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Assuming all things are possible, then statements like "All things are not possible" are also possible since statements are things.

Then we have:

All things are possible and All things are not possible

Does this line of reasoning work to show that the initial premise is always false.

  • 1
    You have an ambiguity regarding the word "things." Usually the sentence "all things are possible" uses the word "things" to mean actions, something like "all actions are possible." It doesn't make much sense to say that "a sentence is possible." Possible to what? To exist? What does it mean to say that a sentence exists? I don't think that its a contradiction because "all things are possible" usually has a specific meaning. It sounds like you're making a fallacy of equivocation in regards to the word "things." – Not_Here Mar 22 '17 at 23:07
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    Sure, I mean what you are describing is similar to something like "There are no absolute truths" which is an antinomy because if its true then it itself is an absolute truth so it contradicts itself. You might be interested in reading more about antinomies and paradoxes like that, I would start here – Not_Here Mar 22 '17 at 23:30
  • Rephrasing your suggestion into "all statements are possibly true", i.e. "possibly, all statements are true", we do get an (always) false statement. Because then "possibly, P and not P are both true" (for any P), but "necessarily, P and not P are never both true" is a modal tautology. – Conifold Mar 23 '17 at 0:17
  • "All things are not possible" also contains a self-contradiction. – user18800 Mar 27 '17 at 21:33
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Regarding the transcendental determination of the idea of 'everything' - e.g. 'the universe' - all predicates are possible to it: i.e. "all things are possible". Once existence comes into play specific possibilities are crystalised and mutually exclusive ones disappear - they are no longer possibilities.

This transcendental concept is laid out in Immanuel Kant's Critique of Pure Reason:-

Ch. III. Section ii. Of the Transcendental Ideal (Prototypon Trancendentale).

If a transcendental substratum lies at the foundation of the complete determination of things - a substratum which is to form the fund from which all possible predicates of things are to be supplied, this substratum cannot be anything else than the idea of a sum-total of reality (omnitudo realitatis). In this view, negations are nothing but limitations - a term which could not, with propriety, be applied to them, if the unlimited (the all) did not form the true basis of our conception.

This conception of a sum-total of reality is the conception of a thing in itself, regarded as completely determined; and the conception of an ens realissimum is the conception of an individual being, inasmuch as it is determined by that predicate of all possible contradictory predicates, which indicates and belongs to being. It is, therefore, a transcendental ideal which forms the basis of the complete determination of everything that exists, and is the highest material condition of its possibility - a condition on which must rest the cogitation of all objects with respect to their content. Nay, more, this ideal is the only proper ideal of which the human mind is capable; because in this case alone a general conception of a thing is completely determined by and through itself, and cognized as the representation of an individuum.

That is to say, a thing - in our case 'everything', or 'the universe' - notionally has every possibility available to it. Once actualised, the possibilities become limited. If the universe had the possibility of not existing and the eventuality was that it didn't, then the situation would be that "all things are not possible". The possibilities of being possible and not being possible wouldn't exist simultaneously.

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If all things are possible, then among those possibilities are the truth and falsehood of any given proposition. This can be expressed in modal logic as:

◇A & ◇~A

However, that expression is not itself a contradiction.

In terms of possible worlds, it could be said that there is at least one possible world in which A is true, and there is at least one possible world in which ~A is true, but there is nothing to compel us to assert that those conditions actually do or even could coexist in the same world.

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Phrase A: "all things are possible", contains the possibility of failure as an outcome. The term "all things" implies universality of application. Phrase B: "all things are not possible" would either acknowledge a set of thing (or a singular thing) is impossible, or the universality that no things are possible, depending on how you emphasize the term "all".

However, the term "possible" is limited to only account for the potential of things. If we consider that "possible" does not necessarily imply that it must, should or does occur, then the two statements do not require mutual exclusivity.

If A, then B is true until B is confirmed.

The reciprocal statement would contain a false premise.

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Yes, it contradicts itself because, if "all things are possible," then it is possible for nothing to be possible, thereby contradicting itself!

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