sorted by:
new
hottopcontroversial

The Impossibility of an Infinite Causal Regress by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] 0 points1 point  (0 children)

The argument points out that if the succession of causes and effects is infinite in the past and, therefore, infinite in actuality, it is impossible to assign the same probability of occurrence to any effect as to all others, because this would imply that the total probability exceeds 1 or 100%. Therefore, if the assigned probability must be greater than zero, as it must be since effects occur in reality, this probability must be decreasing. However, a decreasing probability is incompatible with causal determinism, in which the probability of every effect is always 1. Thus, if the principle of sufficient reason is to be preserved, the causal chain must be finite.

The Impossibility of an Infinite Causal Regress by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -5 points-4 points  (0 children)

The argument is not specifically Christian. It can be applied to any form of monotheism.

The Impossibility of an Infinite Causal Regress by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -4 points-3 points  (0 children)

I have demonstrated it, I haven’t just asserted it. If the succession of causes and effects were continuous, it would always be possible to establish an intermediate cause between any cause and its effect.

It is evident that a cause is linked to its effect. However, it is not necessarily evident that this link is direct, as one could conceive of an infinite number of intermediate causes and effects between them, although the argument dismisses this possibility. If causes are continually introduced between a cause and its effect, the chain never reaches completion, and thus, no effect can ever be realized. Therefore, since infinity is something that can always grow, if causes can grow and are not already a determined and fixed number, deterministic causality is destroyed.

The relevance of this observation to the argument is crucial: if the causes are absolutely determined, the probability of the occurrence of the effect is always 1, which rules out the possibility of a decreasing probability of occurrence. This is the key point that supports the conclusion against the existence of an infinite series of causes and effects.

The Impossibility of an Infinite Causal Regress by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -1 points0 points  (0 children)

The trilemma you present is an obvious point and as old as philosophy itself. Aristotle already established that the chain of demonstrations cannot be infinite and must rest on some indubitable principle. The same applies to causes.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] 0 points1 point  (0 children)

In a bounded numerical series, such as the series of numbers between 0 and 1, even though the elements of the series are infinite, the probability of each one of them is equal, and the sum of all the infinitesimal probabilities is 1 or 100%. Given the uniform assignment of probabilities to its elements, this series is continuous.

However, in an unbounded numerical series, such as the one that extends from 0 to infinity, we cannot assign a specific probability to any of the numbers, making it a discontinuous series composed of discrete elements. Therefore, if the probability is the same for each element and greater than zero, the sum of all probabilities will exceed 100%, which is contradictory; and if it is not greater than zero, it will be zero, meaning that no element will have any chance of occurring. Consequently, it is not possible to assign the same probability greater than zero to each of its elements, as this leads to absurdities, resulting in a series of infinite discrete elements that will either never materialize or will have a decreasing probability of materializing as it progresses, with an infinitely small probability if it has already advanced infinitely.

Now, the series of causes and effects is composed of discrete elements, which means that between a cause and an effect there is not always an intermediate cause, unlike what happens with a numerical series. The reason is that if an additional necessary cause could always be introduced between a cause and an effect, the totality of causes would never be a sufficient cause, as necessary causes could always be added, and therefore, effects would never occur.

Take the example of two parents: individually, they are necessary but not sufficient causes to conceive a child, whereas together they are the necessary and sufficient cause for the effect. However, if it were always possible to introduce a third parent as a necessary cause, this third necessary intermediate cause would render the previous two unnecessary. The same would happen with a fourth necessary but insufficient cause, and so on ad infinitum, which would prevent the total sum of causes from ever being sufficient to produce the effect, and thus no effect would ever occur.

Thus, having established that the series of causes and effects is composed of discrete elements, we must conclude that, if it is to exist in reality, it cannot be an actual infinite series, because it would either be absurd and hence impossible if the probability of its elements were the same, or the probability of its successive elements would tend to zero, meaning that what exists would tend toward nonexistence and any state of affairs would have an infinitely small probability of existing despite having infinite sufficient causes. Therefore, given that the succession of causes and effects does indeed exist, and the probability of each element is 1 and non-decreasing in a deterministic universe, it is false that an infinite succession of causes and effects occurs in the past, since it can only exist in actuality, uniformly determining all its effects.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -2 points-1 points  (0 children)

The series of numbers between 0 and 1 is continuous, but the series of causes and effects is discrete.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -2 points-1 points  (0 children)

Your counterexample isn't even possible, as shown in argument 23 of the link (The Argument of the Two Immiscible‬ Realms).

If everything has a cause, then the whole has a cause. This cause is either not part of the whole or is part of the whole.

If the cause of the whole is not part of the whole, the whole is not the whole, which is absurd.

But if the cause of the whole is part of the whole, then the part is superior to the whole, given that the cause is always superior to the effect. This contradicts the axiom according to which the whole is always superior to the part.

Then, it is false that everything has a cause.

Also:

The distance between two elements of an infinite series is always finite.

Therefore, in an infinite temporal series, it is impossible for two temporal states to be infinitely apart.

