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SP.2H3 Ancient Philosophy and Mathematics (MIT) SP.2H3 Ancient Philosophy and Mathematics (MIT)

Description

Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.

Subjects

mathematics | mathematics | geometry | geometry | history | history | philosophy | philosophy | Greek philosophy | Greek philosophy | Plato | Plato | Euclid | Euclid | Aristotle | Aristotle | Rene Descartes | Rene Descartes | Nicomachus | Nicomachus | Francis Bacon | Francis Bacon | number | number | irrational number | irrational number | ratio | ratio | ethics | ethics | logos | logos | logic | logic | ancient knowing | ancient knowing | modern knowing | modern knowing | Greek conception of number | Greek conception of number | idea of number | idea of number | courage | courage | justice | justice | pursuit of truth | pursuit of truth | truth as a surd | truth as a surd

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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ES.SP.2H3 Ancient Philosophy and Mathematics (MIT) ES.SP.2H3 Ancient Philosophy and Mathematics (MIT)

Description

Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.

Subjects

mathematics | mathematics | geometry | geometry | history | history | philosophy | philosophy | Greek philosophy | Greek philosophy | Plato | Plato | Euclid | Euclid | Aristotle | Aristotle | Rene Descartes | Rene Descartes | Nicomachus | Nicomachus | Francis Bacon | Francis Bacon | number | number | irrational number | irrational number | ratio | ratio | ethics | ethics | logos | logos | logic | logic | ancient knowing | ancient knowing | modern knowing | modern knowing | Greek conception of number | Greek conception of number | idea of number | idea of number | courage | courage | justice | justice | pursuit of truth | pursuit of truth | truth as a surd | truth as a surd

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.241 Logic I (MIT) 24.241 Logic I (MIT)

Description

Introduction to the aims and techniques of formal logic. The logic of truth functions and quantifiers. The concepts of validity and truth and their relation to formal deduction. Applications of logic and the place of logic in philosophy. Introduction to the aims and techniques of formal logic. The logic of truth functions and quantifiers. The concepts of validity and truth and their relation to formal deduction. Applications of logic and the place of logic in philosophy.

Subjects

formal logic | formal logic | truth functions | truth functions | quantifiers | quantifiers | validity | validity | truth | truth | formal deduction | formal deduction | applications of logic | applications of logic | logic in philosophy | logic in philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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ES.2H3 Ancient Philosophy and Mathematics (MIT) ES.2H3 Ancient Philosophy and Mathematics (MIT)

Description

Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.

Subjects

mathematics | mathematics | geometry | geometry | history | history | philosophy | philosophy | Greek philosophy | Greek philosophy | Plato | Plato | Euclid | Euclid | Aristotle | Aristotle | Rene Descartes | Rene Descartes | Nicomachus | Nicomachus | Francis Bacon | Francis Bacon | number | number | irrational number | irrational number | ratio | ratio | ethics | ethics | logos | logos | logic | logic | ancient knowing | ancient knowing | modern knowing | modern knowing | Greek conception of number | Greek conception of number | idea of number | idea of number | courage | courage | justice | justice | pursuit of truth | pursuit of truth | truth as a surd | truth as a surd

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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ES.2H3 Ancient Philosophy and Mathematics (MIT) ES.2H3 Ancient Philosophy and Mathematics (MIT)

Description

Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.

Subjects

mathematics | mathematics | geometry | geometry | history | history | philosophy | philosophy | Greek philosophy | Greek philosophy | Plato | Plato | Euclid | Euclid | Aristotle | Aristotle | Rene Descartes | Rene Descartes | Nicomachus | Nicomachus | Francis Bacon | Francis Bacon | number | number | irrational number | irrational number | ratio | ratio | ethics | ethics | logos | logos | logic | logic | ancient knowing | ancient knowing | modern knowing | modern knowing | Greek conception of number | Greek conception of number | idea of number | idea of number | courage | courage | justice | justice | pursuit of truth | pursuit of truth | truth as a surd | truth as a surd

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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24.241 Logic I (MIT)

Description

Introduction to the aims and techniques of formal logic. The logic of truth functions and quantifiers. The concepts of validity and truth and their relation to formal deduction. Applications of logic and the place of logic in philosophy.

