Three logicians walk into a bar: a formal explanation

spikedmath.com/445.html —– Let E refer to the propositions expressed by the sentence: “Everyone wants beer” “everyone” refers to the three people on the right. Let’s call them “a”, “b”, “c” from left to right. Let “Wx” =df “x wants beer”. We could try to show this but let’s just take it intuitively that the following […]

“Do you still beat your wife?” formalized

Using the formalization system I wrote of earlier, let’s take a look at this famous question. First we should note that this is a yes/no question which is different from the questions that I have earlier formalized. The earlier questions sought to identity a certain individual, but yes/no questions do not. Instead they ask whether […]

Language, the modal fallacy and the symbolic representation of a conditional

“[W]hat follows from a true premiss must be true” (The Problems of Philosophy, p. 60, link) Wrote Russell as an example of a principle of logic that is more self-evident than the inductive principle. If we were to formalize this we would perhaps write it like this: E1. □[([∀P][Q∧Q⇒P])→P]1 Or perhaps just just in propositional […]

Using propositions as variables

I have encountered the following problem a couple of times. This problem is this: When formalizing something in predicate logic, the predicate uses propositions as variables.1 We may refer to this as the predicate acting upon the variable. The predicate is a function similar to functions in mathematics like “F(x) = x4”. Predicates were also […]

Modal logic formalization, multiple kinds of possibilities

Formatting requires a PDF file. modal-logic-formalization