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If the proposition “It rains today” is false, then the situation “It rains today” does not exist.

If a proposition is false, the situation it represents does not exist

If (p=false and a=true and q=true and p->a->q) then

The first cause of the situation represented by q is the situation represented by p.

Since p is false, the situation represented by p does not exist

This means that there is no first situation that causes the situation represented by q.

You can attach a false antecedent to any consequent and the proposition becomes true.

so, The first cause of every situation do not exist.

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It’s most helpful to not read any causality from P to Q when interpreting P->Q. Take this sentence for instance:

“If you hit a home run, then you went up to bat.”

Clearly, hitting a home-run isn’t the efficient cause of going up to bat; one could say that it is the final cause of going up to bat, so long as the batter was intending on hitting a home run as opposed to a line-drive. However, most people use the word ‘cause’ to mean efficient causation, that is A causes B just if B happens as a result of A happening. This interpretation can and often does fit the mold of material implication, but it definitely does not always work.

To be clear, ‘efficient cause’ and ‘final cause’ are both versions of causation that Aristotle is credited as introducing to the literature. Roughly,

  1. A is the efficient cause of B just if B happens as a result of A happening. For example, hitting a home run is the efficient cause of clearing the bases.
  2. A is the material cause of B just if B occurs due to being composed of A. For example, the material cause of a wooden bed-frame is a tree/are trees.
  3. A is the formal cause of B just if B occurs as a result of having the form of A. For example, a ball rolls down a hill because of its circular shape.
  4. A is the final cause of B just if B happens for the sake of A, or B is the end/goal for A. For example, getting a good job is often the final cause of going to college.

Ultimately, material implication has little to do with notions of causation; further, the vacuous truth of the material conditional A->B when A is false hinges on the fact that in explosive logics {A,~A} cannot be satisfied, so in whatever case that set of formulas is satisfied, B is also satisfied for any formula B.

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  • "final cause" seems like bad wording. Wanting to get a good job is a reason to go to college, but it doesn't seem like a cause at all. Choosing to do something to get a desired result is not like the other cases of 'cause'. There is no certainty of achieving a desired result.
    – Scott Rowe
    Commented Dec 1, 2023 at 21:21
  • A: “Honey, why did you get the ketchup?” B: “Because I’m making veggie burgers.” This is just Aristotelian language; if you don’t like it you don’t have to use it, but don’t talk like person B in the dialogue.
    – PW_246
    Commented Dec 2, 2023 at 2:30
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    @ScottRowe it’s certain that there is no guarantee of the result without the final cause, though the final cause doesn’t need to be sufficient. Not all acorns grow up to be oak trees.
    – PW_246
    Commented Dec 2, 2023 at 2:35
  • Ok. Well, I used to think in terms of teleology: the result literally causes the things that came before it. But I don't think this way now. Final Cause sounds like that, but I'm probably missing something.
    – Scott Rowe
    Commented Dec 2, 2023 at 3:57
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    @ScottRowe Either way, final causes are definitely causes in the sense that without them, the process that leads to them wouldn’t occur. A cause doesn’t have to be a sole cause, and an end doesn’t have to be met in order for it to be a cause for what would otherwise lead to it.
    – PW_246
    Commented Dec 2, 2023 at 4:15

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