Subjects

formal logic | truth functions | quantifiers | validity | truth | formal deduction | applications of logic | logic in philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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24.400 Proseminar in Philosophy I (MIT) 24.400 Proseminar in Philosophy I (MIT)

Description

This course is an intensive seminar on the foundations of analytic philosophy for first-year graduate students. A large selection of classic texts, such as Frege's Foundations of Arithmetic, Russell's Problems of Philosophy, and Wittgenstein's Philosophical Investigations, is covered in this course. This course is an intensive seminar on the foundations of analytic philosophy for first-year graduate students. A large selection of classic texts, such as Frege's Foundations of Arithmetic, Russell's Problems of Philosophy, and Wittgenstein's Philosophical Investigations, is covered in this course.

Subjects

philosophy | philosophy | Frege | Frege | Meinong | Meinong | Russell | Russell | On Denoting | On Denoting | Theory of Objects | Theory of Objects | Brentano | Brentano | Husserl | Husserl | Wittgenstein | Wittgenstein | Tractatus | Tractatus | Moore | Moore | Principia Ethica | Principia Ethica | intrinsic value | intrinsic value | common sense | common sense | Ayer | Ayer | language | language | truth | truth | logic | logic | Ryle | Ryle | concept of mind | concept of mind | Austin | Austin | Sense and Sensibilia | Sense and Sensibilia | Foundations of Empirical Knowledge | Foundations of Empirical Knowledge | analytic philosophy | analytic philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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s Argument Concerning Induction

Description

Part 3.1. Briefly introduces the problem of induction: that is, the problem that it is difficult to justify claims to knowledge of the world through pure reason, i.e. without experience. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

knowledge | philosophy | experience | truth | induction | hume | knowledge | philosophy | experience | truth | induction | hume

License

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s Famous Argument

Description

Part 3.2. Responses to and justifications of Hume's argument concerning the problem of induction. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

knowledge | philosophy | reichenbach | experience | reason | truth | mellor | strawson | induction | hume | knowledge | philosophy | reichenbach | experience | reason | truth | mellor | strawson | induction | hume

License

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4.3 Cartesian Dualism

Description

Part 4.3. Introduces Descartes' idea of dualism, that there is a separation between the mind and the body, as well as some of the philosophical issues surrounding this idea. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

dualism | body | scepticism | descartes | knowledge | meditations | philosophy | mind | truth | skepticism | dualism | body | scepticism | descartes | knowledge | meditations | philosophy | mind | truth | skepticism

License

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4.4 The Mind-Body Problem

Description

Part 4.4. Looks at some of the modern responses to Cartesian Dualism including Gilbert Ryle's and G. Strawson's responses to the idea. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

dualism | body | scepticism | descartes | knowledge | philosophy | mind | ryle | truth | skepticism | strawson | dualism | body | scepticism | descartes | knowledge | philosophy | mind | ryle | truth | skepticism | strawson

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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5.3 Gettier and Other Complications

Description

Part 5.3. The difference between internalist and externalist accounts of knowledge; whether we need external factors to justify knowledge or whether internal accounts are sufficient, and the Gettier cases. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

epistemology | belief | gettier | philosophy | truth | knowledge | epistemology | belief | gettier | philosophy | truth | knowledge

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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5.4 Scepticism, Externalism and the Ethics of Belief

Description

Part 5.4. Looks at the role the concept of knowledge plays in life, the different levels of knowledge we require in certain contexts and the return of scepticism over knowledge. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

epistemology | descartes | knowledge | gettier | philosophy | belief | truth | moore | putnam | epistemology | descartes | knowledge | gettier | philosophy | belief | truth | moore | putnam

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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ES.2H3 Ancient Philosophy and Mathematics (MIT)

Description

Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.

