necessity also applies to things with essential properties. E.g. "3 sides" is an essential property of a triangle. Thus, if a thing is a triangle, it logically or necessarily follows that it has 3 sides. Therefore, we can call essential properties "necessary properties". — A Christian Philosophy

Triangles are abstractions, and don't exist in the real world. Rather, objects exist that have 3-sides. What you're calling "essential properties" is simply the definition we've assigned to the word "triangle". A word necessarily having its definition is just semantics, not metaphysical essentialism.

Would this mean that this type of first cause exists without a reason, and thus would violate the PSR? Whereas my first cause, the being whose existence is an essential property, has a sufficient reason to exist: it is an internal reason, that is, its existence is explained logically or inherently. — A Christian Philosophy

No internal reason is needed for a first cause to exist necessarily. A first cause cannot exist contingently, because it is logically impossible for it to be contingent upon anything*. So there's no need for the (ad hoc) contrivance of treating a term in logic as an ontological property.

----------------
*Y is contingent iff there exists an X that accounts for Y, and it is metaphysically possible for X to account for ~Y.

The existence of a being whose existence is an essential property is deduced directly from the PSR. — A Christian Philosophy

What is deduced from a questionable principle is questionable.

This thing whose existence you posit designs the laws of nature that cannot be explained naturally.
— Fooloso4
What else could it possibly be? — A Christian Philosophy

Positing a super-natural being in order to explain what you cannot explain is question begging. It assumes what is in question, that there must be a comprehensive reason for what is.

To avoid the risk of infinite regress, the fundamental laws must be explained by something that requires an explanation but not a cause. — A Christian Philosophy

What is this something? What is the explanation for this something?

There are different formulations of the PSR. You cite one version of it. See SEP - Principle of Sufficient Reason. — RussellA

I asked you:

Whose version of the PSR are you relying on? — Fooloso4

The closest you came to answering is:

For Leibniz, God knows all events whether known or unknown by humans. — RussellA

You say:

A principle that cannot be justified shouldn't be used. — RussellA

but when I asked:

Are you arguing against the PSR? — Fooloso4

your response was:

No, I am arguing that the PSR cannot be applied to unknown events — RussellA

Once again, whose version of the PRS are you relying on?

And again, the Webb telescope makes known to us events that were previously unknown. According to Leibniz version, the reason for the existence of these events is present in the events whether we are aware of the event or not. The reason is inherent to the event, not to our knowledge of it.

I asked you.................Whose version of the PSR are you relying on?: — Fooloso4

There is no one version of the PSR. There are different formulations. The PSR is a family of principles (SEP - PSR).

For Leibniz, God knows all events whether known or unknown by humans. I am making the case that in the absence of a God, it wouldn't be sensible to apply a PSR to unknown events.

Is there any argument that could explain how we can know something about an unknown event, such as the unknown event having a reason?

There is no one version of the PSR. There are different formulations. The PSR is a family of principles (SEP - PSR). — RussellA

And which of those versions says that it is contingent on our knowing that an event has occurred? Or is that your own contribution?

I am making the case that in the absence of a God, it wouldn't be sensible to apply a PSR to unknown events. — RussellA

How does our knowing that an event has occurred affect the event such that prior to our knowledge of it it did not or might not have a reason for occurring? We can now see events that occurred millions of years ago, how does our seeing it now but not previously change what occurred or why it occurred?

Is there any argument that could explain how we can know something about an unknown event, such as the unknown event having a reason? — RussellA

We cannot say anything about an event we know nothing about, but we do know that billions of events occurred without our knowledge of them occurring until billions of years later. In what way does our coming to know them change the reason for them occurring?

And which of those versions says that it is contingent on our knowing that an event has occurred? — Fooloso4

There is no one definitive version of the PSR.

You interpret the PSR as saying that every event, known or unknown, must have a reason.

It is not a contradiction. An event is something that happens. According to the PSR there is a reason for it happening. Our knowledge of something happening is not a requirement for it to happen. The Webb telescope has detected the earliest known galaxy, JADES-GS-z14-0, which formed about 290 million years after the Big Bang. There is a reason for it happening, whether we know it happened or not. — Fooloso4

I don't believe that the PSR can logically be formulated to apply to unknown events.
===============================================================================

We can now see events that occurred millions of years ago, how does our seeing it now but not previously change what occurred or why it occurred? — Fooloso4

I agree that our seeing an event that occurred millions of years ago doesn't change the original event

It might be that the original event occurred for a reason, or it might be that the original event occurred for no reason. EG, if an event happens where two single objects come together to form two objects, in what sense can the reason for two objects be two single objects.

