These are in progress and subject to revision. Feedback welcomed.
I offer arguments for the Principle of Sufficient Reason (PSR) with respect to any ontologically necessary existent, any modally contingent state of affairs, change and coming into existence.
The subpoints provide further clarifying thoughts or definitions.
Presupposition of each argument
Self-contradictions cannot take place or be true.
No existents have any real shared properties or any intrinsic features of reality. So what something "is" depends on how it is classified within a framework of human understanding rather than an independent property it possesses.
PSR for any ontologically necessary existent
It must be the case that an ontologically necessary existent is real with an explanation or without an explanation. (Logical Dichotomy)
Ontological necessity refers to being independent of any external causes, circumstances, conditions or factors.
“Existent” refers to an entity that are real and instantiated. It does not assume that an existent has any real shared properties or any intrinsic features of reality.
The phrase “is real” refers to being present in the here-and-now.
“With an explanation” means it is in principle explainable, whether or not the explanation is currently known. The explanation does not necessarily have to be entailing.
Assume for reductio that an ontologically necessary existent is real without an explanation. (Assumption for Reductio)
If an ontologically necessary existent is real without an explanation, then not anything explains why it is real, not even that the observable characteristics we observe are not identical to the its concrete existence.
This asserts that the similarities (the observed characteristic or resemblances) are distinct from the existence (the particular’s actuality as a concrete entity). In nominalist terms, the characteristics a particular has (e.g., its specific perfection, beauty, or morality) describe what it is like. The existence of the particular refers to the act of being present in here-and-now. These are distinct because the characteristics a particular has (e.g., its perfection) are not the same as its being present in the current reality. For example, we can conceive of a perfect mountain’s traits (similar to other perfect particulars) without it being actual in the here-and-now.
If true, then the observable characteristics of an ontologically necessary existent that is real without an explanation are not identical to the its concrete existence.
Let O denote “an ontologically necessary existent that is real without an explanation.”
Therefore, the observable characteristics of O are not identical to its concrete existence. (Hypothetical Syllogism on #2-4)
If the observable characteristics of something are not identical to the its concrete existence, then it is composed of physical or metaphysical parts.
In other words, it can be understood in terms of physical or conceptual components, without assuming these components are inherent or fixed.
If something is composed of physical or metaphysical parts, it is dependent upon its parts coming or remaining together.
Therefore, O is dependent upon its parts coming or remaining together. (Hypothetical Syllogism on #5-7)
An ontologically necessary existent is real if and only if it isn't dependent on any circumstances to be or not be the case.
Therefore, O, an ontologically necessary existent that is real without an explanation, is mutually dependent (per #8) and not dependent (per #9) on its parts coming or remaining together, which is a contradiction. (Hypothetical Syllogism on #8-9, leading to contradiction)
Therefore, the assumption that an ontologically necessary existent is real without an explanation is false. (Reductio ad Absurdum on #2 & #10)
Therefore, an ontologically necessary existent is not actual without an explanation. (Disjunctive Syllogism on #1 & #11)
PSR for any contingent state of affairs
It must be true that a modally contingent 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.
“With an explanation” means it is in principle explainable, whether or not the explanation is currently known. The explanation does not necessarily have to be entailing.
Assume for reductio that a modally contingent state of affairs obtains without an explanation. (Assumption for Reductio)
If a modally contingent state of affairs obtains without an explanation, there is nothing (not even it exhibiting the potency to bring about or receive that state) accounts for its obtaining in that respect.
The phrase “exhibiting the potency” refers to an existent recognized as being able to bring about or receive something that becomes actual or present in the world.
If active potency: the thing causes something to happen or be present.
If passive potency: the thing is changed or brought into being in some way.
Potency is the capacity within a being to bring about a state of affairs or to undergo change, either by being the cause of something (active potency) or by receiving change (passive potency).
“Capacity” refers to what a thing can do or is possible for it to do.
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.
If true, then a modally contingent state of affairs that obtains without an explanation (S) cannot possibly be explained by it it exhibiting the potency to bring about or receive that state.
Let S denote “a modally contingent state of affairs that obtains without an explanation.”
Therefore, S cannot possibly be explained by it exhibiting the potency to bring about or receive that state. (Hypothetical Syllogism and Definitional Substitution on #3-4)
A modally contingent state of affairs can possibly obtain if and only if it is exhibiting the potency to bring about or receive that state.
Therefore, if a modally contingent state of affairs obtains without an explanation, then S (a modally contingent state of affairs that obtains without an explanation) cannot possibly obtain. (Hypothetical Syllogism on #2 and Modus Tollens on #6-7, leading to contradiction)
Therefore, the assumption that a modally contingent state of affairs obtains without an explanation is false. (Reductio ad Absurdum on #2 & #7)
Therefore, a modally contingent state of affairs cannot obtain without an explanation. (Disjunctive Syllogism on #1 & #12)
PSR for change
A particular cannot be described as both able to become a certain way and already being that way in the same sense at the same time.
For example, if a door were simultaneously able to be open and already open, then it would simultaneously be actually closed and actually open, which is a contradiction.
If true, then it must either be the case that an existent that experiences change must have its able to become a certain way reduced or have had no able to become a certain way at all in that respect prior to becoming that way it is. (Logical Dichotomy)
An “existent” refers to something we describe as being real or existing.
Assume for reductio that an existent that experiences change had no ability at all in that respect prior to becoming that way it is. (Assumption for Reductio)
If an existent can be described as changing in some respect, then it continues to be identified as the same thing while being described as having a different state after the change compared to before in that way.
The phrase "in the same respect" means considering the same attribute or property to avoid equivocation.
If true, then it can be described as able to change in that respect.
Something can be described as able to change in a respect if and only if it can be described as having the ability to become a certain way in that respect.
