Michael

Let's take mathematical antirealism; we might say that a mathematical proposition is true if it is provable from the axioms. The mathematical antireal...

What does it mean that something counts as its justification? Are you just repeating the claim "p can be justified"? What is the difference between (1...

I don't even know what (3) is. You won't explain it. Again, I suspect you are equivocating. First you treat (2) and (3) as meaning different things, a...

So you have: P1. If (1) then (3) P2. If (2) then (3) And then you seem to go: C1. If not (2) then not (3). That's denying the antecedent. It would sti...

You're the one who has introduced new grammar, so you need to explain it. 1. p can be justified 2. p is justified 3. p has a justification I can't hel...

What is the difference between "is justified" and "has a justification"? What? It doesn't follow because it doesn't follow, just as the spouse example...

That simply does not follow. If some entity is a person then in some possible world it has a spouse. Therefore, every person has a spouse? No, obvious...

The point of that was to show that there is a meaningful difference between these two propositions: 1. If A is B then it can C 2. A can be B only if i...

No I don't. Just as the realist doesn't have to show us an unknowable truth.

Another example: 1. If the vase is fragile then it can break 2. The vase can be fragile only if it has a break These do not mean the same thing. (1) i...

No we can't. Dropping modality changes meaning. These mean different things: 1. All truths are believed and justified 2. All truths are believable and...

What does that mean? It doesn't even appear to be grammatically correct.

No it's not. That would be: 1. p ? Jp That's not what is argued. What is argued is: 2. p ? ?Jp Do you understand the difference?

To better explain it, I am saying: 1. If something is mortal then it can die You are misinterpreting/misrepresenting this as: 2. Something can only be...

You’re making the same mistake. I explained it clearly above: Do you understand what (1) and (3) mean?

You’re right, it shouldn’t. Which is why I don’t understand why you are taking issue with what I am saying. It is simply an a priori fact that from “p...

I don’t know what you mean by “appealing” to the principle of explosion. It’s like saying that we “appeal” to modus ponens. We use modus ponens to der...

I don’t know what you mean by “presupposing” the principle of explosion.

See the “? Q” at the end? That means that Q follows from the bit before. We’ve already established that “(P ? Q) ? ¬P” is true, so therefore “Q” is tr...

Yes

Because of the reasoning explained here.

I don't really understand what you're asking. We have realists claiming that some truths are unknowable and antirealists claiming that all truths are ...

It's valid. I don't even know what you mean by "not presupposing the principle of explosion".

As I said, there aren't two arguments; there is one argument: P1. P ? ¬P P2. P ? ¬P ? P (conjunction elimination) P3. P ? P ? Q (disjunction introduct...

No I'm not.

Anyone can suppose anything. 1. Suppose that I am a woman. 2. I am not a woman. 3. Therefore, supposition (1) is false. If you don't believe that (2) ...

That's basically what I said. The issue is that if realism is true then supposition (1) is true. Given that supposition (1) is false, realism is false...

No I don't. I'm saying that P ? ¬P ? Q is valid and that P ? ¬P ? Q is called "the principle of explosion". Much like P ? Q, P ? Q is valid and that P...

It's a simple modus tollens: 1. If realism is true then it is possible that we are (unknowably) brains in a vat 2. It is (knowably) not possible that ...

Yeah, going over it again I think I misunderstood what the article was saying about the relationship between the two.

The principle of explosion is simply the acknowledgement that if we apply the rules of inference to a contradiction then we can derive any conclusion ...

But that's not what has been said. What has been said is that if a proposition is true then it is justifiable.

So it entail global skepticism, which might be seen as undesirable. And if Putnam's argument is a sound refutation of global skepticism then it's a so...

Every unjustifiable truth is unjustified but not every unjustified truth is unjustifiable. Realism allows for unjustifiable truths, and that is a prob...

It says "the existence of a contradiction (inconsistency) in a formal axiomatic system is disastrous", which it is. Given that P ? ¬P entails Q, we mu...

He's talking about something else. I'm taking about this: P1. P ? ¬P C1. Q This is literally the principle of explosion: --- See the section titled "P...

There's also Banno.

It's in that post above. There's Hart, McGinn, Mackie, and Routley. And of course Fitch himself.

You ask me for an example and then complain that it's just one example? And you accuse me of sophistry and not being serious... :roll:

How is it sophistry? I have provided the source. It's right there, explicitly saying "the realist believes that it is possible for truth to be unknowa...

I am being serious. Read up on the principle of explosion.

Yes. I'll rephrase the argument in propositional logic: P1. P ? ¬P P2. P ? ¬P ? P (conjunction elimination) P3. P ? P ? Q (disjunction introduction) P...

Try reading the article I directed you to: Notice that antirealism is defined as being the position that believes that all truths are knowable. As rea...

The "argument 1" sits in between the premise and the conclusion of "argument 2" to make a single argument: P1. "I am a man and I am not a man" is true...

Logicians coined the term "valid argument" as a shorthand for "an argument with a conclusion that can be derived from the premises using a priori reas...

I don't understand what misrepresentation you think I've made. Are you denying that the realist rejects the knowability principle? Are you denying wha...

It's one argument that uses deductive reasoning to derive the conclusion from the premise. P2 - P5 simply make explicit the rules of inference and can...

In simple terms, given these two premises: P1. If I am a man then I am mortal P2. I am a man You can use the rules of inference to derive the conclusi...

It's one argument: P1. "I am a man and I am not a man" is true P2. If "I am a man and I am not a man" is true then "I am a man" is true. P3. If "I am ...

This is a valid argument: P1. If I am a man then I am mortal P2. I am a man C1. Therefore, I am mortal This is an invalid argument: P1. If I am a man ...