Argument for PSR
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Last revised: 02/18/25
I offer arguments for the PSR (Principle of Sufficient Reason) with respect to any state of affairs, change and coming into existence.
The subpoints provide further clarifying thoughts or definitions.
PSR for any state of affairs
It must be true that a state of affairs either obtains with an explanation or without an explanation. (Logical Dichotomy)
“Obtains” means is the case or is present, without presupposing a transition or process for why it is the case.
Assume for reductio that a state of affairs obtains without an explanation. (Assumption for Reductio)
If a state of affairs obtains without an explanation, then not anything (including a reduction of potentiality) occurred to obtain in that respect.
The term “reduction of potentiality” refers to the process by which something moves from a state of possibility to being the case. For example, in the case of a door, a slab of raw wood has the potential to become a door. As the wood is shaped and properly fitted into a frame, its potential is gradually brought into being the case that it’s a door. Each step in the process reduces its former state as raw wood and brings it closer to the reality of being a door, until it’s the case of just being a door.
“Potentiality” means the capacity or possibility to be the case.
The phrase “in that respect” is regarding the aspect lacking an explanation. It specifies that, in terms of there being no explanation, nothing contributed to the state of affairs' being the case (obtaining).
“Obtaining” means being the case or being present.
If true, then a reduction of potentiality didn’t occur in that respect for a state of affairs that obtains without an explanation (S).
Let S denote “a state of affairs that obtains without an explanation.”
If a state of affairs obtains (with or without an explanation), then it currently has no potentiality in that respect.
Something cannot be simultaneously be the case and in a state of potentiality since they are mutually exclusive. For example, if it were the case that a door were open and potentially open in the same respect at the same time, then it would be the case that the door is both open and actually closed, which is a contradiction.
Therefore, a reduction of potentiality didn’t occur in that respect for S and S currently has no potentiality in that respect. (Hypothetical Syllogism on #2-5)
If true, then S has never had potentiality in that respect in or during its being the case (obtaining).
Since there was no reduction, and since S has no potentiality now, it logically follows that potentiality was absent and that nothing else contributed its potentiality to S in that respect.
Potentiality is the capacity or possibility to be the case in a respect.
Therefore, S has never had the capacity or possibility to be the case in that respect in or during its being the case (obtaining). (Hypothetical Syllogism on #6-8)
A state of affairs obtains if and only if it has the capacity or possibility to be the case.
Therefore, S, a state of affairs that (obtains) has the capacity or possibility to be the case in that respect without an explanation, has never had the capacity or possibility to be the case in that respect in or during its being the case (obtaining), which is a contradiction. (Hypothetical Syllogism on #10-11, leading to contradiction)
Therefore, the assumption that a state of affairs obtains without an explanation is false. (Reductio ad Absurdum on #2 & #11)
Therefore, a state of affairs cannot obtain without an explanation. (Disjunctive Syllogism on #1 & #12)
PSR for change
An existent cannot simultaneously have potentiality and actuality in the same respect.
For example, if a door were simultaneously potentially open and actually open, then it would simultaneously be actually closed and actually open, which is a contradiction.
“Existent” refers to anything that has being or existence, whether it's a physical or non-physical object, event, state, or property.
“Potentiality” refers to the the capacity to attain actuality in a certain respect, which is more than mere possibility or hypothetical capability.
“Actuality” refers to the the realization or fulfillment of potentiality to indicate a state of being fully realized with no further potentiality.
If true, then it must either be the case that an existent that experiences change must have its potentiality reduced or have had no potentiality at all in that respect prior to becoming actual. (Logical Dichotomy)
Assume for reductio that an existent that experiences change had no potentiality at all in that respect prior to attaining actuality. (Assumption for Reductio)
If an existent can change in a respect, then it persists while entering a different state after the change than before in that respect.
The phrase "in the same respect" means considering the same attribute or property to avoid equivocation.
If true, then it has the capacity for change in that respect.
Something has the capacity for change in a respect if and only if it has the potentiality for change in that respect.
Therefore, if an existent can change in a respect, then it simultaneously has the potentiality for change in that respect. (Hypothetical Syllogism on #4-6)
Therefore, an existent that has no potentiality at all in a respect simultaneously has potentiality for change in that respect, which is a contradiction. (Modus Ponens on #3 & #7, leading to contradiction)
Therefore, the assumption that an existent that experiences change has no potentiality at all in that respect prior to attaining actuality is false. (Reductio ad Absurdum on #3 & #8)
Therefore, it must be the case that an existent that experiences change must have its potentiality reduced in that respect prior to attaining actuality. (Disjunctive Syllogism on #2 & #9)
If true, then it must either be the case that the reduction of potentiality to attain actuality occurs due to some reason or no reason at all. (Logical Dichotomy)
The phrase “reduction of potentiality” means the transition from potentiality to actuality.
Assume for reductio that the reduction of potentiality to attain actuality occurs due no reason at all (i.e., it happens without any cause or explanation). (Assumption for Reductio)
If true, then potentiality attains actuality without anything bringing it about.
If true, then potentiality is sufficient to attain actuality in a respect.
If true, then potentiality guarantees to attain actuality in a respect.
If true, then potentiality necessarily entails actuality in that respect.
If true, then the reduction of potentiality to attain actuality occurs for a reason.
Therefore, the reduction of potentiality to attain actuality, which occurs for a reason, occurs due to no reason at all, which is a contradiction. (Hypothetical Syllogism on #13-16, leading to contradiction)
Therefore, the assumption that the reduction of potentiality to attain actuality occurs due no reason at all is false. (Reductio ad Absurdum on #12 & #17)
Therefore, it must either be the case that the reduction of potentiality to attain actuality occurs due to some reason. (Disjunctive Syllogism on #11 & #18)
Change is the reduction of potentiality to attain actuality.
Therefore, it must be the case that change occurs due to some reason. (Hypothetical Syllogism on #19-20)
PSR for coming into existence
Nothing can give itself existence since it would have to exist prior to giving itself existence, which is impossible.
If true, then it must be the case that an entity whose essence does not include or entail existence itself either receives existence itself from something else or from not anything at all.
"Entity" refers to something that has a distinct existence.
“Essence” refers to the "whatness" of an entity (what it is fundamentally, not including its accidental features or properties). For example, the essence of a unicorn is a horse-like creature with a single horn on its forehead. The essence of a tree is a perennial, woody plant with roots, a trunk and branches with leaves or needles.
“Existence itself” refers to the act of being or actuality that makes an essence real or present in reality (in contrast to potential existence).
An entity that whose essence does not include existence would be a modally contingent entity.
Assume for reductio that an entity whose essence does not include existence itself receives existence itself from not anything at all. (Assumption for Reductio)
If true, then its essence is sufficient to come into existence.
If true, then its essence guarantees the entity’s existence without requiring anything external.
If an essence guarantees an entity’s existence without requiring anything external, then the essence includes or entails existence itself.
Therefore, an entity whose essence does not include or entail existence itself includes or entails existence itself, which is a contradiction. (Hypothetical Syllogism on #3-6, leading to contradiction)
Therefore, the assumption is false that an entity whose essence does not include existence itself receives existence itself from nothing at all. (Reductio ad Absurdum on #3-7)
Therefore, an entity whose essence does not include existence itself receives existence itself from something else. (Disjunctive Syllogism on #2 & #8)
If true, then all entities whose essence does not include existence itself have a cause or reason for coming into existence (namely that it has received existences from something else).
Therefore, all entities whose essence does not include existence itself have a cause or reason for coming into existence. (Modus Ponens on #9-10)