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More Precisely: The Math You Need to Do Philosophy
More Precisely provides a rigorous and engaging introduction to the mathematics necessary to do philosophy. It is impossible to fully understand much of the most important work in contemporary philosophy without a basic grasp of set theory, functions, probability, modality and infinity. Until now, this knowledge was difficult to acquire. Professors had to provide custom handouts to their classes, while students struggled through math texts searching for insight. More Precisely fills this key gap.
Eric Steinhart provides lucid explanations of the basic mathematical concepts and sets out most commonly used notational conventions. Furthermore, he demonstrates how mathematics applies to many fundamental issues in branches of philosophy such as metaphysics, philosophy of language, epistemology, and ethics.
Eric Steinhart provides lucid explanations of the basic mathematical concepts and sets out most commonly used notational conventions. Furthermore, he demonstrates how mathematics applies to many fundamental issues in branches of philosophy such as metaphysics, philosophy of language, epistemology, and ethics.
208 pages, Paperback
First published January 29, 2009
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523 people want to read
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Displaying 1 - 7 of 7 reviews
April 24, 2014
I'm too tired (and too busy) for a proper review right now. All I'll say is that this is a great overview of some of the formal tools needed to understand philosophical issues: set theory, infinity, Turing machines and computability, formal semantics, probability theory. It's not a book on philosophical issues, it's a book on math and logic that is motivated by philosophical issues. The attempt is not to tackle these philosophical issues themselves, but rather to present the purely formal mathematical (not philosophical) tools needed to understand the debates going on regarding the philosophical issues. It's a sort of "mathematics for philosophers" book, and a very good one.
May 30, 2014
An easy and straightforward introduction into some of the most important formal tools in philosophy, including set theory, semantics, probability, and transfinite mathematics.
April 1, 2020
Pretty good book. Suitable for raw beginners. High school or first year college,
or the equivalent thereof. Excellent book for you. But an idle read for anyone else.
Very elementary - but doesn't pretend to be otherwise. The math content
is no more than high school level for the most part. I might have hoped for
just a bit more depth than that. And many of the harder more interesting questions
are barely touched on and then rapidly withdraw from.
A bit unbalanced too. The treatment of utilitarianism is tediously thorough whilst
some of the later discussions on infinity though pretty good are a bit rushed.
I don't think anyone who didn't know it already could learn much if this was
their first exposure to the concepts. And that's the criterion for an excellent
book that actually teaches. Isn't it? You can't just chronicle what you know.
In the interests of 'more precision' I have to add you just can't define a set using
a construction such as {x | condition on x }. You just can't. It's just too loose.
Made my hair stand on end. It leads quickly to nonsense as was
discovered very early on. You have to use {x in A | condition on x } where A is
a known set. (see specification axiom et al). I am certain the author knows
this. I think it was a mistake not to include it.
or the equivalent thereof. Excellent book for you. But an idle read for anyone else.
Very elementary - but doesn't pretend to be otherwise. The math content
is no more than high school level for the most part. I might have hoped for
just a bit more depth than that. And many of the harder more interesting questions
are barely touched on and then rapidly withdraw from.
A bit unbalanced too. The treatment of utilitarianism is tediously thorough whilst
some of the later discussions on infinity though pretty good are a bit rushed.
I don't think anyone who didn't know it already could learn much if this was
their first exposure to the concepts. And that's the criterion for an excellent
book that actually teaches. Isn't it? You can't just chronicle what you know.
In the interests of 'more precision' I have to add you just can't define a set using
a construction such as {x | condition on x }. You just can't. It's just too loose.
Made my hair stand on end. It leads quickly to nonsense as was
discovered very early on. You have to use {x in A | condition on x } where A is
a known set. (see specification axiom et al). I am certain the author knows
this. I think it was a mistake not to include it.