Subjects

mathematics | geometry | history | philosophy | Greek philosophy | Plato | Euclid | Aristotle | Rene Descartes | Nicomachus | Francis Bacon | number | irrational number | ratio | ethics | logos | logic | ancient knowing | modern knowing | Greek conception of number | idea of number | courage | justice | pursuit of truth | truth as a surd

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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24.900 Introduction to Linguistics (MIT) 24.900 Introduction to Linguistics (MIT)

Description

This course studies what is language and what does knowledge of a language consist of. It asks how do children learn languages and is language unique to humans; why are there many languages; how do languages change; is any language or dialect superior to another; and how are speech and writing related. Context for these and similar questions is provided by basic examination of internal organization of sentences, words, and sound systems. No prior training in linguistics is assumed. This course studies what is language and what does knowledge of a language consist of. It asks how do children learn languages and is language unique to humans; why are there many languages; how do languages change; is any language or dialect superior to another; and how are speech and writing related. Context for these and similar questions is provided by basic examination of internal organization of sentences, words, and sound systems. No prior training in linguistics is assumed.

Subjects

language | language | linguistics | linguistics | syntax | syntax | phonetics | phonetics | consonants | consonants | vowels | vowels | McGurk effect | McGurk effect | phonology | phonology | phoneme | phoneme | allophone | allophone | lexicon | lexicon | affixes | affixes | topicalization | topicalization | pronunciation | pronunciation | semantics | semantics | truth conditions | truth conditions | synchronic | synchronic | diachronic | diachronic | language families | language families | Ebonics | Ebonics | dialect | dialect

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.251 Introduction to Philosophy of Language (MIT) 24.251 Introduction to Philosophy of Language (MIT)

Description

This course explores the nature of meaning and truth, and their bearing on the use of language in communication. No knowledge of logic or linguistics is presupposed. This course explores the nature of meaning and truth, and their bearing on the use of language in communication. No knowledge of logic or linguistics is presupposed.

Subjects

Meaning and reference | Meaning and reference | empiricist theories | empiricist theories | psychological theories | psychological theories | truth-conditional theories | truth-conditional theories | pretense and attitude ascriptions | pretense and attitude ascriptions | hidden indexical theory | hidden indexical theory | implicature theory | implicature theory | pragmatic theory | pragmatic theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.729 Topics in Philosophy of Language: Modeling Representation (MIT) 24.729 Topics in Philosophy of Language: Modeling Representation (MIT)

Description

The seminar will be devoted to understanding what we're up to when we ascribe contents to a person's assertions and mental attitudes. We seek to make clear the rules of the game for the philosophy of language. We'll survey classic discussions of the issue by Field, Lewis and Stalnaker. But much of the emphasis of the class will be on getting clear about the limitations of our theoretical tools. I'd like to focus on places where our theorizing runs into trouble, or breaks down altogether. The seminar will be devoted to understanding what we're up to when we ascribe contents to a person's assertions and mental attitudes. We seek to make clear the rules of the game for the philosophy of language. We'll survey classic discussions of the issue by Field, Lewis and Stalnaker. But much of the emphasis of the class will be on getting clear about the limitations of our theoretical tools. I'd like to focus on places where our theorizing runs into trouble, or breaks down altogether.

Subjects

radical interpretation | radical interpretation | mathematical truth | mathematical truth | self-location | self-location | degrees of belief | degrees of belief | incoherent belief | incoherent belief | language of thought | language of thought | representation system | representation system | modeling representation | modeling representation | intentionality | intentionality | philosophy of language | philosophy of language | Putnam's paradox | Putnam's paradox | semantics | semantics | logical omniscience | logical omniscience | epistemology | epistemology | knowledge argument | knowledge argument

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Edith T.A. Gracie (LOC) Edith T.A. Gracie (LOC)

