"Wittgensteinian themes: essays, 1978-1989" by Norman Malcolm,Georg Henrik Wright,1959

His works include:
Ludwig Wittgenstein: A Memoir
Moore and Ordinary Language
Wittgenstein: A Religious Point Of View?
Nothing Is Hidden: Wittgenstein's criticism of his early thought
Problems of Mind: Descartes to Wittgenstein
Knowledge and Certainty
Consciousness and Causality (with D. M. Armstrong)
Memory and Mind
Dreaming and Skepticism
Wittgenstein: The Relation of Language to Instinctive Behaviour
Thought and knowledge
Wittgensteinian themes (edited by Georg Henrik von Wright) and Dreaming.
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In 1949, Wittgenstein was a guest of the Malcolms in Ithaca, New York. In that year Malcolm introduced O.K. Bouwsma to Wittgenstein. Bouwsma remained close to Wittgenstein until Wittgenstein's death in 1951.
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In 1959, his book Dreaming was published,
in which he elaborated on Wittgenstein's question as to whether it really mattered if people who tell dreams "really had these images while they slept, or whether it merely seems so to them on waking".
This work was also a response to Descartes' Meditations.
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Other than that he is known for propagating the view that common sense philosophy and ordinary language philosophy are the same.
He was generally supportive of Moore's theory of knowledge and certitude, though he found Moore's style and method of arguing to be ineffective.
His critique of Moore's articles on skepticism (and also on Moore's 'Here is a hand' argument) lay the foundation for the renewed interest in common sense philosophy and ordinary language philosophy.
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Malcolm was also a defender of a modal version of the ontological argument.
In 1960 he argued that the argument originally presented by Anselm of Canterbury in the second chapter of his Proslogion was just an inferior version of the argument propounded in chapter three.
His argument is similar to those produced by Charles Hartshorne and Alvin Plantinga.
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Analytic Philosophy

Analytic Philosophy

To analyse means to break something down into its constituent parts.
Analytic philosophy attempts to clarify, by analysis, the meaning of statements and concepts. Analytic philosophy has been important in the in the English speaking academic world since the beginning of the 20th century.

Following Kant a split occurred between Anglo-American academic philosophy and the philosophy practised on the European continent. 'Continental' philosophy took off in an Idealist direction with Hegel, took an existentialist turn via Nietzsche and Heidegger and entered a less certain phase with post-structuralism.

Analytic philosophers on the other hand, saw the German philosopher Gottlob Frege (1848-1925) as the most important thinker since Kant.

Frege wanted to put a rigorous logic at the heart of philosophy.
He was influential in the philosophy of mathematics, logic and language. He thought that the basis for mathematics could be securely derived from logic and that a rigorous analysis of the underlying logic of sentences would enable us to judge their truth-value.

The British philosopher Bertrand Russell (1872-1970)
combined Frege's logical insights with the influence of David Hume's empiricism. Russell thought that the world was composed of 'atomic facts'. Sentences, if they were to be meaningful, had to correspond to these atomic facts. Ludwig Wittgenstein (1889-1951) studied under Russell, his early ideas influenced the Vienna Circle and help form the logical positivism of the 1920's and 30's.

There is a radical break between the early and the later works of Wittgenstein.

In his earlier work Wittgenstein saw language as picturing the world, in his later philosophy he understands language by using the metaphor of a game. This change in direction spurred the development of 'Linguistic philosophy', in the mid 20th century. Linguistic philosophers such as Gilbert Ryle (1900-76) thought many of the traditional problems of philosophy could be dissolved by the careful study of language as it is used.

By the 1970's there was a growing dissatisfaction with linguistic philosophy, and philosophers began to show more interest in the philosophy of mind and the application of philosophical methods to wider issues in politics, ethics and the nature of philosophy itself. Richard Rorty (1931-) has used the methods of analytic philosophy to deconstruct its assumptions. Rorty is influenced as much by Heidegger as he is by Wittgenstein, and his approach echoes the ideas of the post-structuralists. It may be that the future will see the concerns of 'analytic' and 'continental' philosophies converge.