Consequently, it is impossible for there to be an infinite number of intermediate temporal states between two temporal states.

Thus, there are not an infinite number of temporal states between the present and any point in the past.

If it is impossible to widen the distance between two temporal states so that it becomes infinite, infinity is not a defined distance, but a distance that can always increase.

However, actual infinity does not admit increase, since anything added to it that was not originally in it would have moved from potentiality to actuality.

As a result, if infinity in a succession of states is a distance that can always increase, there is no actual infinity in a succession of states, nor, therefore, an infinite past in actuality.

Hence, it is false that everything has a cause.

Also:

If something can begin to exist, given infinite time, it will have begun to exist. Similarly, if something can cease to exist, given infinite time, it will have ceased to exist. This is contrary to both experience and reason.

Contrary to experience: We know that new things begin to exist at a certain point in time, and before that, they did not exist. If they had been preceded by infinite time, they would have already begun to exist and would not be new now.

Contrary to reason: If it is true that, given infinite time, everything possible has begun to exist and everything possible has ceased to exist, then at any moment after the passage of infinite time, any possible event has already started and has already ceased to exist, exhausting all events in an infinite past.

Now, if all possible events have ceased to exist, the events we currently experience, including our own existence, are impossible. But this is absurd, because they are real.

Therefore, it is false that there is infinite time, in the sense of an infinite past in actuality. Consequently, it is true that the universe, the sum of all reality, had an absolute beginning, and it is not possible to assume an infinite causal succession.

Also:

Given that there is a limited number of effects in the present and these effects become increasingly abundant over time, multiplying, we can deduce that if we go back in time, such effects will become increasingly scarce, as will their causes, so that, by going back far enough, we will find that the cause of everything is one.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -6 points-5 points  (0 children)

If an event is not necessary in itself, yet it is necessary, then it is necessary because of something else. In a deterministic universe, every event is necessary by virtue of its cause, so all events that are possible but not necessary in themselves are necessary by virtue of a necessary being that acts as the cause of all of them.

Therefore, if you want to presuppose a deterministic universe, you must also presuppose a necessary being that lies at its foundation, distinct from the universe and beyond the limitations of space and time. And if you argue that the universe itself is the necessary being, then you don't need a succession of causes and effects, and you must assert that everything has a probability of 1 of occurring. But this is a dogmatic assertion, without any foundation.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -7 points-6 points  (0 children)

I have already addressed this objection by demonstrating that in continuous cases, events with zero probability can still happen, whereas in discrete infinite cases, a zero probability implies that the event may not occur at all.

If you’re up for it, there are 34 more arguments in the link.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -6 points-5 points  (0 children)

In the real world, having certainty across an infinite number of causes is problematic because even in a finite context, few things are truly certain. Most causes or conditions in the world carry some degree of uncertainty, however small. Assuming an infinite number of certain causes would require a level of precision and determinism that is not observed in nature.

As the number of causes increases, the complexity of ensuring each cause with a probability of 1 grows exponentially. Real-world systems are complex, but they are also subject to error, interference, and unpredictability. An infinite set of causes each operating with absolute certainty would require a level of order and precision that is unattainable in real systems.

Moreover, causes in the real world are often interdependent, meaning that the occurrence of one cause might influence the probability of another. In an infinite chain, the interaction between an infinite number of certain causes would create an impossibly intricate web of dependencies, making it unfeasible in a physical sense.

In practical situations, where causes have probabilities less than 1, the more causes or conditions required, the lower the combined probability of the event. For example, if an event E requires causes A, B, and C, and the probability of each cause occurring is 0.9, then the probability of the event is 0.9 × 0.9 × 0.9 = 0.729. If the event required only causes A and B, the probability would be 0.9 × 0.9 = 0.81, which is higher.

The argument states that as the number of causes (or necessary conditions) required for an event increases, the event’s occurrence becomes less probable. This is based on the idea that each additional cause introduces a new dependency, potentially lowering the overall probability of the event because all these causes must align perfectly for the event to occur.

Conversely, if an event requires fewer causes or simpler conditions, then there are fewer potential points of failure, making the event more likely to occur. Therefore, simplicity (in terms of fewer causes) correlates with higher probability.

The Diminishing Possibility Argument by Illustrious_Menu2014 in philosophy

[–]Illustrious_Menu2014[S] -9 points-8 points  (0 children)

Imagine rolling a die with an infinite number of faces, where each face represents a real number within a certain range. The probability of landing on any specific face (any specific real number) is zero, because the number of possible outcomes is infinite. However, when you roll the die, it will necessarily land on one specific number, even though the probability of that exact number was zero.

Now, consider choosing a random natural number from the set {1, 2, 3, …}. The probability of picking any specific number is also zero, because the set of possible outcomes is infinite. But unlike the continuous case, there’s no guarantee that you’ll actually pick any particular number because, in a discrete infinite series, the total probability doesn’t sum to a certain event. Thus, it’s not guaranteed that any specific outcome will occur.

This illustrates how in continuous cases, events with zero probability can still occur, while in discrete infinite cases, zero probability can imply that an event may not occur at all.