Modal argument from motion

Last revised: 12/23/24

These are in progress and subject to revision. Feedback welcomed.
Simplified seven-step argument linked here.
The subpoints provide further clarifying thoughts or definitions.

Presuppositions

1. Self-contradictions cannot take place or be true.

2. This syllogism does not presuppose either A-theory or B-theory of time, but allows for either view. A-theory says time flows. The present moment is special. Events move from future to present to past. Under B-theory, time does not flow. All moments exist equally and simultaneously. Past, present, and future are just different locations in time like different places in space.

3. The argument uses the S5 axiom of modal logic. In S5, all possible worlds are accessible from each other. If something is possible, then it is possible in all possible worlds. If something is necessary, then it is necessary in all possible worlds.

   S5 also includes the principle that if something is possibly necessary, then it is necessary. This follows from the idea that possibility and necessity apply across all possible worlds without restriction.

   The modality used is metaphysical possibility. A proposition is metaphysically possible if it is not logically contradictory and follows from necessary truths and nature of things. For example, “a triangle has three sides” is necessarily true in all possible worlds, while “a triangle has four sides” is not possible in any.

Premises

1. If motion is a progression of distinct states, whether sequentially (A-theory) or relationally (B-theory), then motion entails a real relation between distinct states.

   1. Real relation means a connection between states that is not merely conceptual or abstract but has a concrete basis, either in time (for progression) or in the structure of the relationships between states (for coexistence).

   2. A “state” refers to a way of being that describes an internal or external condition, attribute, or parameter at a given moment. For example, a person could be in a state of sitting down or a state of standing up, while also in a state of reading a book. A state is not necessarily active. It describes how something is, whether moving or still, whether acting or being acted upon.

   3. A “real relation” refers to a relation that exists objectively, independent of perspective or description. It contrasts with a Cambridge or rational relation, which depends only on a change in description or comparison, not on any real change in the things related. For example, if I grow taller than anyone in my household, our height relation changes. That is a real relation. If everyone but myself leaves a room, I am tallest person in the room, not because of any change in me, but because of a change in the other people’s location.

      This makes my being the tallest a Cambridge relation since it depends on something external to me, not on any real change in my height.

   4. The structure of relations describes the way in which states are interrelated or positioned, either through its attributes, logical dependencies or causal connections. (E.g., the structure of relations could describe how two states, like the height of a building and its weight distribution, are organized in a way that they mutually define the stability of the building. The structure is inherent in the way these attributes interrelate to produce the overall effect.)

2. Motion is a progression of distinct states, whether sequentially (A-theory) or relationally (B-theory).

   1. Under A-theory, causality drives the transition from one state to another in time.

   2. Under B-theory, the relational differences between states can still be seen as dependently linked in a logical sense, even if not temporally ordered.

3. Therefore, motion entails a real relation between distinct states. (Modus Ponens on #1-2)

4. If true, the relation between states could be independent (having no reliance on or influence from external factors) or be dependent (having a readiness or capacity to be influenced by an external factor).

   1. A “dependent relation” refers to the capacity or possibility for change or motion that depends on something else to bring it about. Motion, on the other hand, is an independent relation because once something is in motion, the state of being in motion is self-sustaining unless acted upon by another. Motion is an actuality, not a potentiality.

   2. Motion, on the other hand, is an independent relation because once something is in motion, the state of being in motion is self-sustaining unless acted upon by another force. Motion is an actuality (what is happening), not a potentiality (what could happen).

   3. E.g., a 16-oz cup possesses the continuous capacity to hold up to 16 ounces of coffee at any given time, remaining receptive to that volume as long as it is not already filled.

5. Therefore, the relation between states could be independent (having no possible dependence on external factors to) or be dependent (having a readiness or capacity to be influenced by an external factor). (Modus Ponens on #3-4)

6. If a relation between states could mutually exhibit independence and dependence in the same respect and in the same manner, then the relation would mutually have no further dependence on, or influence from, external factors and have a readiness or capacity to be influenced by an external factor.