Description

Subjects

washingtondc | washingtondc | gracie | gracie | adams | adams | worldwari | worldwari | libraryofcongress | libraryofcongress | titanic | titanic | pneumonia | pneumonia | graciemansion | graciemansion | débutantes | débutantes | longislandnewyork | longislandnewyork | adamschewinggum | adamschewinggum | 77thdivision | 77thdivision | dunbaradams | dunbaradams | edithtgracie | edithtgracie | edithtemplegracie | edithtemplegracie | captaindunbaradams | captaindunbaradams | dunbarburchelladams | dunbarburchelladams | colonelarchibaldgracieiv | colonelarchibaldgracieiv | constanceelisegracie | constanceelisegracie | constanceeliseschack | constanceeliseschack | johndunbaradams | johndunbaradams | susanburchelladams | susanburchelladams | thetruthaboutthetitanic’ | thetruthaboutthetitanic’ | titanicasurvivorsstory’ | titanicasurvivorsstory’

License

No known copyright restrictions

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24.729 Topics in Philosophy of Language: Vagueness (MIT) 24.729 Topics in Philosophy of Language: Vagueness (MIT)

Description

The objective of the graduate-level course is to give people a sense of what "accounting for vagueness" is all about, why it's hard, and why it's important. This will involve surveying some prominent accounts of vagueness. The objective of the graduate-level course is to give people a sense of what "accounting for vagueness" is all about, why it's hard, and why it's important. This will involve surveying some prominent accounts of vagueness.

Subjects

vagueness | vagueness | sorites paradox | sorites paradox | truth | truth | supervaluationism | supervaluationism | epistemicism | epistemicism | contextualism | contextualism | nihilism | nihilism | relativism | relativism | logical revisionism | logical revisionism | interdeterminacy | interdeterminacy | language | language | inexact knowledge | inexact knowledge | logic | logic

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.251 Introduction to Philosophy of Language (MIT) 24.251 Introduction to Philosophy of Language (MIT)

Description

In this introductory course on the philosophy of language, we examine views on the nature of meaning, reference, truth, and their relationships. Other topics may include relationships between language and logic, language and knowledge, language and reality, language and acts performed through its use. No knowledge of logic or linguistics presupposed. In this introductory course on the philosophy of language, we examine views on the nature of meaning, reference, truth, and their relationships. Other topics may include relationships between language and logic, language and knowledge, language and reality, language and acts performed through its use. No knowledge of logic or linguistics presupposed.

Subjects

philosophy of language | philosophy of language | nature of meaning | nature of meaning | nature of reference | nature of reference | nature of truth | nature of truth | language and logic | language and logic | language and knowledge | language and knowledge | language and reality | language and reality | language and acts performed through its use | language and acts performed through its use

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.241 Logic I (MIT) 24.241 Logic I (MIT)

Description

This course provides an introduction to the aims and techniques of formal logic. Logic is the science of correct argument, and our study of logic will aim to understand what makes a correct argument good, that is, what is it about the structure of a correct argument that guarantees that, if the premises are all true, the conclusion will be true as well? Our subject (though, to be sure, we can only scratch the surface) will be truth and proof, and the connection between them. This course provides an introduction to the aims and techniques of formal logic. Logic is the science of correct argument, and our study of logic will aim to understand what makes a correct argument good, that is, what is it about the structure of a correct argument that guarantees that, if the premises are all true, the conclusion will be true as well? Our subject (though, to be sure, we can only scratch the surface) will be truth and proof, and the connection between them.

Subjects

techniques of formal logic | techniques of formal logic | truth functions | truth functions | quantifiers | quantifiers | validity | validity | formal deduction | formal deduction | logic applications | logic applications | philosophy | philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.251 Introduction to Philosophy of Language (MIT) 24.251 Introduction to Philosophy of Language (MIT)

Description

This course is an introduction to the philosophy of language. It examines different views on the nature of meaning, truth and reference, with special focus on the problem of understanding how linguistic communication works. This course is an introduction to the philosophy of language. It examines different views on the nature of meaning, truth and reference, with special focus on the problem of understanding how linguistic communication works.

