TonesInDeepFreeze

You're mixed up as you don't know the basic concepts. Reading just a little in a textbook in the subject would help you. No sentence that proves a con...

I don't know what that is supposed to mean. An antecedent is the part of a conditional that comes before '->'. The argument under discussion: A -> ~A ...

Your post is hopelessly confused because you don't know the basic concepts. If you would just read a little bit in an introductory textbook, in print ...

You would do a lot better not to reference me by saying that you believe that what you posted is what I am looking for.

Calculus uses infinite sets on day one. Even before a student gets to calculus, with analytical geometry we're using infinite sets. The real line and ...

That is BS. Handwaving to the extent you execute it is very much BS. The category of BS includes both falsehood and nonsense. EDIT: And the falsehood ...

What is the edited conditional? The conditional is "If Michael is American then Michael is president". That conditional is true since "Michael is Amer...

The word 'valid' is equivocal. There are different definitions and understandings of the word 'valid'. One of the formal definitions of 'valid' is a c...

I do understand the difference between taking 'true' as defined and taking 'true' as primitive.

How do you state that contest?

Regarding 'formal language' from, 'Notes on Metamathematics' by William Goldfarb: "A formal language is specified by giving an alphabet and formation ...

I reference it because it is rigorous, captures a common and basic intuition I share with logicians and mathematicians, and it seems the most prevalen...

I'm not going to draw diagrams. I'm not debating that. We can make any defiinitions we want. And I am not claiming that the definition of 'valid' in o...

I get that joke. Thank you.

That's ambiguous. It could mean two things: (1) A certain argument that ends with that conclusion is valid. (2) The conclusion is valid (i.e., it is a...

There are two definitions: Df. An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion ...

Explosion is the property of a set of statements entailing all statements. But it's still the case that no argument can be both valid and invalid.

Usually, we don't say that arguments are consistent/inconsistent. Sets of sentences are consistent/inconsistent. All combinations: (1) sound (thus sat...

Indeed. EDIT: But "Red fast what" and "Glooblefooble" are not even premises since they are not statements. So it's not even an argument, since {"Red f...

Whatever @"Michael" meant, I don't take it as a definition. It only states: If a set of statements is inconsistent, then it is incoherent. It doesn't ...

My hunch is that we can; but my amended attempt might not be satisfactory. Even just an uncountable set of symbols knocks it out of being formal. For ...

I don't know what you mean. The most basic "structure" is that an argument is an ordered pair, with the first coordinate being a set of sentences and ...

That argument doesn't seem for me to work. A logical monist could say that certain supposed laws of entailment are not correct and thus not laws of lo...

I'm not happy with my response to the question of distinguishing between formal and informal languages. Your challenge could be taken as: Provide a de...

It would help if you provided a definition of 'coherent' such that its a matter of form alone. We do have the definition per form alone of 'inconsiste...

(When I write, 'well formed formula', take that as short for 'well formed formula of the language'.) Of course, people may have different ideas about ...

You should think of a word for 'follows from' so that it is not conflated with other common senses. I suggest 'P raps Q' (equivalently, 'Q raps from P...

I would think 'follows from' is reflexive and transitive, but not symmetric. I would need to doublecheck these (and depends on knowing more about 'fol...

Depends on what 'needs' means. Mathematics pretty much needs sets to work with. But if one denies that mathematics needs to be axiomatized, then mathe...

I tried to put something together along the lines you have in mind. The best I came up with is this: (1) For any sentence P, the set of all sentences ...

We have that. You want to use that to define inconsistency in general without using the notions of semantic or syntactical consequence? We already hav...

I don't know what you mean by "minimal inconsistency guard".

Okay. What sense of "consequence"? Entailment? Do you mean how to define 'inconsistent'? (First order in this post and generally in posts unless said ...

We do have a definition of 'formal language': the set of well formed formulas is a recursive set*; and perhaps add unique readability. * More exactly,...

For writing, I would accept ordinary punctuation, but don't know about formatting or special characters given an ad hoc role. Also, I recognize that t...

Impressive that you did it without a bot. I just let the bot give me the English translation, but it too used specially formatting - bullet points and...

Of course, you can use special formatting to do it, with a convention as to what it signifies. But is that natural? That is, try to do it spoken.

I guess that' similar to the prisoner's dilemma. Okay, but consistency is defined in terms of derivability (which, in first order, is equivalent with ...

Said in natural language? Includes using parentheses to mark arbitrarily deep nested sub-sentences? In natural language, how would you say?: ?x ?y ?z ...

Nice.

Interesting. Very much bears looking into. By the way, I greatly enjoyed the video linked in the 'Logical Nihilism' thread. I have a lot of thoughts a...

I'm not sure that I recall Tarski correctly (perhaps he does mention the notion of a 'consistent or inconsistent language'?) But usually languages are...

In one view, we have a formal object-language, and an informal or formal meta-language that includes the formal object-language.

I don't know of anyone who thinks natural language conveyance of mathematics is unimportant. 'set' can be defined from 'element of'.

Just to be clear, one form of formalism is the extreme view that mathematics is mere symbol games. But formalism is not at all confined to such an ext...

It's more like the chicken and the egg (as you mention later in your post). You can take the logic as given to base math on it. And you can take a cer...

Don't know what you're driving at. People use variables outside of math books too.

At the outset of talking about unions (U) and intersections (/\), we get an interesting consideration. For any S, US = {x | there is a y in S such tha...

Set theory axiomatizes classical mathematics. And the language of set theory is used for much of non-classical mathematics. Those are two answers to "...

What pretending? Would you mention a specific writing?