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A Logical Consequence, in terms for formal language, is derivable from a given set of statements by manipulating symbols according to fixed rules. That I understand, for that is the only way to move ahead.

In real life, what does this mean? What does it mean for an event E" to be consequence of another event E? Is there a characteristic defining property of this transition (which can be universally applied to check if indeed E" is a consequence of E)? What is philosophical viewpoint of consequence?

  • For a review of the notions of logical consequence see Shapiro, Logical consequence: Models and modality. But the relation applies to statements/propositions, not to events. We can more or less ignore the difference on the modal view, where F is a consequence of E if in every possible world where E happens, so does F. – Conifold Jan 23 at 22:45
  • Here's something nice to study on this: iep.utm.edu/logcon – Overmind Jan 29 at 12:18
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Logical consequence is a relation between statements, i.e. linguistic entities and not between facts of the world.

The relation between facts can be a causal relation.

  • Semantic consequence is relation between what these linguistic entities (of formal language) mean (model arguments); so causal theory differs from semantics theory only because facts aren't fully representable in a formal system? – Ajax Jan 19 at 20:16
  • @Ajax - see Semantic consequence. – Mauro ALLEGRANZA Jan 19 at 20:24
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When speaking about causality, you should consider this: there are essentially two levels of contexts where natural dynamics occur. First, the level determined by our perception, and second, what we can call physical. I personally consider that Kant's Critique Of Pure Reason is the ultimate reference to such approach.

Russell stated that... "the law of causation,… is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm". I consider such point of view completely wrong, under the light of the kantian approach. It would be this:

  • first, we have the context determined by our perception. What Kant named phenomena. Causality is a necessity on this level. Our understanding is basically the capacity to establish relationships between mental concepts, and causality is just that, except that time is involved. An example of a relationship is the knowledge that bachelors are single. The concepts bachelor and single are different in our mind, but they are clearly related. As said, causality is the same thing involving time, that is, the relationship is just sequential. For example, if you put your hand in quiet water, and move it, waves will be produced. What is essential here is that there's a mental relationship between the fact of moving your hand (adequately), and the 100% of probabilities that waves are produced (in proper conditions). That is causality: a knowledge that a fact will always trigger another related fact. Note apart, the quantum world is probabilistic, and our perception has to deal with probabilities, not certainties. Russell is wrong upon this context: causality is part of the essential framework of our knowledge.

  • second, the context that Kant called the noumena, what really happens in the physical reality, but we don't have access to. At such level, there are no things, no systems, therefore, no relationships. Nature is a fuzzy stuff where there are no boundaries. What we call fundamental particles are just fluctuations in quantum fields. Russell is right about causality, at this level. If we need to apply causation rules in this context, we are forced to "thingify" nature. We need to establish boundaries, that define things, objects and then we can establish relationships, and then we would have a relative understanding of causality in this context. But that doesn't work. As said, in QM, the universe is not causal, but probabilistic. A teacher used to state that to get a notion of this idea, you can use the same example of the hand waving into the water. Physically, it's a mess of changes, which cannot be written as equations. When and where does a water wave exists? It even depends on the point of view! What is the influence of the hand? We only can write equations if we "thingify" nature. But even if we are formal, things become probabilistic: there's no way to accept that 100% of times a hand woven into the water will produce waves. So, causality is definitively not a fact in this context.

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I think that the most familiar example of causality is agent-causality: your own actions. How do you know that you caused something?

Is there a characteristic defining property of this transition (which can be universally applied to check if indeed E" is a consequence of E)?

I would say that one defining characteristic is when you know that what happened would have gone differently if you had made a different choice.

This is not to say that every idea that we have about whether we caused things is really true: many people imagine that they are more influential than they truly are, and some that they are less. But often enough, the following is clear: "If I had not done A, that B would not have happened. I may not ever find out what would have happened, and I may not know that B would never have happened, but I know that I caused B to happen when I did A."

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