Subjects

nature of meaning | reference | truth | and their relationships | nature of meaning | reference | truth | and their relationships | relationships between language and logic | language and knowledge | language and reality | language and acts performed through its use | relationships between language and logic | language and knowledge | language and reality | language and acts performed through its use | logic | logic | linguistics | linguistics | language | language | philosophy | philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.242 Logic II (MIT) 24.242 Logic II (MIT)

Description

This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt Gödel's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt Gödel's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus;

Subjects

Logic | Logic | theory of computability | theory of computability | Kurt G?del | Kurt G?del | theorem | theorem | system | system | true | true | arithmetical | arithmetical | statements | statements | axiomatic basis | axiomatic basis | proving | proving | truths of arithmetic | truths of arithmetic | history applications | history applications | technique | technique | Church?s theorem | Church?s theorem | algorithm | algorithm | formula | formula | valid | valid | predicate calculus | predicate calculus | Tarski?s theorem | Tarski?s theorem | G?del?s second incompleteness theorem. | G?del?s second incompleteness theorem.

License

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24.03 Relativism, Reason, and Reality (MIT) 24.03 Relativism, Reason, and Reality (MIT)

Description

Are moral standards relative to cultures and/or moral frameworks? Are there incompatible or non-comparable ways of thinking about the world that are somehow equally good? Is science getting closer to the truth? Is rationality--the notion of a good reason to believe something--relative to cultural norms? What are selves? Is there a coherent form of relativism about the self? Guided by the writings of Thomas Kuhn, Gilbert Harman, Judith Thomson, John Perry and Derek Parfit, we attempt to make these vague questions precise, and we make a start at answering them. Are moral standards relative to cultures and/or moral frameworks? Are there incompatible or non-comparable ways of thinking about the world that are somehow equally good? Is science getting closer to the truth? Is rationality--the notion of a good reason to believe something--relative to cultural norms? What are selves? Is there a coherent form of relativism about the self? Guided by the writings of Thomas Kuhn, Gilbert Harman, Judith Thomson, John Perry and Derek Parfit, we attempt to make these vague questions precise, and we make a start at answering them.

Subjects

relativism | relativism | moral standards | moral standards | science | science | truth | truth | rationality | rationality | cultural norms | cultural norms | Thomas Kuhn | Thomas Kuhn | Karl Popper | Karl Popper | Gilbert Harman | Gilbert Harman | Judith Thomson | Judith Thomson | Derek Parfit | Derek Parfit

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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21W.749 Documentary Photography and Photo Journalism: Still Images of A World In Motion (MIT) 21W.749 Documentary Photography and Photo Journalism: Still Images of A World In Motion (MIT)

Description

Documentary Photography and Photojournalism: Still Images of A World In Motion exposes students to the work of a number of great documentary photographers and photojournalists, as well as to writing about the documentary tradition. Students work throughout the term on a photo documentary project of their own, attempting to reduce a tiny area of the moving world to a set of still images that convey what the viewer needs to know about what they saw - without hearing the sounds, smelling the odors, experiencing what was happening outside the viewfinder, and without seeing the motion. Students also write papers about the subjects of their photo documentaries. Documentary Photography and Photojournalism: Still Images of A World In Motion exposes students to the work of a number of great documentary photographers and photojournalists, as well as to writing about the documentary tradition. Students work throughout the term on a photo documentary project of their own, attempting to reduce a tiny area of the moving world to a set of still images that convey what the viewer needs to know about what they saw - without hearing the sounds, smelling the odors, experiencing what was happening outside the viewfinder, and without seeing the motion. Students also write papers about the subjects of their photo documentaries.

Subjects

Photography | Photography | Photojournalism | Photojournalism | Writing | Writing | Journalism | Journalism | Documentary | Documentary | News | News | Image | Image | Photo | Photo | Camera | Camera | Picture | Picture | Newspaper | Newspaper | Magazine | Magazine | documentary photography | documentary photography | photojournalism | photojournalism | Susan Sontag | Susan Sontag | Robert Coles | Robert Coles | Ken Light | Ken Light | Eugene Richards | Eugene Richards | Sebastian Salgado | Sebastian Salgado | still images | still images | documentary photographers | documentary photographers | photojournalists | photojournalists | slides | slides | photographs | photographs | photo project | photo project | contact sheets | contact sheets | objectivity | objectivity | myth | myth | reality | reality | truth | truth | reporters | reporters | voyeurs | voyeurs

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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