Logic in philosophy and mathematics Textbook

In summary, the conversation is about the speaker's interest in philosophy and the connection between mathematics and logic. They are searching for a textbook that covers logic and includes mathematical notations. Suggestions for books such as Popper's "Logic of Science" and Russel's book on set theory are mentioned, but ultimately the speaker recommends Loveland et al's book on logic.
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Phylosopher
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Hello,Lately, I have been interested in philosophy and in particular the branches of philosophy where there is a tie with mathematics and physics. From this point, I think the best branch to start studying would be the most robust one for scientists. i.e Logic.

But I am having a problem finding a textbook to read from. Mathematicians usually focus on, well "math"! While philosophers goes for the whole spectrum of logic, but without using the privilege of mathematical notation.

So I am basically searching for a broad textbook that cover Logic as whole, but includes mathematical notations as well. (So that I can link my knowledge of math with the logic).
Note: I already know introductory set theory.

Can Anyone help me finding a suitable textbook?
 
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I have Popper's Logic of Science but from a mathematical point of view, I cannot recommend it. It is basically a book which belongs to philosophy and its influence on science has to be considered critical. At least it contains the letters Einstein wrote who wasn't a fan either.

I've also searched the net for Russel's book about set theory, but it is so full of special notations, that it is hard to read. So it might be better to read about Russel than to read Russel himself.

So, all in all I have not really a good idea. If you asked for a good book in the field of popular science, I would recommend Hofstadter's Gödel, Escher, Bach. It's a good book, but it isn't meant to be scientific.

From a mathematical point of view, I would chose an introductory book on set theory, leaving the philosophical part outside. Another idea is to look for mathematical history of the late 19th and early 20th century, say 1840 - 1960, when the mathematical revolution took place (Cantor, Hilbert, Gödel). A further approach is to study the various systems and models of logic. We basically use only the predicate logic, but there are more. In how far these systems influenced or affected philosophy is beyond my knowledge. I'm a fan of Kant and not very interested in what came after.
 
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  • #3
Phylosopher said:
So I am basically searching for a broad textbook that cover Logic as whole, but includes mathematical notations as well.
Can Anyone help me finding a suitable textbook?
I think you need Loveland et al https://www.amazon.com/dp/0691160449/?tag=pfamazon01-20

See also Science Jokes P2 :biggrin:
 
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1. What is the difference between deductive and inductive reasoning?

Deductive reasoning involves starting with a general principle and using it to draw a specific conclusion. It is often used in mathematics and philosophy. Inductive reasoning, on the other hand, involves using specific observations to make a general conclusion. It is commonly used in science and everyday life.

2. How do logic and mathematics relate to each other?

Logic is the foundation of mathematics, providing the rules and principles that govern mathematical reasoning. It helps to ensure that mathematical arguments are valid and sound. In turn, mathematics provides a concrete application for logical principles.

3. What is the difference between a valid and a sound argument?

A valid argument is one in which the conclusion logically follows from the premises. This means that if the premises are true, the conclusion must also be true. A sound argument is one that is valid and has true premises. In other words, the conclusion is not only logically correct, but also based on true information.

4. Can a logical argument be subjective?

No, a logical argument is based on objective facts and principles. It is not influenced by personal opinions or biases. However, the premises of a logical argument can be based on subjective beliefs, which can lead to a flawed argument.

5. How does the study of logic in philosophy and mathematics benefit us?

Studying logic helps to improve critical thinking skills and the ability to reason and analyze information. It also allows us to better understand and evaluate arguments, making us better equipped to make informed decisions. In mathematics, logic is essential for constructing valid proofs and solving complex problems.

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