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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. “Present an object to a man whose skill and intelligence are as great as you like;” he wrote, “if the object is of a kind that is entirely new to him, no amount of studying of its perceptible qualities will enable him to discover any of its causes or effects. Adam [the Biblical first man], even if his reasoning abilities were perfect from the start, couldn’t have inferred from the fluidity and transparency of water that it could drown him, or from the light and warmth of fire that it could burn him. The qualities of an object that appear to the senses never reveal the causes that produced the object or the effects that it will have; nor can our reason, unaided by experience, ever draw any conclusion about real existence and matters of fact.” [[CiteRef:: Hume (1748) |p. 12]] 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(1784)| p. 11]] 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 (1784)| p. 11]] 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| p. 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)]]
==== Hume’s problem of induction ====
While championing Newton’s inductive method, Hume also exposed its limitations by showing that conclusions drawn by inductive reasoning could not be rationally justified. As discussed above, Hume argued that knowledge of cause and effect comes only from the constant conjunction of particular phenomena in experience, which allows the use of induction to draw conclusions about cause and effect. [[CiteRef::Morris and Brown (2016)]][[CiteRef::De Pierris (2006)]] Hume envisions such an inductive argument as follows: