# Instantaneous response to — when did mathematical logic start influencing philosophical thinking?

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Mathematical logic began to influence philosophical thinking in the late 19th and early 20th centuries with the development of symbolic logic and its use in analyzing arguments and concepts in philosophy.

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Mathematical logic began to influence philosophical thinking in the late 19th and early 20th centuries with the development of symbolic logic and its use in analyzing arguments and concepts in philosophy. The use of mathematical logic allowed philosophers to analyze more complex arguments, and to do so with greater precision.

One of the pioneers of this movement was the philosopher and mathematician Gottlob Frege, whose work on symbolic logic paved the way for the development of modern predicate logic. He believed that mathematics and logic were closely related, and that the methods of symbolic logic could be applied to philosophy more broadly.

Another key figure in the development of mathematical logic was Bertrand Russell, who worked on the foundations of mathematics and used logical analysis to clarify philosophical problems. He wrote extensively on the subject, both in his philosophical work and in his mathematical writings.

Several pivotal works helped to popularize the use of mathematical logic in philosophy. In particular, Bertrand Russell and Alfred North Whitehead’s Principia Mathematica (1910-13) attempted to derive all mathematical truths from logical axioms, while Ludwig Wittgenstein’s Tractatus Logico-Philosophicus (1921) sought to clarify philosophical problems through logical analysis.

Finally, it’s worth noting that the use of mathematical logic in philosophy has continued to grow in importance in the decades since its initial development. Today, scholars across a range of fields use logical analysis and tools from mathematical logic to explore philosophical problems.

Table: Key Works in the Development of Mathematical Logic

Work Date Author(s) Summary
Begriffsschrift 1879 Gottlob Frege Introduces the concept of a logical calculus, laying the groundwork for modern predicate logic
Principia Mathematica 1910-13 Bertrand Russell and Alfred North Whitehead Attempts to derive all mathematical truths from logical axioms
Tractatus Logico-Philosophicus 1921 Ludwig Wittgenstein Seeks to clarify philosophical problems through logical analysis
“On the Concept of Logical Consequence” 1936 Alfred Tarski Defines the concept of logical consequence in formal terms
“Two Dogmas of Empiricism” 1951 Willard Van Orman Quine Argues that the distinction between analytic and synthetic statements is untenable
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## Video response

In his video, philosopher Denis Bonnay explores the relationship between logic and mathematics, highlighting the debate around whether mathematics requires additional intuition beyond logical principles. While Immanuel Kant believed in the need for mathematical intuition, philosopher Gottlob Frege believed a broader view of logic could prove mathematical truths. However, his system of logic was found to be inconsistent, and later systems required putting axioms in logical systems that were not necessarily logical. The challenge of aligning logic and mathematics is palpable in set theory, where questions of what belongs to logic and mathematics arise. A clearer understanding of the distinction between the two is needed, and this is an active area of debate in the philosophy of logic and mathematics.

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1950s

Progress in mathematical logic in the first few decades of the twentieth century, particularly arising from the work of Gödel and Tarski, had a significant impact on analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.

Progress in mathematical logic in the first few decades of the twentieth century, particularly arising from the work of Gödel and Tarski, had a significant impact on analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.

Well as far as mathematics is an expression of Logic as a philosophical discipline, the influence is huge in that discourse.

Math helps us understand the world relative to ourselves – distance, time, quantity, pattern, location… so it is pretty self-evident as a form derived simply from the way human beings (and animals) think. From the Egyptians, Zeno’s paradox and Al Ma’mun to Frege, Gödel and Wittgenstein, we have always been fascinated by this and its influence on thought and theorising.

Mathematics is a philosophy, so to refer to philosophy in wider generality (as I assume you meant), it would be better to ask ‘’how has mathematics influenced philosophy”? There are many other philosophical discourses in which math has very little importance or bearing, such as religion, law and existentialism.

## Also, individuals are curious

When did philosophy of logic begin?
Response to this: 5th century bce
Precursors of ancient logic. There was a medieval tradition according to which the Greek philosopher Parmenides (5th century bce) invented logic while living on a rock in Egypt.

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Beside above, Is mathematical logic philosophical?
As an answer to this: Some formal work on logic is quite mathematical, but mathematics itself raises many deep philosophical questions. The Philosophy of Mathematics addresses fundamental questions about mathematics itself, our knowledge of mathematics, and the concepts which it involves.

Additionally, When was mathematical logic invented? Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics.
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Correspondingly, Who applied mathematical principles to philosophy? Aristotle uses mathematics and mathematical sciences in three important ways in his treatises. Contemporary mathematics serves as a model for his philosophy of science and provides some important techniques, e.g., as used in his logic.

In this regard, When did mathematics become a philosophy?
This perspective dominated the philosophy of mathematics through the time of Frege and of Russell, but was brought into question by developments in the late 19th and early 20th centuries. A perennial issue in the philosophy of mathematics concerns the relationship between logic and mathematics at their joint foundations.

Regarding this, Who invented logic? They write new content and verify and edit content received from contributors. history of logic, the history of the discipline from its origins among the ancient Greeks to the present time. There was a medieval tradition according to which the Greek philosopher Parmenides (5th century bce) invented logic while living on a rock in Egypt.

How did mathematics influence philosophy in the 1950s?
The answer is: Advances were also made in ordinal analysis and the study of independence results in arithmetic such as the Paris–Harrington theorem . This was also a period, particularly in the 1950s and afterwards, when the ideas of mathematical logic begin to influence philosophical thinking.

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How did Greek philosophy influence mathematics?
In reply to that: Greek philosophy on mathematics was strongly influenced by their study of geometry. For example, at one time, the Greeks held the opinion that 1 (one) was not a number, but rather a unit of arbitrary length. A number was defined as a multitude.

In this regard, When did mathematics become a philosophy?
The answer is: This perspective dominated the philosophy of mathematics through the time of Frege and of Russell, but was brought into question by developments in the late 19th and early 20th centuries. A perennial issue in the philosophy of mathematics concerns the relationship between logic and mathematics at their joint foundations.

Who invented logic?
Answer: They write new content and verify and edit content received from contributors. history of logic, the history of the discipline from its origins among the ancient Greeks to the present time. There was a medieval tradition according to which the Greek philosopher Parmenides (5th century bce) invented logic while living on a rock in Egypt.

Herein, What is logic in mathematics?
In reply to that: Logicism is the view that (some or all of) mathematics can be reduced to (formal) logic. It is often explained as a two-part thesis. First, it consists of the claim that all mathematical truths can be translated into logical truths or, in other words, that the vocabulary of mathematics constitutes a proper subset of the vocabulary of logic.

In this way, How did mathematics influence philosophy in the 1950s?
Advances were also made in ordinal analysis and the study of independence results in arithmetic such as the Paris–Harrington theorem . This was also a period, particularly in the 1950s and afterwards, when the ideas of mathematical logic begin to influence philosophical thinking.

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