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Consider the summary of the story as follows: Take an arbitrary model of a finite world of entities, referred to as the C model. The C model assumes that entities are connected in a network of relations, called CE-type relations, which collectively form a network without loops.

This C model, as described, results in the presence of some starting nodes and some ending nodes. This outcome has nothing to do with the CE relation necessarily being causal.

However, if the CE relation is interpreted as causation, as suggested in Lemma B, this model cannot be consistent. The reason is that the ending nodes do not influence anything, just as "nothing" influences nothing, yet the ending nodes exist, creating a contradiction.

Explanation of the concept of "undefined": Mathematical structures may begin with undefined concepts. "Point" in Euclidean geometry and "membership" in set theory are examples of concepts considered "undefined." However, as the framework develops, concepts such as point and membership implicitly reveal their meanings through definitions, theorems, and the overall structure of the theory.

Definition 1: We assume "absolute nothingness" is undefined term. The set of all its effects on the mind and subsequent effects on other things (through the mind) is called "null-effects."

Assumption A: If entity X and entity Y are not identical, then in an effect that is not among the null-effects, they can be distinguished from one another.

Conclusion D: "Absolute nothingness" has no effects other than null-effects.

Reason: This follows from Definition 1.

Lemma B: An entity that has no effects other than null-effects does not exist.

Reason: If an entity has no effects other than null-effects, it is indistinguishable from "absolute nothingness" in terms of effects (based on Conclusion D). Thus, according to Assumption A, the two are identical, meaning this entity is "absolute nothingness." ✓

Relation of Lemma B to the Principle of Causality:

In short, the principle of causality implies the existence of entities that exist but have no effects—something clearly in contradiction with Lemma B.

How does this contradiction arise?

Consider causality in a graph/chain of non-null causes and effects. At least one "cause of causes" or starting node must exist (provided that in the graph/chain there is no: 1- loop or cycle, and 2- infinite regression).

However, in this case, there will also be at least one (and often many) end nodes, meaning "effects of effects."

What’s the problem with the effects of effects? They exist but are not the cause of anything; they have no effect on anything, which contradicts Lemma B.

Proposition C: The principle of causality is logically inconsistent.

Reason: The principle of causality leads to the existence of ineffective entities or "effects of effects," which, according to Lemma B, cannot exist.

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    "the principle of causality implies the existence of entities that exist but have no pure physical effect" Why? See Principle of Causality
    – Mauro ALLEGRANZA
    Commented Dec 9 at 11:38
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    I edit the text
    – dt128
    Commented Dec 9 at 11:48
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    If you restrict the graph from having loops/abysses, for reasons of the intuitive content of the concept of causality, why wouldn't you keep the graph from ceasing to grow outwardly, to offset the issue of representing inert effects-of-effects? Also, Assumption A, being an assumption, can be discarded fairly easily.
    – Kristian Berry
    Commented Dec 9 at 11:53
  • Literature regarding Causation is huge...
    – Mauro ALLEGRANZA
    Commented Dec 9 at 11:55
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    Please, take care of the LOGICAL FORM of the argument: Def.1 needs a clear indication of the term define. Conclusion D follows directly after Assumption A: where is the deductive step? Then follows Lemma B: what about a misisng Step C?
    – Mauro ALLEGRANZA
    Commented Dec 9 at 11:57

3 Answers 3

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Your post is simply playing around with words:

  1. You basic word is “absolute nothingness”. As long as you do not give a definition of this word, all your subsequent reasoning hangs in the air. That's not the ground for reasoning about causality.

  2. It is a trap of our language to form a noun like “nothingness”. “Nothing” is a shorthand for the expression “There is no entity such that …”. It is not a definite entity.

