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The relation of cause and effect is pivotal in reasoning, which Hume defines as the discovery of relations between objects of comparison. The three natural relations are resemblance, contiguity, and cause and effect. What is meant when some event is judged as cause and effect? But cause and effect is also one of the philosophical relations, where the relata have no connecting principle, instead being artificially juxtaposed by the mind. Hume therefore recognizes cause and effect as both a philosophical relation and a natural relation, at least in the Treatise, the only work where he draws this distinction. Some cannot. Cause and effect is one of the three philosophical relations that afford us less than certain knowledge, the other two being identity and situation. By so placing causation within Hume’s system, we arrive at a first approximation of cause and effect. Nevertheless, ‘causation’ carries a stronger connotation than this, for constant conjunction can be accidental and therefore doesn’t get us the necessary connection that gives the relation of cause and effect its predictive ability. Hume does not hold that, having never seen a game of billiards before, we cannot know what the effect of the collision will be.

Hume challenges us to consider any one event and meditate on it; for instance, a billiard ball striking another. But note that when Hume says "objects", at least in the context of reasoning, he is referring to the objects of the mind, that is, ideas and impressions, since Hume adheres to the Early Modern "way of ideas", the belief that sensation is a mental event and therefore all objects of perception are mental. This book traces the various causal positions of the Early Modern period, both rationalist and empiricist. This book is perhaps the most clear and complete explication of the New Hume doctrines. Hume points out that this second component of causation is far from clear. Of these, Hume tells us that causation is the most prevalent. In the Treatise, Hume identifies two ways that the mind associates ideas, via natural relations and via philosophical relations. And here it is important to remember that, in addition to cause and effect, the mind naturally associates ideas via resemblance and contiguity. There is nothing in the cause that will ever imply the effect in an experiential vacuum.

We are still relying on previous impressions to predict the effect and therefore do not violate the Copy Principle. But if the denial of a causal statement is still conceivable, then its truth must be a matter of fact, and must therefore be in some way dependent upon experience. That was an error to which I was accustomed and which it was not my habit to rectify unless the matter seemed important. I come now to the matter of your inquiry. Therefore, knowledge of the PUN must be a matter of fact. In both the Treatise and the Enquiry, we find Hume’s Fork, his bifurcation of all possible objects of knowledge into relations of ideas and matters of fact. The mind may combine ideas by relating them in certain ways. We may therefore now say that, on Hume’s account, to invoke causality is to invoke a constant conjunction of relata whose conjunction carries with it a necessary connection. Thus, objections like: Under a Humean account, the toddler who burned his hand would not fear the flame after only one such occurrence because he has not experienced a constant conjunction, are unfair to Hume, as the toddler would have had thousands of experiences of the principle that like causes like, and could thus employ resemblance to reach the conclusion to fear the flame.

We don’t mark our tables up only to mark them down again, so customers think they are getting a deal. We always do our best to make sure our customers receive the best prices available. And we can charitably make such resemblances as broad as we want. Evening meditation and morning work somewhat allayed her fears, and having decided that she wouldn't be vain enough to think people were going to propose when she had given them every reason to know what her answer would be, she set forth at the appointed time, hoping Teddy wouldn't do anything to make her hurt his poor feelings. The next morning I hastened to where my brother was employed and met him coming out of the office with a number of bills that he was to collect. Causation is a relation between objects that we employ in our reasoning in order to yield less than demonstrative knowledge of the world beyond our immediate impressions. The more common Humean reduction, then, adds a projectivist twist by somehow reducing causation to constant conjunction plus the internal impression of necessity. Impressions, which are either of sensation or reflection (memory), are more vivid than ideas.

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