Bertrand Russell: Logical Atomism

Bertrand Russell (1872-1970) began his philosophical career as an Idealist, but was converted by G E Moore (1873-1958) to a common sense empiricism. He worked with A N Whitehead (1861-1947) on the philosophy of mathematics, where, like Frege, he attempted to show how mathematics could be derived from logic. His work in logic led him to examine language. Russell thought that the grammar of ordinary language was misleading. He thought that the world was composed of atomic facts, and that propositions, if true, would correspond to these atomic facts. One of the tasks of philosophy was to analyse propositions to reveal their 'proper logical form'.

Russell thought that terms such as 'the average man' could lead to confusion. In the sentence, 'The average woman has 2.6 children'; the term 'average woman' should be understood as a logical construction. The term is not an atomic fact but a complex mathematical statement relating the numbers of children to the numbers of women. Russell thought that terms like 'the State' and 'Public Opinion' were also logical constructions and that philosophers were mistaken in treating these concepts as though they really existed.

Ludwig Wittgenstein (1889-1951): Tractatus

Wittgenstein came to study under Russell in 1912 and contributed to the theory of logical atomism. His Tractatus Logico-Philosophicus was published in 1921. In the Tractatus Wittgenstein put forward the picture theory of meaning. A picture may mirror reality by showing objects and arrangements of objects. Wittgenstein argued that sentences, if they are to mean anything, must mirror reality in the same way that a picture does. Sentences contain names that refer to objects or states of affairs in the world. Like Russell, Wittgenstein thought that the surface grammar of statements disguised their logical form. Through analysis a true statement would be shown to consist in elementary particles which pictured the world and logical constants such as 'if', 'not', 'and' and 'or'. A sentence, which did not picture the world, was devoid of meaning.

If only statements which picture the world, i.e. statements about facts, are meaningful then statements about ethics, religion and much of philosophy are not, strictly speaking, meaningful. This applies as much to Wittgenstein's ideas in the Tractatus as other philosophical ideas. As he says at the end of the Tractatus, "My propositions serve as elucidations in the following way: anyone who understands me eventually recognises them as nonsensical, when he has used them - as steps - to climb up beyond them. He must, so to speak, throw away the ladder after he has climbed up it."

The Vienna Circle: Logical Positivism

The Vienna Circle consisted of a group of philosophically minded scientists and logicians. Moritz Schlick (1882-1936) was the official leader; other members included Rudolf Carnap (1891-1970), Otto Neurath (1882-1945) and Kurt Gödel (1906-78). The Circle was heavily influenced by the work of Frege and Russell. Wittgenstein, although not a member of the group, discussed philosophy with Schlick and Carnap. The group was active from the mid 1920's. However, the combination of Schlick's assassination by a deranged student in 1936 and the growing hostility of the Nazis forced the Circle to disperse.

The logical positivism that the Circle practised can be seen as a development of Wittgenstein's Tractatus. Only verifiable statements were meaningful, as Schlick put it: "The meaning of a proposition is the method of its verification". Anything that was not empirically verifiable was meaningless. Statements about God, ethics, art and metaphysics, were, for the Circle, literally nonsense. This emphasis on positivism was a reaction against the romantic Idealism that had been influential in German philosophy. The role of philosophy was no longer to outline the self-awareness of Geist; rather it was seen as a handmaiden to science, content simply to clarify concepts.

Wittgenstein: Language Games

In the 1930's, Wittgenstein became critical of his earlier picture theory of meaning. In his latter work, he uses a tool metaphor for language: the meaning of a word is no longer it's relation to some atomic fact: the meaning of a word is in its use. We use language in a variety of ways, to talk about science, religion, art and so on. The latter Wittgenstein does not agree with the logical positivists that only scientific statements have meaning: science is only one way to talk about the world, only one 'language game'. A language game reflects a human activity, a form of life. As well as a scientific language game, we can participate in a religious language game, an aesthetic language game and many others. Words derive their meaning from the function they perform within the language game.

Words are no longer seen as having a particular essence, or to refer to a particular object. A word may have a variety of usages: what these different usages have in common Wittgenstein calls a 'family resemblance'. Members of a family bear a resemblance to each other, but no two members of a family (apart from identical twins) look exactly alike. The same is true for the use of words. The word 'game', for example, is used to talk about board games, card games, Olympic games, soccer games etc. These games do not hold one essential quality in common, rather there are overlapping and criss-crossing similarities.

