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If p->q, then p is the cause of q

P is a proper subset of Q

A proper subset of a proper subset of a proper subset...

In other words, the cause of the cause of the cause of the cause...

For this to continue infinitely, there must be infinitely many elements of Q.

Let's repeat the process by subtracting elements from the set one by one to create proper subsets.

if you subtract all elements one by one from infinite elements

Therefore, you will end up with a set from which you can no longer create a "proper subset".

I think that the proposition that has that set as the truth set will be the first cause.

to sum up,

Even if the cause of the cause of the cause continues infinitely,

Mathematically, it means that there is a first cause.

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  • One of your main arguments is not correct: If you subtract from the set of integers, 0,+/-1,+/-2, ... (positive and negative) the set of positive numbers then you get the set of negative numbers together with the number zero, Hence "inf - inf = inf" is also possible.
    – Jo Wehler
    Commented Nov 9, 2023 at 3:05
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    I wonder if we can similarly prove that there is a last effect?
    – Scott Rowe
    Commented Nov 9, 2023 at 3:29
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    I’ve voted to close as this isn’t really a question.
    – Paul Ross
    Commented Nov 9, 2023 at 8:06
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    You are trying again and again to prove - using "logic" (or something that you think is logic...) - some metaphysical claims: every proof needs axioms, i.e. starting points on which anchor the argument. Thus, the conclusions - if any - will not be true (in some "absolute" sense) but at most consequences of the first axioms/assumptions. Commented Nov 9, 2023 at 8:06
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    Look, I'm not trying to be rude here, but you just don't understand how to present a coherent argument. You need to read a book on informal logic and spend a little time reading philosophy to gain the expertise you need. Commented Nov 9, 2023 at 8:14

2 Answers 2

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For this to continue infinitely, there must be infinitely many elements of Q.

Let's repeat the process by subtracting elements from the set one by one to create proper subsets.

if you subtract all elements one by one from infinite elements

Therefore, you will end up with a set from which you can no longer create a "proper subset"..

Unfortunately, no this is not always correct. Infinity is very hard to reason about without tools from mathematics.

If Q is countably infinite (i.e., can be placed in 1-to-1 correspondence with the integers), then you can remove an infinite number of items one by one and still have an infinite number left (e.g., remove all positive integers, or all the primes, etc.)

To get to what you want we could say we will remove all elements of Q whose integer index falls within -[n,n] for some integer n. We assume either Q is ordered or we just use axiom of choice to say we can pick some assignment of elements of Q to the integers. With this, you'd be making a limiting argument that as n → ∞ we arrive at the empty set.

However, if Q is uncountably infinite (i.e., a continuum or higher cardinality) then you can have a decreasing sequence of sets that converge to a non-empty set.

Since we really have no idea why Q would be one or the other, I don't see how this helps get to the necessity of a first cause.

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If p->q, then p is the cause of q

This is not necessarily true, for example: Let P = "You are shaking" and Q = "Your brain is sending nerve signals", the expression p->q would be represented in English as: If [you are shaking] then [your brain is sending nerve signals]. It seems to be patently the case that the latter causes the former and not vice versa.

P is a proper subset of Q

A proper subset of a proper subset of a proper subset...

In other words, the cause of the cause of the cause of the cause...

P -> Q, as far as I'm aware, does not entail P being a proper subset of Q as it may be an improper subset of Q (in the case of material equivalency for example). Furthermore, it is not always proper to model implication using sets as oftentimes the linguistic and, by extension, logical context is lost (the example earlier provided would be an apt exemplification of this).

For this to continue infinitely, there must be infinitely many elements of Q.

Let's repeat the process by subtracting elements from the set one by one to create proper subsets.

if you subtract all elements one by one from infinite elements

Therefore, you will end up with a set from which you can no longer create a "proper subset".

This function dosen't seem to be well-defined, what exactly is meant by "subtracting all elements one by one from infinite elements?" If one "subtracts" all the elements, this would result in the empty set, though I doubt that this is what you meant. It seems as if you are describing some sort of recursive algorithm that removes elements one by one, though such an algorithm would never be able to remove enough elements "one-by-one" until there is a set such that it has no proper subsets (the only set of that nature is the empty-set, seeing that the empty-set is a proper subset of every set except its own set), as the object the algorithm is being applied to is infinite.

I think that the proposition that has that set as the truth set will be the first cause. To sum up, even if the cause of the cause of the cause continues infinitely, mathematically, it means that there is a first cause.

This does not follow, please refer to the comments above.

-Thank you

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  • Isn’t P the cause of “figuring out Q”? Commented Nov 9, 2023 at 4:15

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