6 votes
Accepted

Why aren't Kripke semantics "syntax in disguise"?

Algebraic semantics give a good organising framework for models of a logic, but they don’t give examples of models, except syntax itself. Kripke models give an easy way to construct lots of concrete ...
4 votes

Can we logically derive a value for 0÷0?

There is also some Circular Reasoning here, which is straightforwardly a logical mistake, in addition to any mathematical errors. On line 5, you cancel out the equal divisor and numerator values (10 - ...
  • 5,453
3 votes

Can we logically derive a value for 0÷0?

This proof is disguising a trick that seems like it would work mathematically but actually doesn't. The factoring of the 100 - 100 into different polynomials is just to make the problem seem more ...
  • 126
3 votes

Why do many philosophers state their arguments without using mathematics or formal language?

Main Answer When I write something down and then show it to someone else, my intention is to communicate an idea I have to them. Therefore, the method of writing that communicates my idea the best is ...
  • 849
2 votes

Why aren't Kripke semantics "syntax in disguise"?

Answer EDIT 2021-12-24 The initial presumption of my response that all model-theoretic models is wrong per the comments below. I'm letting the answer remain as the text is instructive to people such ...
  • 11.6k
2 votes

Can we logically derive a value for 0÷0?

As you've noticed, compared to +, - and ×, division is special. There are three schools of thought around questions like this: 0÷0 is undefined Whenever you try to define it, you end up with a ...
  • 1,240
1 vote

Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?

For very simple events, like particle interactions or dice rolls, we can derive quite rigorous models. Our intuition is often misleading about these cases, because while we recognise the cat is ...
  • 11.6k
1 vote

Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism?

Short Answer Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism? No. Structuralism is defined in terms of isomorphisms, and there are not ...
  • 11.6k
1 vote
Accepted

Why is conjunction interposed with intersection instead of union?

The reason in set theory is these identities: A∩B={x∈U∣x∈A∧x∈B} A∪B={x∈U∣x∈A∨x∈B} In normal English, AND is used as a joining operator: "This activity will be enjoyable for boys and girls", ...
1 vote

Why do many philosophers state their arguments without using mathematics or formal language?

Your fifth point is in fact correct, for example Ed Zalta (of SEP fame) uses Isabelle ($\textit{inter alia}$ other interactive theorem provers) to show/verify theorems on abstract object models. But ...
  • 1,298

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