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Hume took Newton’s opposition to demonstrative science much further, questioning the idea of a necessary mechanical connection between cause and effect. "Let an object be presented to a man of ever so strong natural reason and abilities;" he wrote, "if that object be entirely new to him, he will not be able, by the most accurate examination of its sensible qualities, to discover any of its causes or effects. Adam [the Biblical first man], though his rational faculties be supposed, at the very first, entirely perfect, could not have inferred from the fluidity and transparency of water, that it would suffocate him, or from the light and warmth of fire, that it would consume him. No object ever discovers, by the qualities which appear to the senses, either the causes, which produced it, or the effects, which will arise from it; nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact." [[CiteRef::Hume (1975)|p. 109-110]] The connection between a cause and its effect was learned by observation and experience, and could not be shown by demonstrative argument. [[CiteRef:: Bell (2009)]][[CiteRef::De Pierris (2006)]][[CiteRef:: Morris and Brown (2016)]]
Hume recast Aristotle's distinction between knowledge and opinion as a distinction between '''Relations of ideas''' and '''Matters of fact'''. [[CiteRef::Hume (1975)| pp. 108-113]] Relations of ideas are ''a priori'' truths that are discoverable independent of experience, and can be shown with certainty by demonstration or intuition. Because they must be true in any world, they cannot provide any new information about our own world. Relations of ideas are confined to the formal sciences of mathematics, geometry, and logic. Examples of such statements include 'a square’s sides add up to 360 degrees', '1 + 1 = 2', or, 'all bachelors are unmarried'. Relations of ideas can not be denied as their denial would imply a contradiction in their very definition. [[CiteRef:: Morris and Brown (2016)]][[CiteRef::Hume (17841975)| ppp. 11108-113]] Matters of fact, by contrast, are ''a posteriori'' statements based on knowledge obtained from the world through observation or experience. Examples of such statements include 'the sky is blue', or 'water is odourless'. Note that the contrary of a matter of fact is not something impossible. The claim that ‘the sun will not rise tomorrow’ is just as intelligible as, and no more contradictory than the claim that ‘the sun will rise tomorrow’. The two claims are only distinguishable by observation and experience. [[CiteRef::Morris and Brown (2016)]][[CiteRef::Hume 1784(1975)| ppp. 11]] Unlike relations of ideas, matters of fact do not hold true in all possible worlds and cannot be established by demonstration. They can never be known with certainty.
Hume’s new categories of knowledge made it clear that natural philosophy, since it relied on knowledge of matters of fact, could never aspire to the kind of certainty that Aristotle supposed for scientific knowledge, and should be content with the modest sort of knowledge available through Newton’s inductive method. [[CiteRef::De Pierris (2006)]]