What was Wittgenstein’s argument against Cantor’s transfinite numbers and where did he make his objection?

What was Ludwig Wittgenstein famous for?

Ludwig Josef Johann Wittgenstein (/ˈvɪtɡənʃtaɪn, -staɪn/ VIT-gən-s(h)tyne; German: [ˈluːtvɪç ˈjoːzɛf ‘joːhan ˈvɪtɡn̩ʃtaɪn]; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.

What did Wittgenstein say about language?

Wittgenstein, who lived from 1889 to 1951, is most famous for a handful of oracular pronouncements: “The limits of language are the limits of my world.” “Whereof one cannot speak, thereof one must be silent.” “The human body is the best picture of the human soul.” They sound great; they are also hopelessly mysterious …

Was Wittgenstein a Finitist?

Given Wittgenstein’s rejection of infinite mathematical extensions, he adopts finitistic, constructive views on mathematical quantification, mathematical decidability, the nature of real numbers, and Cantor’s diagonal proof of the existence of infinite sets of greater cardinalities.

Was Wittgenstein a mathematician?

Ludwig Wittgenstein considered his chief contribution to be in the philosophy of mathematics, a topic to which he devoted much of his work between 1929 and 1944.

What is Wittgenstein’s point in the rule following discussion?

the answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. and so there would be neither accord nor conflict here.

What is Wittgenstein’s picture theory of meaning?

Wittgenstein claims there is an unbridgeable gap between what can be expressed in language and what can only be expressed in non-verbal ways. The picture theory of meaning states that statements are meaningful if, and only if, they can be defined or pictured in the real world.

Did Wittgenstein believe in God?

Not everyone who is not religious construes the difference between the believer and the non-believer as “believing the opposite”. The philosopher Ludwig Wittgenstein did not hold religious beliefs.

What is the theory of logical atomism?

Metaphysically, logical atomism is the view that the world consists in a plurality of independent and discrete entities, which by coming together form facts. According to Russell, a fact is a kind of complex, and depends for its existence on the simpler entities making it up.

What is an object Wittgenstein?

What does it mean to say that an object is simple? One thing Wittgenstein seems to mean is that it cannot be analyzed as a complex of other objects. This seems to indicate that if objects are simple, they cannot have any parts; for, if they did, they would be analyzable as a complex of those parts.

What is proposition according to Wittgenstein?

Although something need not be a proposition to represent something in the world, Wittgenstein was largely concerned with the way propositions function as representations. According to the theory, propositions can “picture” the world as being a certain way, and thus accurately represent it either truly or falsely.

What does Wittgenstein mean by atomic facts?

According to Russell, an atomic fact consists of at least one simple object (sense datum) and at least one universal. Here, Wittgenstein claims that atomic facts consist of objects. There is no mention of properties (universals). At the fundamental level, it would seem, we have just objects—no properties.

What is World According to Wittgenstein?

The world has always been a limiting concept in Wittgenstein’s. philosophy. According to him, the world as reality presents itself to us as. an unquestioned and necessary experiential fact. All of us believe in the.

What is the necessity for introducing names according to Wittgenstein in Tractatus?

The theory of naming in the Tractatus.

Wittgenstein postulates the existence of simple objects as references for the names so as to guarantee the reference and meaningfulness of language. It is essential to names that they are not analyzable any further, that they are indefinible.

Which philosophical doctrine is fundamental to logical positivism?


According to logical positivism, there are only two sources of knowledge: logical reasoning and empirical experience. The former is analytic a priori, while the latter is synthetic a posteriori; hence synthetic a priori does not exist.

Was Wittgenstein a logical positivism?

Logical Positivism was a theory developed in the 1920s by the ‘Vienna Circle’, a group of philosophers centred (unsurprisingly) in Vienna. Its formulation was entirely driven by Wittgenstein’s Tractatus, which dominated analytical philosophy in the 1920s and 30s.

What was the main argument of logical positivism in the twentieth century?

logical positivism, also called logical empiricism, a philosophical movement that arose in Vienna in the 1920s and was characterized by the view that scientific knowledge is the only kind of factual knowledge and that all traditional metaphysical doctrines are to be rejected as meaningless.

What are the criticisms of the logical positivism?

The nature of knowledge is different, hence, the tools to verify the knowledge are different. First, this paradigm overstated the notion of verification. Second, it failed to take into account that there are spheres which may not be proven in a scientific way. Science has a better alternative position.

Why is positivism Criticised?

The first – and perhaps most fundamental – flaw of positivism is its claim to certainty. As Crotty says, ‘articulating scientific knowledge is one thing; claiming that scientific knowledge is utterly objective and that only scientific knowledge is valid, certain and accurate is another’.

What is the main criticism of positivism philosophy?

Historically, positivism has been criticized for its reductionism, i.e., for contending that all “processes are reducible to physiological, physical or chemical events,” “social processes are reducible to relationships between and actions of individuals,” and that “biological organisms are reducible to physical systems …