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  • In any structure based on definitions and theorems, the theorems depend on previous definitions\theorems, and definitions depend on prior definitions until we reach the initial definitions. Since something cannot be created from nothing, there are always some definitions that remain undefined. Suppose I define something you consider key using other concepts like D1 and D2. You would still say those need to be defined as well. My friend, if there are flaws in the definitions, they will reveal themselves in the line of proofs, not in speechs
    – dt128
    Commented Dec 9 at 14:59
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    Definitions are, by definition, not undefined: the moment you define something to be a way, that thing is not undefined anymore. In your Definition 1 you say that absolute nothingness is defined but you don’t actually do any defining.
    – controlgroup
    Commented Dec 9 at 15:34
  • @controlgroup I edit the text
    – dt128
    Commented Dec 9 at 15:46
  • So now, “absolute nothingness” being undefined as per your post, you agree with this answer? It’s sort of pointless to say something is undefined in a definition…
    – controlgroup
    Commented Dec 9 at 16:13
  • @controlgroup This undefinedness is the initial assumption; the definition itself pertains to the null-effect.
    – dt128
    Commented 2 days ago
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You put up a picture of a finite, directed graph of nodes where the direction represents a temporal relation of "cause" and "effect", the arrow of time. You declare that in reality any event should also have effects. This implies that the finite graph does not cover all your "real events" (however you want to define those). It does not imply that therefore the concept of causality is inconsistent. In your modeling of "reality" you could simply extend the graph. (A theory of infinite graphs is also perfectly possible without internal inconsistencies, if you would want to extend it to infinity.)

The concept of causality that you abstractly modeled in this graph is the prescientific, Aristotelian everyday notion of effective cause where a "cause" precedes its "effect" in time. This concept of causality is fine for the pushes and pulls of everyday usage -- though Hume and others showed its severe limitations --, but it's not really the most relevant concept underlying physical laws. What we now consider to be physical laws (formal structures and equations) are more similar to what Aristotle called formal causes. -- Simply consider: Was there first fire and then, some discrete (?) (or infinitesimal?) moment later, there was smoke? How could that ever be the case? :)

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  • the discussion is about a graph; the term "chain/graph of causality" is explicitly mentioned in the text. The conditions of this chain/graph have also moved from the traditional philosophical form to its mathematical representation. As for Hume, he did not address the logical conception of a chain/graph of causality. Specifically, he stated that the estimation of such a relationship—that is, the estimation of a causal relationship between two entities—always involves a degree of error and cannot be a matter of pure logic.
    – dt128
    Commented 2 days ago
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    Yes, I saw that. But that graph is a pure fiction. There are no a priori reasons to assume a finite graph with a unique root, and no loops (basically a finite tree) as in anyway representing physical reality. If you consider effective causes, then there is also no reason to for instance (1) deny that infinite regression is impossible (2) assume that there are no loops (3) assume that every node is not connected to every other node. A fully connected finite or infinite graph would perhaps be a strange model of effective causality, but still not an inconsistent one.
    – mudskipper
    Commented 2 days ago
  • There seems to be a misunderstanding about the uniqueness of the starting node and the connectivity of the graph. This text only assumes the graph is finite and without loops, which results in having some starting nodes (not necessarily one) and some ending nodes. Lemma B states that this exact model of causality is logically inconsistent.
    – dt128
    Commented yesterday
  • The main point is really that if you assume there is a state of the world (or many states) that is an "effect" but not a "cause", then this by itself does not make the concept of causality inconsistent. If the universe ends in a big crunch, this would by definition not an observable effect, but it is a conceivable effect. And whether or not the universe will end like that is still a question of empirical theory.
    – mudskipper
    Commented yesterday
  • In the proof of Lemma B, this consideration has been precisely taken into account: the inclusion of the "nothing" and the "nothing effect" into the proof was for this reason. The proof of the initial version was much simpler. In a finite acyclic causal chain, there is both a starting node and an ending node. However, the ending node cannot be the cause of anything, so it has no effect on anything. Therefore, it does not exist (this was the reasoning gap). But the ending node does exist, which leads to a contradiction.
    – dt128
    Commented yesterday
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Re. "meaning this entity is "absolute nothingness.""

"In short, the principle of causality implies the existence of entities that exist but have no effects"

First of all, nothing cannot be an entity. What Heidegger calls nothing is that which is not an entity.

"The nothing is the "not" of beings, and is thus being, experienced from the perspective of beings." (1949 preface to On the Essence of Ground in Pathmarks, p. 97)

How is nothing being? Imagine Descartes declaring "cogito ergo sum". Suddenly a thought has appeared evidencing existence. But where did the thought come from? Aside from the thought Descartes has nothing. His thought is conditioned; its source is unconditioned.

In terms of grounding, Descartes' thought is grounded by existence. Since existence grounds entities existence cannot be an entity, otherwise it would be its own ground.

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