Wittgensteins early prose was notoriously obscure and difficult to parse. Thus to call it ‘obviously’ anything seems very wrong-headed.
This is possibly why he gave up on his former philosophy calling it not philosophy at all and completely wrong.
His later philosophy is far more human in that it’s concerned with human values.
According to Wikipedia the domain of discourse for a classical first-order logic is usually considered to be non-empty:
An interpretation (or model) of a first-order formula specifies what each predicate means and the entities that can instantiate the variables. These entities form the domain of discourse or universe, which is usually required to be a ...
Philosophy aims at the logical clarification of thoughts. Philosophy
is not a body of doctrine but an activity
If Godel shows that "P = ΠP and ¬P = Π¬P" are not valid then any use of his ideas that also use "P = ΠP and ¬P = Π¬P" are, assuming we're talking philosophy, surely a misuse of "P = ΠP and ¬P = Π¬P".
Any activity that misuses logic (or language) ...
Descartes' Meditations arguably directly address this point, since a core part of his philosophical journey is to question his own rationality. However, he ultimately concludes that there are some logical relationships that can be directly apprehended as true by the intellect. For this reason, many critics believe he didn't take your line of argument ...
I can see we will need to use existential elimination and introduction, but I do not understand why these rules are the way they are.
Existential Introduction is easy. [Just avoid scope collisions when binding a term to the existential quantifier.]
: | : :
7.| | Q(b)
8.| | ∃y Q(y) ∃I, 7
If a predicate is true for a term that does exist in the ...
I have a couple of quibbles about the question that might partially answer it if not quite make it go away.
The rule that all statements must be true or false is the Principle of Bivalence, not the LEM. The LEM is a rule for statements that obey the PB and take the form A/not-A. If they do not they cannot be decided in the dialectic but they are still ...