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He thus laid the way open for the view, which we adopt, that every assertion of a particular causal connexion involves the assertion of a causal law, and that every general proposition of the form ‘C causes E’ is equivalent to a proposition of the form ‘whenever C, then E’, where the symbol ‘whenever’ must be taken to refer, not to a finite number of actual instances of C, but to the infinite number of possible instances. He himself defines a cause as ‘an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second’, or, alternatively, as ‘an object followed by another, and whose appearance always conveys the thought to that other’;5 but neither of these definitions is acceptable as it stands. For, even if it is true that we should not, according to our standards of rationality, have good reason to believe that an event C was the cause of an event E unless we had observed a constant conjunction of events like C with events like E, still there is no self-contradiction involved in asserting the proposition ‘C is the cause of E’ and at the same time denying that any events like C or like E ever have been observed; and this would be self-contradictory if the first of the definitions quoted was correct. Nor is it inconceivable, as the second definition implies, that there should be causal laws which have never yet been thought of. But although we are obliged, for these reasons, to reject Hume’s actual definitions of a cause, our view of the nature of causation remains substantially the same as his.

Let's take a more precise look at this part:

For, even if it is true that we should not, according to our standards of rationality, have good reason to believe that an event C was the cause of an event E unless we had observed a constant conjunction of events like C with events like E, still there is no self-contradiction involved in asserting the proposition ‘C is the cause of E’ and at the same time denying that any events like C or like E ever have been observed; and this would be self-contradictory if the first of the definitions quoted was correct.

Why if we accept Hume's first definition would it be self contradiction to say 'C is the cause of E' and 'C and E have never been observed' at the same time?

Can you give me logical formula to support your answer?

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  • Because Hume's "following" refers to the following in our observations of events. An object cannot be "followed by another", as Hume's definition requires, if we never observed them in the first place. "Logical formulas" are irrelevant here.
    – Conifold
    Jan 24 at 21:22
  • Sorry for misunderstanding. I just asked for logical formulas (I'm not native speaker) for Hume's causation. And then I wanted to ask to show me how is this incompatible with Ayer picture of causation. For example: x (subject) - causation, O (predicate) - being observed. Then by quantifiers it could be shown, as Hume assumed, that every x is O. But Ayer supposed that not every x is O. And those two pictures are incompatible, so that's why Ayer can't accept Hume's picture of causation. I would be glad to take either this kind of answer or even pure formulas. Jan 25 at 0:29
  • @ЕгорГалыкин It is a bit misleading to present the same quote with a similar question two times. - Due to this confusion I restrict myself to post an answer to your first question and delete my answer to the above version.
    – Jo Wehler
    Jan 25 at 10:02
  • I'm sorry. The second question has emerged when I got some answers on the first one. And the second one is to clarify some moments in these answers. Jan 25 at 12:09

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Although it isn't completely clear in Ayer's quote of it, an intrinsic part of Hume's definition is that we observe C and then we observe E, not just once, but repeatedly. We thus define causation as a type of observation ("constant conjunction").

This is obviously in contradiction of the claim that C can cause E even without being observed because we are now claiming both that (a) causation is a type of observation (Hume) AND (b) exists without observation (Ayer).

Part of the general project of modern analytical philosophy, and the British Empiricist tradition of Ayer, is to recover larger philosophical concepts such as causation, in the face of Humean skepticism about the existence of things that cannot be reduced to empirical observations.

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  • Last question. Could I somehow find out that observation is assumed only from this quote: ‘an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second’? Or Ayer really should have pointed this out? Didn't he do this because he assumed that a reader would be familiar with Hume and, consequently, with the context of the quote? Your opinion would be really helpful for me as for non-native English speaker. Jan 24 at 21:13
  • I think he assumed, reasonably, that HIS readers would be familiar with Hume's commitments. All British Empiricism takes place in the shadow of Hume. But you're correct, the passage, just as given, lacks necessary context that even a native speaker wouldn't be able to pick up without extra-textual background knowledge. Jan 24 at 21:17
  • Unfortunately for Ayer, now I'm his reader too Jan 24 at 21:22
  • Unfortunately for you :D If you do want to understand Ayer, I would highly suggest reading Hume's Enquiry on Human Understanding first, or at least the section on causation. Jan 24 at 21:30
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    I kinda knew about Hume's causation. I just wanted to clarify what could I see in the quoted definition. Because I felt like I didn't notice something there. Because Ayer literally argues with things that wasn't mentioned there (I mean the necessity of observation). And I just wanted someone to say that Ayer kinda forgot to ascribe to Hume the opinion about the necessity of man's observation for causation to exist. Jan 25 at 0:11

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