Wittgenstein thought that philosophical problems arise when "language goes on holiday", that is, when we take a word and try to look at it in isolation from its language game. If we try to define the essence of beauty or knowledge, rather than seeing how these concepts are used in context, we will become confused. The job of philosophy for the latter Wittgenstein is therapeutic: "The philosopher's treatment of a question, is like the treatment of an illness". The "illness" in question is the bewitchment of intelligence by language.

The Private Language Argument

Since Wittgenstein's death there has been much discussion around Wittgenstein's assertion that there could not be a 'private language'. Philosophy since Descartes began from the assumption that the most secure knowledge is based on our private experience, indeed Descartes distinction between the mental and the material rests on this assumption. The British empiricist Hume also begins from the starting point of the certainty of the individual's private experience.

Wittgenstein sees language as a rule governed social activity. Wittgenstein thought that it was incomprehensible to imagine an individual creating their own private language. How would this person know if, when they used a word, that they were using it correctly? To rely on their own memory would be "as if someone were to buy several copies of the morning newspaper to assure himself that what it said was true." As this individual has no way of externally checking the way he is using a concept, he cannot be said to be using a language. If a private language is not possible then the rug has been pulled from under the feet of modern philosophy's Cartesian foundations. Meaning is no longer understood as private or individual, but as public and social. The individualistic first-person certainty which underlies both rationalist and empiricist approaches to philosophy is shown to be in error.

Richard Rorty: Philosophy and the Mirror of Nature

Richard Rorty (1931-) is an American philosopher who was trained in the analytic tradition. Unlike many of his contemporaries, he has been influenced as much by Sartre and Heidegger as by Wittgenstein. Rorty has been able to articulate the post-modern concerns of 'continental philosophy' in the language game of Anglo-American academia. Rorty argues that ever since Descartes' "invention of the mind" philosophy has attempted to provide rock solid foundations for our understanding of the World. Kant thought that we interpret the world through universal timeless categories. The distinction was made between a mirroring non-natural mind and a mirrored natural world. The purpose of philosophy was to expose the shape of this mirror.

For Rorty human understanding is not based some objective structure of 'mind'. Rather we interpret the world through a variety of paradigms. If there is no objective philosophical standpoint then the idea that philosophy should be seen as the "queen of sciences", clarifying what counts as knowledge, is unsustainable. For Rorty the aim of philosophers should be, "to help their readers, or society as a whole, break free from outworn vocabularies and attitudes, rather than to provide 'grounding' for the intuitions and customs of the present."

"The Parable of the Invisible Gardener" by John Wisdom,

John Wisdom was a leading British philosopher considered to be an ordinary language philosopher, a philosopher of mind and a metaphysician.

He was influenced by G.E. Moore, Ludwig Wittgenstein and Sigmund Freud, and in turn explained and extended their work.

Wisdom was for most of his career at Trinity College, Cambridge, and became Professor of Philosophy at Cambridge University. Near the end of his career he was Professor of Philosophy at the University of Oregon. He was president of the Aristotelian Society from 1950 to 1951.
His famous "Parable of the Invisible Gardener" is a profound dialectic on the existence or absence of God.

Major Writings
Interpretation and Analysis, (1931)
Other Minds, (1952)
Philosophy & PsychoAnalysis, (1953)
Paradox and Discovery, (1965)
Proof and Explanation (The Virginia Lectures 1957), (1991)
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The Parable of the Invisible Gardener is a tale told by John Wisdom. It is often used to illustrate the perceived differences between assertions based on faith and assertions based on scientific evidence, and the problems associated with unfalsifiable beliefs. The tale runs as follows:
"Two people return to their long neglected garden and find, among the weeds, that a few of the old plants are surprisingly vigorous. One says to the other, 'It must be that a gardener has been coming and doing something about these weeds.' The other disagrees and an argument ensues. They pitch their tents and set a watch. No gardener is ever seen. The believer wonders if there is an invisible gardener, so they patrol with bloodhounds but the bloodhounds never give a cry. Yet the believer remains unconvinced, and insists that the gardener is invisible, has no scent and gives no sound. The sceptic doesn't agree, and asks how a so-called invisible, intangible, elusive gardener differ from an imaginary gardener, or even no gardener at all."