Therefore, if an existent can be described as able to change in a respect, then it simultaneously can be described as having the ability to become a certain way in that respect. (Hypothetical Syllogism on #4-6)
Therefore, an existent that cannot be described as having the ability to become a certain way in that respect simultaneously can be described as having the ability to become a certain way in that respect, which is a contradiction. (Modus Ponens on #3 & #7, leading to contradiction)
Therefore, an existent that experiences change had no ability at all in that respect prior to becoming that way it is false. (Reductio ad Absurdum on #3 & #8)
Therefore, it must either be the case that an existent that experiences change must have its able to become a certain way reduced in that respect prior to becoming that way it is. (Disjunctive Syllogism on #2 & #9)
If true, then it must either be the case that the change from being described as able to become a certain way to being described as that way happens because of some reason or it happens without any reason. (Logical Dichotomy)
The inference is that there is in principle a reason or not reason, even if the reason is currently unknown. The reason does not necessarily have to be entailing.
Assume for reductio that for a referent the change from being described as able to become a certain way to being described as that way happens without any reason (i.e., it happens without any cause or explanation). (Assumption for Reductio)
If true, then the referent described as able to become a certain way is later described as being that way without any reason to bring it about.
If true, then the referent described as able to become a certain way is sufficient for it to later be described as being that way in that respect (i.e., no intervening cause or reason is needed for it to be observed with different patterns or similarities).
If true, then the referent being able to become a certain way in a respect, based on observable patterns or similarities, is logically prior to when it will later be described as being that way in that respect.
If true, then the referent’s ability to become a certain way in a respect is both sufficient and logically prior to it being described as being that way in that respect.
If true, then for a referent the change from being described as able to become a certain way to being described as that way occurs for a reason.
Therefore, for a referent the change from being described as able to become a certain way to being described as that way, which occurs for a reason, occurs without any reason, which is a contradiction. (Hypothetical Syllogism on #13-17, leading to contradiction)
Therefore, the assumption that for a referent the change from being described as able to become a certain way to being described as that way happens without any reason is false. (Reductio ad Absurdum on #12 & #18)
Therefore, it must either be the case that for a referent the change from being described as able to become a certain way to being described as that way occurs because of some reason. (Disjunctive Syllogism on #11 & #18)
Change is when something described as able to become a certain way, based on observable patterns or conditions, is later described as being that way.
Therefore, it must be the case that for a referent change occurs because of some reason. (Definitional Substitution on #19-20)
PSR for coming into existence
Something cannot be described as causing its own existence, since it would need to be described as already existing in order to cause itself to exist, which is contradictory.
Self-causation is impossible because a particular cannot be both the source and recipient of the same perceived characteristic, as this requires it to already possess what it seeks to produce, leading to a contradiction. Even in temporally simultaneous causation, the cause is ontologically prior in nominalism, as the effect’s occurrence relies on the cause’s presence or action. This means it would already need to have the thing it’s trying to cause. In other words, for a thing to cause itself, it would need to be an existing particular with the perceived characteristics to produce its own existence. But if it doesn’t exist yet, it lacks the perceived characteristics to act as a cause, making self-causation impossible.
In non-nominalist terms, this can be expressed in ontological priority, which means the cause possesses actuality that the effect depends on. If an object were to cause itself, then simultaneously ontologically (explanatorily) and in the same respect it would need to be both the cause (with actuality) and the effect (without that actuality), which is a contradiction. This is why even in temporally simultaneous causation, the cause must be ontologically prior and distinct.
Suppose y didn’t exist. Could it cause anything? No. Then it can’t cause itself, since it would need to exist first. If y causes itself, then y must exist to do the causing. But if it already exists, there's no act of causing left to do. To be a cause, it needs to produce an effect.
A particular might explain its own existence if it is a unique individual that must exist due to its specific characteristics, such that it could not fail to exist. In this case, it would be an uncaused particular, not self-caused, as it exists without depending on another particular, not because it causes itself.
If true, then an existent whose perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how it is described must either be characterized as having its own existence explained by something else or as existing without any identifiable explanation.
An “existent” refers to something we describe as being real or existing.
An entity with perceived characteristics that do not include or imply its own existence as a necessary trait would be a modally contingent entity.
Characteristics can be perceived based on the existent’s appearance, behavior, structure, interaction with other things, or through rational inference.
The inference is that there is in principle a reason or not reason, even if the reason is currently unknown. The reason does not necessarily have to be entailing.
Assume for reductio that an existent whose perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how it is described is characterized as existing without any identifiable explanation. (Assumption for Reductio)
If true, then the existent’s perceived characteristics are sufficient for it beginning to exist.
If true, then the existent’s perceived characteristics are logically prior to it beginning to exist.
If an existent’s perceived characteristics are both sufficient for and logically prior to it beginning to exist without any identifiable explanation, then an existent’s perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how it is described is characterized as having its own existence explained by something else.
Therefore, an existent whose perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how it is described is characterized as existing without any identifiable explanation and is characterized as having its own existence explained by something else, which is a contradiction. (Hypothetical Syllogism on #3-6, leading to contradiction)
Therefore, the assumption is false that that an existent whose perceived characteristics are described are characterized in such a way that its existence is not included or implied as a necessary aspect of how it is described is characterized as existing without any identifiable explanation. (Reductio ad Absurdum on #3-7)
Therefore, that an existent whose perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how it is described is characterized having its own existence explained by something else. (Disjunctive Syllogism on #2 & #8)
If true, then all existents whose perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how they are described are characterized as having their own existence explained by something else (namely that they have received existences from something else).
Therefore, all existents whose perceived characteristics are described in such a way that its existence is not included or implied as a necessary aspect of how it are described are characterized as having their own existence explained by something else. (Modus Ponens on #9-10)