The Principle of Sufficient Reason is a principle, and principles only exist in the mind.

When the original event happened, the event wasn't following the principle that it could only happen if there was a reason.

As principles only exist in the mind, the mind can only apply principles to things it knows about, meaning that the mind cannot apply principles to things it doesn't know about.

The original event wasn't determined by a Principle. It is only the mind that can determine whether an event followed a Principle, and these can only be events known by the mind.
===============================================================================

We cannot say anything about an event we know nothing about — Fooloso4

I agree when you say that we cannot say anything about an event we know nothing about.

But then you say we can say something about an event we know nothing about, ie, that it must have a reason.

There is no one definitive version of the PSR. — RussellA

That is not what I asked. I asked which version says that it is contingent on our knowing that an event has occurred.

I don't believe that the PSR can logically be formulated to apply to unknown events. — RussellA

Then you reject every version of the PSR that does not explicitly state that the principle only applies to events we know of.

The Principle of Sufficient Reason is a principle, and principles only exist in the mind. — RussellA

It makes an ontological claim.

When the original event happened, the event wasn't following the principle that it could only happen if there was a reason. — RussellA

How do you know that?

The original event wasn't determined by a Principle. — RussellA

The principle does not determine the event. The event occurs in accord with the principle. The principle is not the cause.

But then you say we can say something about an event we know nothing about, ie, that it must have a reason. — RussellA

That is not what I said. What I said was:

We cannot say anything about an event we know nothing about, but we do know that billions of events occurred without our knowledge of them occurring until billions of years later. — Fooloso4

I gave the example of

the earliest known galaxy, JADES-GS-z14-0 — Fooloso4

. Until recently we did not know it existed. We now know it does. According to the PSR it must have a reason for existing. That reason was not created by our discovery of it.

That is not what I asked. I asked which version says that it is contingent on our knowing that an event has occurred.............Then you reject every version of the PSR that does not explicitly state that the principle only applies to events we know of.........................It makes an ontological claim. — Fooloso4

There are no definitive versions of the PSR. The PSR is a family of principles.

The PSR is, in fact, a family of principles.......................Variants of the PSR may be generated not only by placing restrictions on the relata at stake (both the explananda and the explanantia), but also on the notion of the relation at stake. (SEP - PSR)

The PSR may be factive, true in actual or possible worlds, or regulative, guiding our study of nature.

Another distinction can be drawn between a factive, as opposed to merely regulative, version of the Principle. A regulative version of the PSR would consider it as a condition for intelligibility (on a par with the Law of Non-Contradiction) and thus as guiding our studying of nature. The factive version simply states that the Principle is true in actuality (or even in all possible worlds). (SEP - PSR)

===============================================================================

How do you know that? — Fooloso4

Principles exist in the mind, not outside the mind.
===============================================================================

Until recently we did not know it existed. We now know it does. According to the PSR it must have a reason for existing. That reason was not created by our discovery of it. — Fooloso4

I can understand a principle that states that we know that things we know about must have a reason, but I find it hard to accept a principle that states that we know that things we don't even know about must have a reason.

Do you know of any argument justifying how we can know that something that we don't even know about must have a reason?

We could continue to go round and round, but I won't.

What the principle of sufficient reason says is that there were causes sufficient to bring P about. Causes sufficient to bring about P can be much more than is necessary. — Clearbury

That's the PSR on the metaphysics side. The PSR on the epistemology side demands that explanations be no more than necessary. This is because the PSR is so strict that it not only demands a reason for the data, but also demands a reason to posit the explanation itself. Thus, the explanation is posited to account for the data, and the data must support the explanation. If the explanation is more than necessary, it means it is not supported by the data, and thus it fails the PSR.

But the principle of sufficient reason - which says that everything has an explanation - must now be applied to the law of non-contradiction. What explains why it is true? — Clearbury

Logic is a first principle of epistemology. This is defended in the OP under section "Argument in defence of the PSR", steps 1 to 4. As a first principle of epistemology, an appeal to logic is a valid form of reasoning that fulfills the PSR.

You also give the examples of things that don't have a sufficient reason, but rather logical necessity, such as "All bachelors are unmarried". — RussellA

Logical necessity is a type of sufficient reason. It is reason type 1 in the OP section "PSR in Metaphysics".

If we know everything in the universe, then the PSR makes sense.
If we can verify everything in the universe, then we know everything in the universe.
We cannot verify everything in the universe.
Therefore we don't know everything in the universe.
==========================================
"Therefore the PSR is makes sense." is not true.