June 9, 2018
4*5
theo analytic thì lúc đầu học đóng toán hơi khổ tí, nhưng sau đỡ mất công suy nghĩ =))
theo analytic thì lúc đầu học đóng toán hơi khổ tí, nhưng sau đỡ mất công suy nghĩ =))
December 18, 2020
This is a pretty friendly introduction to set theory and its application in various areas that are studied in analytic philosophy. For instance, semantics, information theory, machines (although perhaps not objects of study in their own right, machines are formal entities employed in areas such as philosophy of mind), act-utilitarian calculus, and decision/game theory. For someone not learned in mathematics, I strongly recommend it to anyone who is interested in the more technical areas of philosophy but lacks the mathematical background.
Want to read
February 11, 2020Philosophical methodology, then:
Stanford Encyclopedia of Philosophy (http://plato.stanford.edu)
-Metaphysics: Identity over time, Free Will, Mereology, Nominalism, Essentialism, Essential vs. Accidental Properties, Transworld Identity, The Metaphysics of Causation, Intrinsic vs Extrinsic Properties, Events, Types and Tokens, Supervenience, Possible Objects, Possible Worlds, Actualism, Impossible Worlds, States of Affaires, Modal Fictionalism, David Lewis’s Metaphysics, Location and Mereology, Truth, Temporal Parts, Personal Identity, The problem of the many.
-Epistemology: Naturalized Epistemology, Social Epistemology, Virtue Epistemology, Formal Epistemology, Foundationalist Theories of Epistemic Justification, Coherentist Theories of Epistemic Justification, The Analysis of Knowledge, Reliabilism, The Ethics of Belief, Evidence, Epistemic Contextualism, Epistemic Paradoxes, Epistemic Basing Relation, Internalistic vs Externalistic Conceptions of Justification, Epistemic Closure Principle.
-Mind: Externalism about mental content, The Mind/Brain Identity Theory, Consciousness, Functionalism, Teleological Theories of Mental Content, Intentionality, Mental Causation, Causal Theories of Mental Content, Representational theories of Consciousness, Consciousness: Higher Order theories, Qualia, Qualia: The knowledge argument, Connectionism, The Language of Thought Hypothesis, Anomalous Monism. Zombies, Collective Intentionality, The Chinese Room Argument, Behaviorism, Dualism.
-Science: Scientific Realism, Abduction, Constructive Empiricism, Models in Science, Scientific Progress, Structural Realism, Science and Pseudo-Science, Induction, Historicist Theories of Scientific Rationality, The Incommensurability of Scientific Theories, Scientific Progress, Scientific Explanation, Underdetermination of Scientific Theory, Scientific Reduction.
-Language: Philosophy of Linguistics, Reference, Rigid Designators, Theories of Meaning, Meaning Holism, Pragmatics, Two-dimensional Semantics, Descriptions, Convention, Anaphora, Logical Form, Non-existent objects, Metaphor, Indexicals, Propositions, Tense and Aspect, Innateness and Language.
-Math: Naturalism in the Philosophy of Mathematics, Abstract Objects, Ontological Commitment, Formalism, Explanation in Mathematics, Constructive Mathematics, Philosophy of Mathematics, Fictionalism in the Philosophy of Mathematics, Set Theory, Continuum Hypothesis, Indispensability arguments, Frege’s Theorem and Foundations for Arithmetic, Principia Mathematica, Philosophy of Probability
-Logic: Classical Logic, Logical Consequence, Modal Logic, Free Logic, Relevance Logic, Intuitionistic Logic, Deontic Logic, Informal Logic, Temporal Logic, Inductive Logic, Many Valued Logic, Paraconsistent Logic, Logic and Artificial Intelligence, Non-Monotonic Logic, Dialtheism, Logical Pluralism, Epistemic Logic, The Logic of Conditionals, Quantifiers and Quantification.
-History of Philosophy: Gottlob Frege, Paul Grice, Bertrand Russell, David K. Lewis, Willard van Orman Quine, Wilfrid Sellars, Ludwig Wittgenstein, Vienna Circle, Rufolf Carnap (in construction), Karl Popper, Charles Sanders Peirce, Richard Rorty, Donald Davidson, George Edward Moore, John Langshaw Austin, Gilbert Ryle, Thomas Kuhn.
