Where can I learn about the philosophy behind mathematical and logical proofs?

What is a mathematical proof philosophy?

A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

Is logic part of math or philosophy?

Logic is an ancient area of philosophy which, while extensively beein studied in Universities for centuries, not much happened (unlike other areas of philosophy) from ancient times until the end of the 19th century.

How do you do proofs in philosophy?

So in a proof we take premises. Things that we assume are true and what we want to do with those is show that something. Else must be true as a consequence.

Is there a link between math and philosophy?

Historically, there have been strong links between mathematics and philosophy; logic, an important branch of both subjects, provides a natural bridge between the two, as does the Philosophy of mathematics module.

How many mathematical proofs are there?

There are many different ways to go about proving something, we’ll discuss 3 methods: direct proof, proof by contradiction, proof by induction. We’ll talk about what each of these proofs are, when and how they’re used. Before diving in, we’ll need to explain some terminology.

Who modeled his philosophical proofs of mathematical proofs?

Aristotle

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.

How do you learn math proofs?

To learn how to do proofs pick out several statements with easy proofs that are given in the textbook. Write down the statements but not the proofs. Then see if you can prove them. Students often try to prove a statement without using the entire hypothesis.

What are the 9 rules of logic?

Terms in this set (9)

  • Modus Ponens (M.P.) -If P then Q. -P. …
  • Modus Tollens (M.T.) -If P then Q. …
  • Hypothetical Syllogism (H.S.) -If P then Q. …
  • Disjunctive Syllogism (D.S.) -P or Q. …
  • Conjunction (Conj.) -P. …
  • Constructive Dilemma (C.D.) -(If P then Q) and (If R then S) …
  • Simplification (Simp.) -P and Q. …
  • Absorption (Abs.) -If P then Q.

How do you create a logic proof?

Like most proofs, logic proofs usually begin with premises — statements that you’re allowed to assume. The conclusion is the statement that you need to prove. The idea is to operate on the premises using rules of inference until you arrive at the conclusion. Rule of Premises.

What is the most beautiful proof in mathematics?

Quite possible the most famous theorem in mathematics, Pythagoras’ Theorem states that square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Whether Pythagoras (c. 560-c.

What was the first mathematical proof?

The first proof in the history of mathematics is considered to be when Thales proved that the diameter of a circle divides a circle into two equal parts. This is the earliest known recorded attempt at proving mathematical concepts.

What is the purpose of mathematical proof?

According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts. That is why a proof also has the role of explanation.

Who invented the proof theory?

One of the pioneers in mathematical logic was David Hilbert, who developed the axiomatic method around the turn of the twentieth century as a tool for partly philosophical and partly mathematical study of mathematics itself.

Are numbers real philosophy?

Numbers, if they exist, are generally what philosophers call “abstract objects”, and those who maintain that such things exist claim that they exist outside of space and time.

Why do realist believe that mathematics is discovered?

As the realist sees it, mathematics is the study of a body of necessary and unchanging facts, which it is the mathematician’s task to discover, not to create. These form the subject matter of mathematical discourse: a mathematical statement is true just in case it accurately describes the mathematical facts.

What did Plato say about mathematics?

Plato believes that the truths of mathematics are absolute, necessary truths. He believes that, in studying them, we shall be in a better position to know the absolute, necessary truths about what is good and right, and thus be in a better position to become good ourselves.

What is mathematics According to Aristotle?

Aristotle defined mathematics as “the science of quantity“, and this definition prevailed until the 18th century. In his classification of the sciences, he further distinguished between arithmetic, which studies discrete quantities, and geometry that studies continuous quantities.

What is platonism theory?

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental.

What Plato thinks about God?

To Plato, God is transcendent-the highest and most perfect being-and one who uses eternal forms, or archetypes, to fashion a universe that is eternal and uncreated. The order and purpose he gives the universe is limited by the imperfections inherent in material.

Was Nietzsche a Platonist?

(X, 2) This relentless struggle against Socratic ‘moralism’ and Platonic ‘metaphysics’ is the cornerstone of the Nietszchean project of the revaluation of values. The following chart clearly highlights Nietzsche’s claim that his philosophy is, indeed, ‘inverted Platonism’.