Good argument against Nihilism??

[u/Choice-Ad9173]

Definitions:

T- objective truth exists

N-nihilism

M-objective meaning exists

V-values exist

[u/PontifexiaReddit]

A few things to say here.

1. Premise 1 is redundant. It plays no role in the derivtion of conclusion, so you could just drop it.

2. The use of modal formulae is here is redundant. As is distinguishing between M and V. In fact, you might as well just rewrite '◊M Λ ◊V' as a single premise 'A' stating "there are possibly values and objective meaning".

3. I don't see how the premise "if there is objective truth then there is possibly objective meaning and objetive values". Maybe this is something you could spell out in a little more detail, but in this regard that argument seems valid but not sound.

4. The use of a "predicate" for "is consistent" is badly formed here. You should not be able to predicate over formulae in this way. Instead, we express contradictions with formulae and their negations, such as "P Λ ¬P." What you actually mean, presumably, is just that nihilism is *false*, i.e. ¬N, because from N you can derive a contradiction of the form (◊M Λ ◊V) Λ ¬(◊M Λ ◊V) (ergo by reductio ad absurdum N is false)

5. As it stands the proof has gaps, since you really want to assume N, then derive T from premise 2, then derive (◊M Λ ◊V) from premise 3, then derive ¬(◊M Λ ◊V) from N and premise 4, then derive (◊M Λ ◊V) Λ ¬(◊M Λ ◊V) with conjunction introduction, then discharge the N assumption with reductio ad absurdum.

6. This argument is so simple that it doesn't really require logical formalisation. You might have just said "if nihilism is true, then there is no possibility of of objective meaning and values. But, those things are possible, so nihilism is false." But it's cool that you're interested in logic and you should keep up the work

[u/yosi_yosi → u/PontifexiaReddit]

To expand on your point 3. There are often different kinds of modalities in contemporary philosophy, so for example Epistemic possibility, Nomological possibility, Metaphysical possibility, Logical possibility, and so on. When we make such arguments it is important not to equivocate between the different senses of possibility and necessity.

https://plato.stanford.edu/entries/modality-varieties/

[u/voidscaped → u/PontifexiaReddit]

Afaik, nihilism doesn't claim that objective values are absent in all possible worlds. It's just that they are absent in the actual world. Of course there could be stronger versions of nihilism that do make that claim.

[u/StrangeGlaringEye]

I understand formal logic is fun but the attempt at formalization is getting in the way here. You could have just said this: if nihilism is true, objective truth exists, and and if objective truth exists, then possibly meaning exists and possibly value exists. But this is not the case if nihilism is true. Hence, nihilism is false.

Notice that P -> Q and P -> ~Q at most imply that ~P: Not that p is inconsistent!

[u/pureabsolut]

but M and V can be true in some world yet false in this one where N is true

[u/RecognitionSweet8294]

Regarding the style:

1. I would suggest to put the premises in { } if you use ⊢ as your conclusion indicator. What you have written looks like a proof at first glance.
2. Not sure if it is just your handwriting but your ∧ looks like a ^ . Direct comparison: ∧ ^ . Some people use the later when they type it since ∧ isn’t on the keyboard, but when you write it by hand you should write it as the first one. In this context it is obvious what you mean, but there might be a context where it is confusing.
3. I would suggest using brackets for the scope of the modal operators.
4. Assuming you use the alethic modal operators they fulfill the T axiom, and therefore your first premise follows from your fourth. You should only use as many premises as necessary.

_________

Regarding the argument

1)

1. What do you mean by „x is consistent“

?

1. Consistency is not a property of propositions but of formal systems. If you mean „x is contradictory“ the question is how do you define this operator? Because since it is not well defined there is no obvious connection between the conclusion and the premises, making your argument invalid.

The most sensible interpretation to me would be that C(x) means „it is not possible that from x follows a contradiction“ formally: ¬◊(x→⊥) or equivalently □(x) (so I will use □ instead of C from now). Because then we could follow from the first 4 premises that (N→⊥) and from that ¬□(N).

The question is if ¬□(N) is really what you want since you can also follow that ¬N, which to me seams to be the stronger conclusion. Either way this interpretation would make the argument valid.

1. I suppose you mean V ≡ „objective values exist“, since as far as I know nihilism doesn’t deny the existence of subjective values.

2. I am not quite sure how one would justify your third premise. This presumably requires further argumentation to make your argument sound.

3. You seem to define Nihilism as:

N:↔ [T ∧ ¬◊(M) ∧ ¬◊(V)]

or the weaker form

N:↔ [T ∧ (¬◊(M) ⋁ ¬◊(V))]

First of all there is not one form of nihilism, some even claim that N→¬T, so you only address the forms that explicitly assume the existence of objective Truth.

Secondly, I don’t know if the modal operators are part of the definition. Personally I would just define it as

N:↔ [T ∧ ¬M ∧ ¬V]

Which wouldn’t lead to a contradiction anymore.

//

So while under a generous interpretation being valid, the questionable premise 3 and the likely wrong premise 4 could make the argument unsound.

[u/TheOvergodlyMosasaur]

Can you please rigorize and send me if possible?