7. A relation cannot be mutually dependent and independent in the same respect.

   1. For example, the state of a 16-ounce cup becoming full cannot mutually be dependent (potentially holding 16-oz of coffee, requiring external factors such as someone pouring coffee into it to realize that state) and independent (actually holding 16-oz of coffee, fully realized and requiring nothing further to reach that state) of external factors in the same respect and in the same manner.

   2. If the state of the cup becoming full were both dependent and independent in the same respect and in the same manner, it would imply that the cup is both reliant on external factors (e.g., someone pouring coffee into it) to be full and not reliant on them in the same respect (because it’s already full), which is a contradiction. However, just because the state of the cup is independent in one respect and in the same manner (by being actually full) does not mean it is independent in every respect or in the every manner. For instance, its state of remaining full depends on external factors, such as someone not drinking from it or the rate of evaporation.)

8. Therefore, a relation between states cannot mutually exhibit independence and dependence in the same respect and in the same manner. (Modus Tollens on #6-7)

9. If something cannot give to itself what it does not have, then whatever is in a dependent relation cannot not give itself an independent relation in the same respect and in the same manner.

10. A thing cannot give to itself what it does not have.

11. Therefore, whatever is in a dependent relation cannot not give itself an independent relation in the same respect and in the same manner. (Modus Ponens on #9-10)

12. If true, then it must be the case that whatever experiences motion (an independent relation) must have had its dependent relation reduced or have had no dependence at all in that respect prior to going in motion.

    1. “Experience motion” refers to the state of something that is undergoing motion, meaning it is transitioning from one location, position or condition to another.

    2. “Movement” refers to the process or act of undergoing motion.

    3. “Mover” refers to the thing causally or logically responsible for the transition between states or conditions in the thing being moved.

    4. If the mover and moved are parts of the same entity, then the mover is independent in one respect (e.g., the will’s decision to move the arm), while the moved is dependent in another respect (e.g., the arm’s potential to move).

    5. A person’s will is not an exception to the to the principle that nothing moves itself. The will is moved by the intellect (the faculty of knowing), which in turn is moved by our senses and experience by providing material for thought. This means that external reality presents something to the intellect, and that actuality moves the intellect from potential knowledge to actual knowledge. This is not to deny that the will can move the intellect by focusing attention. For example, a person can will to think about a certain topic, thus moving the intellect to consider it. However, this does not mean the intellect is purely self-moved since it still requires an intelligible object to function.

    6. A mover need not be of the same type or nature as the thing it moves; it only needs to possess an independent relation in the relevant respect that is sufficient to bring on the transition between states or conditions. For example, a fire does not need to be started by another fire but by something with an independent relation like an actual spark, friction, or chemical reaction that can initiate the transition to the state of being on fire.

    7. If something were to become actual without any prior potentiality of its own, it wouldn’t be a case of motion but rather of a new thing coming into existence or instantiating. Motion, or change, always involves the reduction of something in potentiality to actuality. Every entity in motion is different at the end of the movement than at the beginning, yet it remains the same in essence. If movement did not involve the reduction of potential to actual, the entity would not truly be in a different state from what it was before; it would go from one state of being to non-being, which is a lack of a state. Consider an example where an apple seed suddenly becomes a shark without any prior potentiality to become one. In this case, the seed would cease to exist in its form, and the shark would come into existence instantaneously, without a natural process of becoming. This would not be a case of motion, but rather of annihilation and replacement, where the apple seed is destroyed, and something entirely different (the shark) appears, without any continuity or development.

13. Assume for reductio that whatever experiences motion has no dependence at all in that respect prior to going in motion.

14. If true, then something can be in an independent relation without anything giving it independence.

15. If true, then dependence is sufficient to be independent.

16. If true, then something with a dependent relation in respect to motion guarantees it is independent in a respect.

17. If true, then something with a dependent relation in respect to motion is necessarily in an independent relation in that respect.

18. If true, then something with a dependent relation in respect to motion must mutually be in an independent relation in that respect.

