I doubt that such a work exists, as there is no single mathematical logic. What usually is referred to as "mathematical logic" is the first order predicate calculus. But there are others. There are even systems with three possible values of truth. As you explicitly mentioned philosophy, the book from Charles (Karl) Popper "The Logic of Scientific Discovery" could be of interest to you. Other relevant scientists are Bertrand Russell and Kurt Gödel. Also of interest could be historical essays about the first half of the 20th century in general (foundational crises), and especially a reflection on Hilbert's program.Tukhara said:
Algebra on high school level.awholenumber said:
Physics. Neihter logic nor foundational nor philosophy.BL4CKB0X97 said:
History of a certain aspect of physics. Not even close to what the OP described.awholenumber said:
I believe that the work, and overview of the history (and an in depth working of said mathmatics)of pythagoreans and euclid would but rather apt to the Ops request. I thought ancient mathematics and how it relates to and birthed modern mathematics would also be pretty foundational. Mathmatics is covered first,then the physics comes en masse. He need not read it all.Mark44 said:
This might be true or not, but it has definitely not the least to do withBL4CKB0X97 said:
Penrose might be entertaining, but he's certainly not the first choice, when it comes to textbooks, and none if mathematical logic is the purpose.Tukhara said:
would suggest.smodak said:
Not really easy to add something upon these. What you're looking for that Grothendiek and Dieudonné haven't addressed? I know of some interesting papers by V. Strassen (Rank and optimal computation of generic tensors, 1982) and others, e.g. on lower bounds of matrix multiplication which uses methods of algebraic geometry (http://www.math.tamu.edu/~jml/LOsecbnd05-28.pdf), and an interesting essay (free download, https://arxiv.org/pdf/1205.5935.pdf, 92 p.) about geometric algebra (which of course is different from algebraic geometry).Tukhara said:
and @laviniamathwonk said:
lavinia said:
Well do you anything close to something that's like the English translations of EGA and SGA?fresh_42 said:
Sorry, no. I assume the Bourbaki approach isn't really a bestseller. I'v seen some interesting books on the internet about the historical developments like the correspondence between Grothendiek and Serre, but no conceptional treatment. Leo Corry seems to have written a nice overview of the modern mathematical structural concepts, but this also looks more like a historical treatment:Tukhara said:
I don't know. I only know about EGA/SGA what is written on Wiki. My assessment is based on what I know about the authors (and an old French version of a Bourbaki text about algebraic geometry I found and had a look into). But I don't think that the historical treatments I mentioned above can be compared to it. I only added them as being interesting on their own. To be honest, I cannot really imagine that a book written Bourbakian style would find many readers on the Anglo-American market. As far as I know, it is a fundamentally different tradition. And the books I have are again in another "wrong" language.Tukhara said:
For the philosophical part, maybe reading the book by Morris Kline: Mathematics in Western Culture? I have not looked at it.Tukhara said:
Mathematical logic is a branch of mathematics that studies the use of formal reasoning and symbols to represent and manipulate mathematical concepts and statements. It is concerned with the study of valid reasoning and proof, and it provides the foundation for many areas of mathematics and computer science.
The foundations of mathematics are the fundamental principles and concepts upon which all of mathematics is built. These include axioms, definitions, and logical rules that are used to construct and prove mathematical statements. The study of foundations of mathematics is closely related to mathematical logic and philosophy of mathematics.
Mathematical logic and philosophy are closely intertwined, as both fields are concerned with the nature of truth, knowledge, and reasoning. Mathematical logic provides the tools and methods for studying and analyzing the logical structure of mathematical statements and arguments, while philosophy addresses broader questions about the nature of reality and our understanding of it.
Mathematical logic is important because it provides a rigorous and formal framework for reasoning and proof in mathematics. It allows us to analyze the structure of mathematical statements and identify which arguments are valid and which are not. It also has practical applications in computer science, artificial intelligence, and other fields.
Some key topics in these books include set theory, propositional and predicate logic, proof theory, computability theory, and philosophical approaches to the foundations of mathematics. Other topics may include non-classical logics, model theory, and the relationship between mathematics and language or reality.