A proof that collapses demonstration and explanation conflates logical necessity with causal sufficiency, two relations Leibniz carefully separates across necessary and contingent truths.

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Reasons For

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Reason for

1.Logical necessity holds in all possible worlds; causal sufficiency only in actual world. Conflating them obscures this modal distinction.
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2.Contingent truths require a reason (Principle of Sufficient Reason) but not logical proof. Leibniz explicitly maintains this separation.
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3.A proof yields certainty independent of existence; explanation requires actual causal chains. These are fundamentally different relations.
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Reasons Against

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Reason against

1.Leibniz's own metaphysics (monads, pre-established harmony) arguably requires explanation to collapse into logical determination anyway.
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2.The distinction between logical and causal necessity may be merely epistemic, not ontologically fundamental as the claim suggests.
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3.Modern logic shows necessity and sufficiency can be formally unified. Leibniz's separation may reflect 17th-century technical limits, not truth.
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Key Terms

Leibniz: Leibniz is a German philosopher and mathematician from the 1600s-1700s who developed calculus (a powerful math tool for measuring change and areas) independently around the same time as Isaac Newton. He's famous for creating much of the notation we still use in mathematics today and for arguing that everything in the universe follows logical principles. His ideas profoundly influenced modern science, mathematics, and philosophy, making him one of history's most important thinkers.
causal sufficiency(Causal modeling and directed acyclic graphs (DAGs)): A set of variables V is causally sufficient if there is no variable W omitted from V such that, if added to V, it would be a direct cause of two variables already in V.
contingent truths(Contrasted with the modal collapse implied by sσ ⊃• □•sσ): Truths that are not necessarily determined; truths that could have been otherwise
demonstration(The target of the skeptical critique; assumed to be the standard model of knowledge acquisition): A method of inferential proof from first principles or definitions, claimed to be the means by which knowledge is acquired
explanation(philosophy of science / epistemology): A concept whose meaning entails that if one theory is more explanatory than another, the former must be more informative than the latter
logical necessity(Distinguishing types of necessity): A property of statements that are true in all possible logical contexts, such as tautologies
necessary truths(Leibniz's argument for God's existence from eternal truths): Truths that hold independently of whether any finite minds exist to think them
proof(Frege's formal system; the definition still used by logicians today): Any finite sequence of statements such that each statement is either an axiom of the formal system or follows from previous members of the sequence by a valid rule of inference.

Connections

2 topics

Truth & Knowledge1 linked Modality & Possibility1 linked

A proof yields certainty independent of existence; explanation requires actual c...A sufficient reason, as Leibniz uses the term, is a proof that is both a demonst...

Details

Type: claim
Perspectives: 2 (1 for, 1 against)
Edits: 1 edit