gibbard has argued for the significance of the role that feelings play in our development and understanding of moral norms.

In his view, if we perceive someone's actions as rational, then we are endorsing the actions, and so, accepting them and the norms that they represent and enforce. Feelings like acceptance, guilt, and resentment, then, significantly affect our sense of moral norms.

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  • Ethical statements cannot be objective, and so, neither are neither true nor false. Web resource: Allan Gibbard's Home Page. Susan Haack received her Ph. Haack's work can be primarily described as pragmatic philosophy, and she has written on logic, philosophy of language, epistemology, metaphysics, philosophy of law, philosophy of science, feminism, and literature.

    Much of her later work has been concerned with defending science and scientific inquiry against skepticism and faulty epistemologies, with religious doctrine being a primary obstacle. Web resource: Susan Haack's Home Page. After some disagreements, Habermas finished his education studying political science at the University of Marburg under notable Marxist Wolfgang Abendroth. Habermas would also teach at the Frankfurt school, retiring in Habermas works in the traditions of critical theory and pragmatism, and has been very influential to philosophy and sociology.

    Habermas has placed a great deal of emphasis on the power of rational discourse. In what is perhaps his most important work, Theory of Communicative Action , Habermas expressed criticism of modern society for the development of the welfare state, corporate capitalism, and its demand for mass consumption. Habermas argued that with the development of modern industrial society since the start of the 19th century, democracy shifted from being participatory to representative, and the body of the public lost its voice in the democratic discourse, as public life became rationalized and quantified.

    With some controversy, Habermas has called for the need to shift from representative democracy to a deliberative one, in which discourse is made equal again among citizens and government. John Haldane studied art before pursuing philosophy, earning a B.

    Logicism Renewed

    Haldane is currently a University Professor at the University of St. Andrews, holds the title of J. Newton Rayzor Sr. Haldane is not just a notable analytical philosopher, but is recognizable in the mainstream; he has published articles in art magazines, and contributed to numerous television programs.

    Haldane is a catholic, he and is a papal adviser to the Vatican. Haldane is most notable for his work on Thomas Aquinas. Analytical Thomism seeks to merge the ideas of contemporary analytical philosophy with the ideas of 13th century thinker and saint Thomas Aquinas. Through his work, Haldane has been influential in developing a space for Catholic philosophy in the modern analytical landscape.

    Graham Harman received his Ph. Harman's work has primarily focused on metaphysics and ontology, and he has been influential as a key figure in speculative realism and the development of object oriented ontology. Harman's goal in philosophy has been to reject anthropocentric philosophical views in favor of a metaphysical realist approach. In his view, everything is an object human, animal, rock, city, etc. Harman's philosophy is primarily concerned with understanding objects in the world as things-in-themselves, without allusion to anthropocentric qualities of being. Web resource: Graham Harman's Home Page.

    John Hawthorne earned his Ph. Hawthorne's work primarily focuses on metaphysics and epistemology, and his most influential book on the subjects is Metaphysical Essays However, Hawthorne grants that this is separate from whether the subject can be said to have knowledge, which depends on the subject's own context.

    Web resource: John Hawthorne's Home Page. Heil's work combines metaphysics with philosophy of mind, using each realm as a way of understanding the other. In his book The Universe as we Find It , Heil considers how our notions of causation and truth making contribute to our ontological understanding of the world, and pursues the application of this ontology to contemporary philosophical problems.

    Modern logic

    Heil is most influential as an educator in philosophy. Web resource: John Heil's Home Page. Ingvar Johansson earned his Ph. Johansson primarily works in the area of ontology, and is an epistemological fallibilist. In his book Ontological Investigations: An Inquiry into the Categories of Nature, Man, and Society Johansson has worked toward developing a modern realist version of Aristotle's theory of categories, in order to update Aristotle's ontology and for the theory to be made compatible with modern science.

    More recently, Johannson has been focused on applied ontology in the area of medical information science, working with the Institute for Formal Ontology and Medical Information Science at Saarland University.

    Web resource: Ingvar Johansson's Home Page.