# Tagged Questions

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### Building math theory on absurd axioms - reducing math to logic

I know similar questions have been asked and i know my terminology might be wrong but I am trying to come to an answer to whether math can be derived from logic. Wikipedia defines logic as use and ...
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### Is mathematics invented or discovered? [closed]

A google search yields millions of results, most of which are made by laymen who have nothing to do with math and it's "just another article" for the authors, so I assume here with so much passion in ...
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### Is $'' \sum_{n = 1}^{\infty} (-1)^n \; \text{is a real number}''$ an invalid statement or a false proposition?

So we're beginning an introductory logic course and my professor is giving examples for valid statements/ propositions - meaningful statements that are either true or false but not both. So he puts ...
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### Three-valued logic as foundation

Isn't it more natural to use Three-valued logic(false-true-unknown) as the foundation of mathematics? It is a better model for natural languages. And it also can model sentences like the lair paradox ...
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### Gödel's incompleteness theorems

In the last paragraph of Stephan Hawking's speech "Godel and the End of the Universe", he mentioned "... I'm now glad that our search for understanding will never come to an end, and that we will ...
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### Are the real numbers really uncountable?

Consider the following statement Every real number must have a definition in order to be discussed. What this statement doesn't specify is how that loose-specific that definition is. Some examples ...
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### Is the “Most Important Property a Set S has” Necessary and Sufficient to Define a Paradox-Free Notion of Set?

About a year and a half ago, while I was looking on the Web for papers regarding the Russell paradox, I chanced to find an interesting concept. This concept was contained in what (for want of a ...
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### Why didn't Frege succeed in his attempts to reduce mathematics to logic?

My background: Sophomore-level understanding of mathematics and philosophical logic. All the explanations I have found online so far are either far too technical or too simplistic. Thanks in advance ...
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### particular property and completeness?

I was puzzeling with the almost standard definition of completeness: In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula ...
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### The standard role of intuitive numbers in the foundations of mathematics

In my career I've been formed mostly in the formal side of mathematics, that is, standard set theory and every classical branch of mathematics that uses set theory. However, I am not quite sure about ...
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### The Major Weaknesses in Ramified Type Theory

I am reviewing a paper on the major weaknesses of Ramified Type Theory in predicative second-order arithmetic. These four are listed as "weaknesses." But, I have my doubts. It seems at least that 3) ...
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### Is it Theoretically Impossible to Demonstrate that Set Theories Are Consistent?

I have to present on the main realist and non-realist arguments for/against set theory. According to one of my sources, it remains a matter of debate as to whether any of the set theories' (ZF, NF, ...
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### Set theoretic realism

What are the main contemporary arguments for and against realism about set theory?
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### Abstract Objects in Logic

I am confused on the concept of extensionality versus intensionality. When we say 2<3 is True, we say that 2<3 can be demonstrated by a mathematical proof. So, according to mathematical logic, ...
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### Why do we formalize conceptions?

Why do we always try to formalize conceptions? Let's take the naive conception of sets, why do we try to write down a list of axioms? what do we earn in doing so? I'm looking especially for ...
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### Study of all published works of Bertrand Russell on foundations of mathematics: Please recommend his works.

Study of all published works of Bertrand Russell on foundations of mathematics: Please recommend his works. I think Bertrand Russell was a special mind and I set a goal for myself to study all his ...
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### Trying to understand Hintikka's logic of Knowledge and belief

I try to understand Hintikka's logic of knowledge and belief but am a bit stumped by it. I study " Knowledge and belief , an introduction to the Logic of the two Notions", (Kings College ...
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### Constructivist Interpretation of a Function

Lets suppose I have an exponential function $a^{x}$, and I desire to show that for any number $n$ in $(0, \infty)$, it is possible to find a value of $x_0$ such that $a^{x_0} = n$. The simplest proof ...
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### What underlies formal logic (or math, generally)?

I read a useful definition of the word understanding. I can't recall it verbatim, but the notion was that understanding is 'data compression': understanding happens when we learn one thing that ...