"Logic and Knowledge" by Bertrand Russell,1956,

Russell's contributions to logic and the foundations of mathematics include his discovery of Russell's paradox, his defense of logicism (the view that mathematics is, in some significant sense, reducible to formal logic), his development of the theory of types, and his refining of the first-order predicate calculus.

Russell discovered the paradox that bears his name in 1901, while working on his Principles of Mathematics (1903). The paradox arises in connection with the set of all sets that are not members of themselves. Such a set, if it exists, will be a member of itself if and only if it is not a member of itself. The paradox is significant since, using classical logic, all sentences are entailed by a contradiction. Russell's discovery thus prompted a large amount of work in logic, set theory, and the philosophy and foundations of mathematics.

Russell's own response to the paradox came with the development of his theory of types in 1903. It was clear to Russell that some restrictions needed to be placed upon the original comprehension (or abstraction) axiom of naive set theory, the axiom that formalizes the intuition that any coherent condition may be used to determine a set (or class). Russell's basic idea was that reference to sets such as the set of all sets that are not members of themselves could be avoided by arranging all sentences into a hierarchy, beginning with sentences about individuals at the lowest level, sentences about sets of individuals at the next lowest level, sentences about sets of sets of individuals at the next lowest level, and so on. Using a vicious circle principle similar to that adopted by the mathematician Henri Poincaré, and his own so-called "no class" theory of classes, Russell was able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set," may not be applied to themselves since self-application would involve a vicious circle. On Russell's view, all objects for which a given condition (or predicate) holds must be at the same level or of the same "type."

Although first introduced in 1903, the theory of types was further developed by Russell in his 1908 article "Mathematical Logic as Based on the Theory of Types" and in the monumental work he co-authored with Alfred North Whitehead, Principia Mathematica (1910, 1912, 1913). Thus the theory admits of two versions, the "simple theory" of 1903 and the "ramified theory" of 1908. Both versions of the theory later came under attack for being both too weak and too strong. For some, the theory was too weak since it failed to resolve all of the known paradoxes. For others, it was too strong since it disallowed many mathematical definitions which, although consistent, violated the vicious circle principle. Russell's response was to introduce the axiom of reducibility, an axiom that lessened the vicious circle principle's scope of application, but which many people claimed was too ad hoc to be justified philosophically.

Of equal significance during this period was Russell's defense of logicism, the theory that mathematics was in some important sense reducible to logic. First defended in his 1901 article "Recent Work on the Principles of Mathematics," and then later in greater detail in his Principles of Mathematics and in Principia Mathematica, Russell's logicism consisted of two main theses. The first was that all mathematical truths can be translated into logical truths or, in other words, that the vocabulary of mathematics constitutes a proper subset of that of logic. The second was that all mathematical proofs can be recast as logical proofs or, in other words, that the theorems of mathematics constitute a proper subset of those of logic.

Like Gottlob Frege, Russell's basic idea for defending logicism was that numbers may be identified with classes of classes and that number-theoretic statements may be explained in terms of quantifiers and identity. Thus the number 1 would be identified with the class of all unit classes, the number 2 with the class of all two-membered classes, and so on. Statements such as "There are two books" would be recast as statements such as "There is a book, x, and there is a book, y, and x is not identical to y." It followed that number-theoretic operations could be explained in terms of set-theoretic operations such as intersection, union, and difference. In Principia Mathematica, Whitehead and Russell were able to provide many detailed derivations of major theorems in set theory, finite and transfinite arithmetic, and elementary measure theory. A fourth volume was planned but never completed.

Russell's most important writings relating to these topics include not only Principles of Mathematics (1903), "Mathematical Logic as Based on the Theory of Types" (1908), and Principia Mathematica (1910, 1912, 1913), but also his An Essay on the Foundations of Geometry (1897), and Introduction to Mathematical Philosophy (1919).