Wittgenstein Tentang Filsafat Logika dan Matematika

Summary

In this presentation, Adi Bedelil Sidkia explores Wittgenstein's shift in philosophy of logic and mathematics. He discusses Wittgenstein's early works, like *Tractatus Logico-Philosophicus*, and his later radical change in *Remarks on the Foundations of Mathematics*. Wittgenstein critiques formal logicism and emphasizes the role of language games and social practices in understanding logic and mathematics. He argues that mathematics is a cultural phenomenon, not just abstract calculation. Key topics include Wittgenstein’s critique of logicism, the nature of rule-following, and how logic and mathematics relate to everyday life and human practice.

Takeaways

• 😀 Wittgenstein was a 20th-century philosopher known for his work in logic and mathematics.
• 😀 His famous works include 'Tractatus Logico-Philosophicus' and 'Remarks on the Foundations of Mathematics.'
• 😀 Wittgenstein’s later philosophy represents a paradigm shift, focusing on the practical and human-centered understanding of logic and mathematics.
• 😀 Early in his career, he viewed philosophy and logic as tools for self-understanding, self-criticism, and clarity.
• 😀 Later, he emphasized 'language games' and rule-following, showing that logic and mathematics depend on social practices, not metaphysical truths.
• 😀 Mathematics is not merely calculation but a cultural and human phenomenon, reflecting everyday life.
• 😀 Wittgenstein criticized logicism (Frege and Russell), arguing that formal proofs are often too abstract, impractical, and disconnected from real-life application.
• 😀 Understanding and following mathematical rules come from social interactions and teaching, rather than from universal logical principles.
• 😀 Everyday examples, like explaining 5 + 7 = 12 using apples, are more intuitive and effective than long formal proofs.
• 😀 Wittgenstein’s later work, especially in 'Philosophical Investigations,' frames mathematics and logic as language games with rules grounded in human practice and daily life.
• 😀 The transition in his thought reflects a move from abstract, formal logic to practical, socially-informed logic and mathematics.
• 😀 His approach highlights that clarity and meaning in mathematics are tied to human practices, not absolute or abstract truths.

Q & A

Who is Ludwig Wittgenstein, and what is his contribution to the philosophy of logic and mathematics?

Ludwig Wittgenstein was a 20th-century philosopher known for his influential works in the philosophy of logic and mathematics. His major contributions include the 'Tractatus Logico-Philosophicus' and 'Remarks on the Foundations of Mathematics.' These works introduced a paradigm shift in understanding logic, language, and mathematics, emphasizing that logic and mathematics are not metaphysical truths but human practices shaped by social interaction.

What is the essence of Wittgenstein's philosophy of logic and mathematics?

Wittgenstein's philosophy revolves around the idea that the meaning of logic and mathematics is not based on universal, metaphysical truths but on human practices, language games, and rule-following. According to Wittgenstein, logic and mathematics are cultural phenomena, and their understanding depends on the social context in which they are applied.

What is Wittgenstein's criticism of logical positivism and the ideas of Frege and Russell?

Wittgenstein initially agreed with Frege and Russell's logicalism, which aimed to reduce all of mathematics to logic. However, Wittgenstein later criticized this view, arguing that while formal proofs may be valid, they often lose practical meaning and are overly complicated. He believed that logic and mathematics should be explained in simpler, more accessible terms based on everyday experiences.

What does Wittgenstein mean by 'language games'?

Language games refer to the idea that the meaning of words and concepts, including logic and mathematics, is determined by how they are used in various social practices. Wittgenstein argued that understanding logic and mathematics comes not from abstract, universal principles but from the rules and norms that emerge from human interaction and cultural practices.

How does Wittgenstein view the relationship between logic and everyday life?

Wittgenstein believed that the understanding of logic and mathematics should be grounded in everyday life. Instead of relying on formal, abstract proofs, he argued that logical and mathematical concepts should be taught and practiced through real-world examples and practical applications.

What is Wittgenstein's stance on the role of formal proofs in mathematics?

Wittgenstein criticized the reliance on long, formal proofs in mathematics, arguing that they often fail to convey practical meaning. He preferred simpler, more intuitive explanations that were based on everyday experiences and could be understood by anyone, including children.

What is Wittgenstein's critique of logicism's approach to mathematics?

Wittgenstein criticized logicism for creating a disconnect between formal mathematical notation and real-world human practices. He argued that logicism fails to address how the rules of logic and mathematics can be applied in everyday situations, and that mathematics should be understood through human interaction and cultural practices rather than abstract formalism.

How does Wittgenstein define rule-following in relation to mathematics?

Wittgenstein's concept of rule-following emphasizes that understanding how to follow rules, including those in mathematics, comes not from a universal logical essence but from social interaction and shared norms. He suggested that students learn mathematical operations and rules through interaction with teachers and their community.

What are the implications of Wittgenstein's later work for the philosophy of mathematics?

In his later work, particularly in 'Philosophical Investigations,' Wittgenstein shifted his view to see mathematics and logic as 'language games.' He argued that the meaning of mathematical concepts is not inherent in abstract rules but depends on the practices and social contexts in which they are used, marking a departure from earlier, more formal approaches.

How does Wittgenstein's philosophy challenge traditional views of mathematics as a universal truth?

Wittgenstein's philosophy challenges the view of mathematics as a set of universal, abstract truths by emphasizing its role as a human activity shaped by cultural practices. He argued that mathematics is not about discovering timeless truths but about engaging in social practices governed by agreed-upon rules and conventions.