1.Contingent and necessary
A contingent being is one that exists but might not have. A necessary being is one whose non-existence is impossible, because its nature is such that it must exist. The distinction is modal, not temporal — a thing could exist eternally and still be contingent, since its endless existence would still call for explanation.
This is what separates contingency arguments from the kalam. The kalam requires a temporal beginning; contingency arguments do not. If the universe turned out to be past-eternal, the contingency argument would be entirely unaffected, which makes it more robust against cosmological revision.
2.The argument in Leibniz's form
Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. If the universe has an explanation of its existence, that explanation is a necessary being. The universe exists. Therefore the universe has an explanation, and that explanation is a necessary being distinct from the universe.
Aquinas's third way approaches the same terrain differently, arguing from the possibility of non-existence to the necessity of something that always exists. Scholars debate whether Aquinas commits a quantifier shift — moving from 'each thing can fail to exist' to 'there is a time when all things fail to exist' — which is why the Leibnizian formulation is usually preferred in contemporary discussion.
3.The Principle of Sufficient Reason
The first premise is a version of the PSR: everything has an explanation. Strong PSR says every fact has an explanation; critics argue this collapses all contingency into necessity, since if every fact including the totality of facts has an explanation, and explanations are entailing, then everything is necessary.
Defenders such as Alexander Pruss and Joshua Rasmussen therefore use restricted forms — for instance, every contingent concrete thing has an explanation — which avoids the modal collapse worry while retaining the argumentative force. The support offered is that the PSR underwrites all rational inquiry: we never accept 'it just happened for no reason' as an answer in science, law, or ordinary life, and the person who applies that standard everywhere except the one case where it produces a theistic conclusion owes an account of the exception.
The most serious objection is Hume's: to conceive of something existing without a cause is not self-contradictory, so the PSR is not a necessary truth. The theistic reply distinguishes conceivability from possibility — we can conceive of many things that turn out impossible — but the objection does real work and cannot be dismissed.
4.Can the totality be explained by its parts?
Hume and Bertrand Russell both argued that once each member of a series is explained, no further explanation of the whole is needed; asking for one commits the fallacy of composition. Russell simply refused the question: the universe is 'just there, and that's all'.
Defenders reply that the collection of all contingent things is itself contingent, and that explaining each member by another member never explains why there is any such collection rather than none. If every member is dependent, invoking further dependent members postpones rather than answers. The standard analogy: a chain of hanging links explains no link's suspension until something not hanging is reached.
Critics counter that the totality may not be a further thing needing explanation, or that the universe itself might be the necessary being. The last suggestion is taken seriously — Spinoza held a version of it — but faces the difficulty that the universe's constituents and configuration appear obviously capable of being otherwise, which is the mark of contingency.
5.From necessary being to God
The bare conclusion is a necessary concrete being. Additional argument is required to say more: it must be uncaused, and if it explains all contingent things it cannot itself be contingent or composed of contingent parts. Classical theists argue from there to simplicity, immateriality, and immutability, since a material thing has parts and configurations that could be otherwise.
Whether this necessary being is personal is the same open joint as in the kalam. And the abstract-object alternative must be addressed: numbers are often said to exist necessarily, but abstract objects are causally inert and cannot explain the existence of anything, so they do not satisfy the explanatory role.
Presented honestly, the argument delivers a necessary, uncaused, non-contingent ground of all contingent reality. That is a substantive metaphysical conclusion incompatible with naturalism as usually understood, and it is still several steps short of the God of any confession.