Stanford Encyclopedia of Philosophy (http://plato.stanford.edu)
-Metaphysics: Identity over time, Free Will, Mereology, Nominalism, Essentialism, Essential vs. Accidental Properties, Transworld Identity, The Metaphysics of Causation, Intrinsic vs Extrinsic Properties, Events, Types and Tokens, Supervenience, Possible Objects, Possible Worlds, Actualism, Impossible Worlds, States of Affaires, Modal Fictionalism, David Lewis’s Metaphysics, Location and Mereology, Truth, Temporal Parts, Personal Identity, The problem of the many.
-Epistemology: Naturalized Epistemology, Social Epistemology, Virtue Epistemology, Formal Epistemology, Foundationalist Theories of Epistemic Justification, Coherentist Theories of Epistemic Justification, The Analysis of Knowledge, Reliabilism, The Ethics of Belief, Evidence, Epistemic Contextualism, Epistemic Paradoxes, Epistemic Basing Relation, Internalistic vs Externalistic Conceptions of Justification, Epistemic Closure Principle.
-Mind: Externalism about mental content, The Mind/Brain Identity Theory, Consciousness, Functionalism, Teleological Theories of Mental Content, Intentionality, Mental Causation, Causal Theories of Mental Content, Representational theories of Consciousness, Consciousness: Higher Order theories, Qualia, Qualia: The knowledge argument, Connectionism, The Language of Thought Hypothesis, Anomalous Monism. Zombies, Collective Intentionality, The Chinese Room Argument, Behaviorism, Dualism.
-Science: Scientific Realism, Abduction, Constructive Empiricism, Models in Science, Scientific Progress, Structural Realism, Science and Pseudo-Science, Induction, Historicist Theories of Scientific Rationality, The Incommensurability of Scientific Theories, Scientific Progress, Scientific Explanation, Underdetermination of Scientific Theory, Scientific Reduction.
-Language: Philosophy of Linguistics, Reference, Rigid Designators, Theories of Meaning, Meaning Holism, Pragmatics, Two-dimensional Semantics, Descriptions, Convention, Anaphora, Logical Form, Non-existent objects, Metaphor, Indexicals, Propositions, Tense and Aspect, Innateness and Language.
-Math: Naturalism in the Philosophy of Mathematics, Abstract Objects, Ontological Commitment, Formalism, Explanation in Mathematics, Constructive Mathematics, Philosophy of Mathematics, Fictionalism in the Philosophy of Mathematics, Set Theory, Continuum Hypothesis, Indispensability arguments, Frege’s Theorem and Foundations for Arithmetic, Principia Mathematica, Philosophy of Probability
-Logic: Classical Logic, Logical Consequence, Modal Logic, Free Logic, Relevance Logic, Intuitionistic Logic, Deontic Logic, Informal Logic, Temporal Logic, Inductive Logic, Many Valued Logic, Paraconsistent Logic, Logic and Artificial Intelligence, Non-Monotonic Logic, Dialtheism, Logical Pluralism, Epistemic Logic, The Logic of Conditionals, Quantifiers and Quantification.
-History of Philosophy: Gottlob Frege, Paul Grice, Bertrand Russell, David K. Lewis, Willard van Orman Quine, Wilfrid Sellars, Ludwig Wittgenstein, Vienna Circle, Rufolf Carnap (in construction), Karl Popper, Charles Sanders Peirce, Richard Rorty, Donald Davidson, George Edward Moore, John Langshaw Austin, Gilbert Ryle, Thomas Kuhn.
May 25, 2024
Excellent book that covers many areas of mathematics relevant to philosophy in a very accessible way. Some of the explanations in here, presumably because they were written for a broader audience, are simply brilliant. Steinhart has done a wonderful job. There are no faults with this book, it does what it says in the title.
Displaying 1 - 7 of 7 reviews