![]() Its exact relation to physical possibility is a matter of some dispute. ![]() Metaphysical possibility is generally thought to be stronger than bare logical possibility (fewer things are possible). Saul Kripke has argued that every person necessarily has the parents they do have: anyone with different parents wouldn't be the same person. For example, it might be metaphysically necessary, as some have thought, that all thinking beings have bodies and can experience the passage of time, or that God exists (or does not exist). Philosophers ponder the properties objects have independently of those dictated by scientific laws. While it is logically possible to travel faster than the speed of light, it is not, according to modern science, physically possible. On the other hand, it is not possible, in this sense, for there to be an element whose nucleus contains cheese. For example, it is possible for there to be an atom with an atomic number of 150, though there may not in fact be one. Something is physically possible if it is permitted by the laws of nature. For example, it is necessary that if Elvis is alive, then he is alive. Something which is logically necessary is called a logical truth. Many logicians also hold that mathematical truths are logically necessary: it is impossible that 2+2 ≠ 4. It is possible that Elvis is alive but it is impossible that Elvis is alive and is not alive. Likewise, almost nothing is logically impossible: something logically impossible is called a contradiction or a logical falsehood. There are a number of different alethic modalities: logical possibility is, perhaps, the weakest, since almost anything intelligible is logically possible: Possibly, pigs can fly, Elvis is still alive, and the atomic theory of matter is false. Thus if something is necessarily true, then it is true if it is true, then it is possible. It could have been otherwise, so it is possibly true, and possibly false. contingent if it is actually true, but not necessarily true.necessary if it could not possibly be false.possible if it might be true (regardless of whether it is or is not actually true).For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as the subject matter of modal logic. Modal logic was first developed to deal with these concepts, and only afterward was extended to others. Necessity and possibility are sometimes called alethic modalities, from the Greek aletheia, truth. 1.4 Confusion with epistemic modalities.Thus it is possible that Jones was murdered if and only if it is not necessary that Jones was not murdered. Each can be defined from the other and negation. The basic modal operators are usually (or L) for Necessarily and (or M) for Possibly. For example, "Jones's murder was a possibility" "Jones was possibly murdered" and "It is possible that Jones was murdered," all contain the notion of possibility in a modal logic this is represented as an operator, Possibly, attaching to the sentence Jones was murdered. Logics for handling a number of other ideas, such as eventually, formerly, can, could, might, may, must are by extension also called modal logics, since it turns out that these can be treated in similar ways.Ī formal modal logic represents modalities using unary modal operators. In the inductive clauses, a standard modality |$\lozenge \varphi$| translates as a first-order formula with |$x$| free, stating there exists a state |$y$| accessible from |$x$| via an edge different from all edges in the set |$E$|, with the translation of |$\varphi$| holding at |$y$|.In philosophical logic, a modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. Sabotage modal logic ( |$_x (\varphi) \right).
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