Editing Deductive reasoning (section)

=== Geometrical method ===
The geometrical method is a method of [[philosophy]] based on deductive reasoning. It starts from a small set of [[self-evident]] axioms and tries to build a comprehensive logical system based only on deductive inferences from these first [[axiom]]s.<ref name="DalyHandbook">{{Cite book |last=Daly |first=Chris |title=The Palgrave Handbook of Philosophical Methods |publisher=Palgrave Macmillan |year=2015 |isbn=978-1-137-34455-7 |pages=1–30 |chapter=Introduction and Historical Overview |doi=10.1057/9781137344557_1 |chapter-url=https://link.springer.com/chapter/10.1057/9781137344557_1}}</ref> It was initially formulated by [[Baruch Spinoza]] and came to prominence in various [[rationalist]] philosophical systems in the modern era.<ref>{{Cite web |last=Dutton |first=Blake D. |title=Spinoza, Benedict De |url=https://iep.utm.edu/spinoza/#H2 |access-date=16 March 2022 |website=Internet Encyclopedia of Philosophy}}</ref> It gets its name from the forms of [[Mathematical proof|mathematical demonstration]] found in traditional [[geometry]], which are usually based on axioms, [[definition]]s, and inferred [[theorem]]s.<ref>{{Cite encyclopedia |title=Geometrical Method |encyclopedia=Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/geo-meth/ |access-date=17 February 2022 |last1=Goldenbaum |first1=Ursula}}</ref><ref>{{Cite book |last=Nadler |first=Steven |url=https://www.cambridge.org/core/books/abs/spinozas-ethics/geometric-method/08550AF622C78ACC388069710D37036E |title=Spinoza's 'Ethics': An Introduction |publisher=Cambridge University Press |year=2006 |isbn=978-0-521-83620-3 |pages=35–51 |chapter=The geometric method}}</ref> An important motivation of the geometrical method is to repudiate [[philosophical skepticism]] by grounding one's philosophical system on absolutely certain axioms. Deductive reasoning is central to this endeavor because of its necessarily truth-preserving nature. This way, the certainty initially invested only in the axioms is transferred to all parts of the philosophical system.<ref name="DalyHandbook" />

One recurrent criticism of philosophical systems build using the geometrical method is that their initial axioms are not as self-evident or certain as their defenders proclaim.<ref name="DalyHandbook" /> This problem lies beyond the deductive reasoning itself, which only ensures that the conclusion is true if the premises are true, but not that the premises themselves are true. For example, Spinoza's philosophical system has been criticized this way based on objections raised against the [[causal]] axiom, i.e. that "the knowledge of an effect depends on and involves knowledge of its cause".<ref>{{Cite book |last=Doppelt |first=Torin |url=https://qspace.library.queensu.ca/bitstream/handle/1974/6052/Doppelt_Torin_201009_MA.pdf |title=Spinoza's Causal Axiom: A Defense |year=2010 |chapter=The Truth About 1A4}}</ref> A different criticism targets not the premises but the reasoning itself, which may at times implicitly assume premises that are themselves not self-evident.<ref name="DalyHandbook" />