Prove Q
P -> Q
R -> P
~R
~P
=======
~Q

What do you think of this proof?

M.P.: from (p>q) ^ p, q. M.T.: from (p>q) ^ ~q, ~p. Yours is neither, not a proof. I think it is called the fallacy of denying the antecedent. And I'm pretty sure you know this, but just got crossed up.

My reading of the PSR is that given a something, one should be able to come up with some reason for it. Thus, the reason for the volcano's not erupting is the sacrifices we make to the volcano gods. And from this it is clear that the master the reason serves is not any kind of ultimate reality - whatever that might be - but whatever works for the narrative being told.

But of course the universe is filled with somethings about which the best we can do is say, "We don't know."

Yours is neither, not a proof. I think it is called the fallacy of denying the antecedent. And I'm pretty sure you know this, but just got crossed up. — tim wood

The argument was to prove Q is untrue.
P -> Q was an assumption.
R -> P was an assumption too.
But we know that by the fact, R is not true (~R), which infers P is not true too (~P). It wasn't a denial of the antecedent. The antecedent which was assumed true was proved untrue. Therefore by MP, Q is untrue. Does this make sense?

R -> P was an assumption too. — Corvus

However, R (apparently) is not true, therefore ~R, therefore R is F.
R>P, then, is F>P, which is itself always true, but that says nothing about P.
In brief, from P>Q, all that can be known about Q from the argument is that if P>Q and P, then Q is true. Period. Btw, you infer, everyone/thing else implies.

That's the PSR on the metaphysics side. The PSR on the epistemology side demands that explanations be no more than necessary. — A Christian Philosophy

We're going on circles. No, they're two completely distinct principles. One says everything has an explanation. The other says that, other things being equal, the simpler explanation is the true one. Or that we have reason to think the simpler is the true one (for it won't necessarily be true).

They're just quite plainly distinct

Logic is a first principle of epistemology. This is defended in the OP under section "Argument in defence of the PSR", steps 1 to 4. As a first principle of epistemology, an appeal to logic is a valid form of reasoning that fulfills the PSR. — A Christian Philosophy

You haven't answered the question. What explains it?

However, R (apparently) is not true, therefore ~R, therefore R is F.
R>P, then, is F>P, which is itself always true, but that says nothing about P.
In brief, from P>Q, all that can be known about Q from the argument is that if P>Q and P, then Q is true. Period. Btw, you infer, everyone/thing else implies. — tim wood

OK, good point. How about this?

P -> Q
Q -> R

~P
~R
~(P -> R)
~R

Therefore ~Q (Contranegative MT)

From Q>R and ~R, you can conclude ~Q. That's just modus tollens.

Triangles are abstractions, and don't exist in the real world. — Relativist

Sure. The reason I used the example of a triangle is because it is easy to understand its identity or essence, and thereby also understand its essential and non-essential properties.

But some things in the real world also have metaphysical identities or essences. Even if we suppose that the world is merely physical, which means that everything supervenes on matter and energy, then at least matter and energy have identities (i.e. as matter is not the same thing as energy, they have different identities), and thus also have essential properties. E.g. matter has the essential properties of having a mass, volume, shape, etc. So, if a thing is made of matter, then it necessarily follows that it has a mass.

No internal reason is needed for a first cause to exist necessarily. A first cause cannot exist contingently, because it is logically impossible for it to be contingent upon anything*. So there's no need for the (ad hoc) contrivance of treating a term in logic as an ontological property. — Relativist

If I understand correctly, you say that the first cause's existence is necessary, but only because there is no prior cause and not because its existence is an essential property of its identity. But then, how do you explain the fact that its existence is necessary, if not inherently? If this fact is left unexplained, then it violates the PSR.

What is deduced from a questionable principle is questionable. — Fooloso4

What is questionable about the PSR?

Positing a super-natural being in order to explain what you cannot explain is question begging. It assumes what is in question, that there must be a comprehensive reason for what is. — Fooloso4

I did not use the word "super-natural". We should simply try to follow the rules of the PSR to its logical conclusion. And my conclusion is that a thing whose existence is essential is necessary to explain the existence of all other contingent things, including the laws of nature. If you can point out an error in the reasoning, then fair, and if not, then the conclusion stands.

