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In formal logic, does the existence of a thing necessarily imply its logical necessity, i.e., is it possible for something to exist without being logically necessary? Can a logically unnecessary thing exist?

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    No. You exist, but that is not logically (or even metaphysically or physically) necessary.
    – Conifold
    Oct 15, 2020 at 0:50
  • There is the question of whether, in order to have something useful/necessary (such as, say, a salad fork) there must also exist the piece of scrap metal resulting from punching out the fork shape in the manufacturing process. This is an artificial example, but there may well be reasons why, say, water could only exist if some "useless" chemical also exists. And you could further apply that metaphor to elements/concepts in what we call "formal logic".
    – Hot Licks
    Oct 15, 2020 at 1:35
  • plato.stanford.edu/entries/logic-free/#1.2 might be worth looking at. Mar 15, 2021 at 0:07

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In some conceptions of modality, a thing in a different logically possible state of affairs is a different thing. This is the idea that there are no trans-world identities, and that it just doesn’t make sense to talk about things existing necessarily.

Instead, what we might sometimes say is that it’s possible or necessary that something satisfying certain predicates exists. I don’t exist in any other possible worlds, but there might exist someone similar to me in certain key respects (depending on the kinds of possibility at work).

This was philosopher David Lewis’s idea in building up his theory of Counterparts (https://plato.stanford.edu/entries/david-lewis/#6.4) - if we take the concept of Possible World talk seriously, it’s our job in talking of Counterfactual situations to talk about the inhabitants of those non-actual worlds, rather than equivocating and overly prioritising our current position in the scope of all possibilities.

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You are trying to give a metaphysical fact (existence of things) of a final truth value (logic). This is kind of comparing peaches with equations. Either you assess metaphysical facts from an metaphysical perspective (for peaches to exist, everyone most have tasted at least one, otherwise its existence is subjective), or from a logical one (for peaches to exist, birds must fly; given that birds fly, peaches do exist_; notice that the logic is perfect, the proposition is necessary, but only in such context).

So, strictly:

  • From an ontological perspective, things existence being necessary is a philosophical aberration: existence would be a necessity for some truth, but philosophical truths are unknown.
  • From a logical perspective, the existence of things is just a proposition with no intrinsic value. If you use it within a logical set of statements, it is you that is providing it of a value of truth. In such case, it is only necessary within a set of logical claims.

For example, in Kant's philosophy, the concept synthetic a priori (knowledge which is universal and necessary) concerns mostly what is called here the logical point of view. Ontology is not possible for Kant, it would be the equivalent to try to study the-thing-in-itself, or the noumena.

But, looking for a metaphysical equivalent in the work of Kant, the existence of things could be a necessity for the deepest truths of our existence, whilst they are basically a tautology, so, no need to follow that path.

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If you accept that there're two types of existence (truth), necessary and contingent. Then only necessary truth implies logical necessity, such as principle of contradiction (PC), principle of identity of indiscernibles (PII). For contingent truth such as free will, there's no necessary logic, but sufficient reason principle (PSR).

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Necessities are subjective. What is necessary for you may not be necessary for amoeba and what is necessary for house fly may not be necessary for you and so on ... I guess existence of a thing implies it’s necessity but whose necessity is it ? That is a different question.

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