19. Therefore, something with a dependent relation in respect to motion must mutually be independent in that respect, which is a contradiction. (Reductio ad Absurdum on #13-16)

20. Therefore, the assumption is false that whatever experiences motion has no dependence at all in that respect prior to becoming independent. (Disjunctive Syllogism on #12 & #18)

21. Therefore, it must be the case that whatever experiences motion (an independent relation) must have had its dependent relation reduced prior to going in motion. (Logical Dichotomy on #12 & #19)

22. If true, then in W, a metaphysically possible world sustained by an essentially ordered causal series, each member in the series that is moved must derive its ability to move from another.

    1. This is not to suppose if or how W was created, only that W is sustained by a essentially ordered causal series.

    2. In an essentially ordered causal series, the causality of each member is not independent but dependent on the direct and ongoing influence of the preceding cause (like how each link in a chain suspended by gravity holds the link beneath it). Each member in the series functions as an intermediate cause that derives its causal efficacy from the one before it, with no independence in its ability to cause, and all members in the series operate together at the same time.

    3. This series cannot extend infinitely backward or be circular because the motion of each member mutually relies on the actual causation happening at every state so there must be a primary source that is not itself moved by something else to initiate and sustain the motion of the entire series. In an essentially ordered series, there is an asymmetric dependence such that the cause sustains the effect, but the effect does not sustain the cause. This is unlike an accidentally ordered series, where each cause can continue to act even if the prior cause ceases (like how a string of dominoes can continue to fall even even if preceding fallen dominoes were removed), allowing the string of causes in theory to stretch back indefinitely or without a beginning. For example, if A depends on B for its existence or operation, and B simultaneously depend on A, then that is not an essentially ordered causal series because the dependence is not symmetrical.

    4. Metaphysical possibility refers to a thing that: (a) is not logically self-contradictory and (b) adheres to eternal or necessary truths (e.g., a triangle must have three sides and cannot have four).

23. Therefore, in W, each member in the series that is moved must derive its ability to move from another. (Modus Ponens on #21-22)

24. If in W, every member of the essentially ordered causal series is moved (i.e., in a dependent relation with respect to movement), then motion would not exist in W.

25. Motion, a progression of states or conditions, exists in W.

26. Therefore, in W, not every member of the essentially ordered series is moved, which entails an unmoved mover (at least one) exists in W. (Modus Tollens on #24-25)

27. If something is not dependent on any external factors in any respect or in any manner, then it has no capacity to be influenced by external factors in any respect or in any manner.

28. An unmoved mover is not dependent on any external factors in any respect or in any manner.

29. Therefore, an unmoved mover has no capacity to be influenced by external factors in any respect or in any manner. (Modus Ponens on #27-28)

30. If true, then it cannot fail or cease to exist.

31. Therefore, the non-existence of an unmoved mover (at least one) is impossible in W. (Modus Ponens on #29-30)

32. If whatever is metaphysically impossible in one possible world is impossible in all possible worlds, including our actual world, then the non-existence of an unmoved mover is impossible in any possible world, including our actual world.

33. Therefore, an unmoved mover (at least one) exists in all possible worlds, including our actual world. (Modus Ponens on #31-32)

Simplified argument (in progress)

1. It must be the case that whatever experiences motion (an independent relation) must have had its dependent relation reduced prior to going in motion. (Steps #1-21)

2. If in W, a metaphysically possible world sustained by an essentially ordered causal series, each member in the series that is moved must derive its ability to move from another.

3. If in W, every member of the essentially ordered causal series is moved, then motion would not exist in W.

4. Motion exists in W.

5. Therefore, in W, not every member of the essentially ordered series is moved, which entails that the non-existence of an mover (at least one) is impossible in W.

6. If what is metaphysically impossible does not vary by world, then what is impossible in one world is impossible in all possible worlds, including our actual world.

7. Therefore, the non-existence of an unmoved mover (at least one) is impossible in all possible worlds, including our actual world, which entails an unmoved mover (at least one) actually exists in our actual world.