Logical necessity is a type of sufficient reason. It is reason type 1 in the OP section "PSR in Metaphysics". — A Christian Philosophy

If you accept an unrestricted form of the Principle of Sufficient Reason (PSR), you will require an explanation for any fact, or in other words, you will reject the possibility of any brute, or unexplainable, facts. (SEP - PSR)

Is logical necessity a brute fact?

For example, is the logical necessity that "A triangle has three sides" a brute fact?

A Brute Fact has no explanation.

I am not clear on the distinction between logical necessity and brute fact.

For example, there is something that has three sides and is named triangle.

In what sense is "triangle" an explanation of "something that has three sides"?

If not an explanation, then it is a brute fact that a "triangle" is "something that has three sides"

In that case, the Unrestricted PSR is no longer valid.

R -> P was an assumption too. — Corvus

However, R (apparently) is not true, therefore ~R, therefore R is F.
R>P, then, is F>P, which is itself always true, but that says nothing about P. — tim wood

This is still not clear to me. What is R is F? Is it a misspelling? Or F for False?

From the assumption R -> P, but we know ~R is true. So we introduce ~R, which makes ~R <-> ~P
It says about the P, that P must be ~P.
It proves ~Q.

P -> Q
~P
~Q

So your comment,

R>P, then, is F>P, which is itself always true, but that says nothing about P. — tim wood

is unclear. Could you please confirm the point? Thanks.

In brief, from P>Q, all that can be known about Q from the argument is that if P>Q and P, then Q is true. Period. — tim wood

Could you not do following?
P -> Q
~P
Therefore ~Q

What is questionable about the PSR? — A Christian Philosophy

We have been through this already.

I did not use the word "super-natural". — A Christian Philosophy

When natural explanations cannot explain why there is anything at all you resort to a super-natural explanation even if you do not use that word.

We should simply try to follow the rules of the PSR to its logical conclusion. — A Christian Philosophy

This is circular reasoning.

And my conclusion is that a thing whose existence is essential is necessary to explain the existence of all other contingent things — A Christian Philosophy

All other contingent things? Something whose existence is necessary is not something that is contingent. If all natural things are contingent then what is necessary is not something natural but rather the cause of what is natural.

Why must there be a reason for what is? Positing a principle that there must be is circular and question begging.

From Q>R and ~R, you can conclude ~Q. That's just modus tollens. — tim wood

According to L. S. Cauman (First-order Logic: An Introduction 1998, pp.29), introducing more premises and inducing the chain-rule derivation in arguments gives us more logically tight proof rather than just relying on the simplest MT or MP.

Chain no stronger than its weakest link, and MP and MT the strongest of links. It takes a while to get used to how the if-then of logic works. Given P>Q, it is easy to suppose something about P or Q. But from just the truth of P>Q alone, nothing about either severally can be concluded.
Consider:
1) If it's raining, the ground is wet. It is raining, (therefore) the ground is wet. And this MP.
2) The ground is not wet, (therefore) it is not raining. And this MT.
3) But suppose it is not raining - denying the antecedent - it is tempting to conclude that the ground is dry. And that is a mistake. And it is a mistake because the original hypothetical speaks only about the consequence of rain. It says nothing, zero, zilch, nada about what happens if it's not raining.

This is elementary stuff; it doesn't do to be mistaken on it. On line or in many books is instruction on very basic logic, which MP and MT are. Consult them; you will be glad you did.

So your comment,
R>P, then, is F>P, which is itself always true, but that says nothing about P.
— tim wood
is unclear. Could you please confirm the point? Thanks. — Corvus

In any P>Q, however simple or complicated looking, if P is false (F), then P>Q is true. And from F>Q, nothing may be concluded about the status of Q. Them's the rules.

In any P>Q, however simple or complicated looking, if P is false (F), then P>Q is true. And from F>Q, nothing may be concluded about the status of Q. Them's the rules. — tim wood

Are you not just talking from Truth table, that nothing may be concluded about the status of Q?
Remember, we were to prove whether Q is true or not. P -> Q is an assumption introduced to embark on the proof.

From the proof process, we came to know that the assumption P -> Q is not true, which infers Q not true. This is a proof process, not Truth table.

This is elementary stuff; it doesn't do to be mistaken on it. On line or in many books is instruction on very basic logic, which MP and MT are. Consult them; you will be glad you did. — tim wood

The proof is inspired by the Cauman's book "First Order Logic". MP MT and also chain-rule are all in use in the proof.

~P, ~R was from chain rule, but ~R therefore ~Q is MT.
Q -> R
~R
Therefore ~Q

They are all there. It is just the chain-rule derivation was adopted in introducing the premises.