There can be an internal explanation: the existence of the first cause is explained inherently if its existence is part of its essence. — A Christian Philosophy

To me, "essence" suggests a set of necessary and sufficient properties that uniquely identify an existing, individual object. Existence isn't a property; that would imply there are objects in the world that lack it - which is absurd. All objects in the world exist.

Perhaps you mean something else. If so, explain what you mean, and why anyone should accept such a metaphysical framework. I'm on the lookout for contrivances that are devised to rationalize a God to the exclusion of a purely natural first cause.

Logic has a reason for existing, as provided in the OP under section "Argument in defence of the PSR". — A Christian Philosophy

Is a logical necessity a sufficient reason or a Brute Fact.

I agree that:
1) The Unrestricted PSR states that everything has a sufficient reason
2) "Logic is part of the fabric of reality"
3) Logically A = A

However, what is the reason that A = A?
What is the reason for the existence of logic?
If logic has no reason, then logic is a Brute Fact.
Brute Facts are unexplainable and uncaused.
That logic is part of the fabric of reality is not sufficient reason why logic is part of the fabric of reality.
If, for example, A = A is a brute fact, then the Unrestricted PSR is no longer valid.

As regards your argument that "logic has a reason for existing"

I agree that
1) Truth means conformity with Reality
2) We discover Truth using Reason
3) Reason uses Deduction and Induction
4) An example of Deduction = i) the sun rises in the east, ii) therefore tomorrow the sun will rise in the east
5) An example of Induction = i) for the past 100 days the sun has risen in the east, ii) therefore the sun rises in the east.
6) If reason can find truth, then reason must mirror reality.

However, I don't agree that
1) "deduction is equivalent to the principle (or laws) of logic, in that deduction is based on an axiom (the sun rises in the east) that may or may not be true.
2) "induction is equivalent to the principle of sufficient reason", in that induction is assuming the regularity of nature, which may or may not be true, as pointed out by Hume.
3) "Reason finds truth", in that there is no logical necessity that either deduction or induction find the truth.

IE, we have no reason to think that logic has a reason for existing.

If logic has no reason for existing, then logic is a brute fact.

If logic is a brute fact, then the Unrestricted PSR is not valid.

Good catch Tim. I would put it slightly differently - there are missing steps/facts in Corvus' "logic":

P -> Q
If John is in Tokyo, then John is in Japan.
R
John is in Paris (not in Tokyo). <=== A fact from real life situation.
S
Paris is not in Japan <=== Another fact from real life situation.
R & S ->~Q
Therefore John is not in Japan.

P -> Q
R
S
R & S->~Q
Therefore ~Q — Corvus

P is irrelevant to getting ~Q. Of course this is all loosey-goosey and not formal 1st order logic

If you don't understand the point from all the examples I have give out with the explanations, then I don't see any point carrying on. I shall not waste my time or yours. I suggest you do the same. Good luck.

What you're not seeing - I don't know why - is that you're making two different arguments.

If john is in Tokyo, then John is in Japan. John is not in Tokyo. Maybe he is in Osaka or Yokohama.

But you're argument really is, If John is in Tokyo then John is in Japan. John is in Paris, therefore he is not in Japan. In this argument is the extra premise.

You can conclude John is not in Japan not because he is not in Tokyo, but because he is in Paris. — tim wood

I thought you wanted to stop discussing on this topic from your last post. I am surprised to see you keep replying.

The point here is, that the proof is about whether John is in Japan or not. (Q or not Q). It is not about whether John is in Tokyo or Osaka or anywhere in Japan. If John is in Tokyo, then he is in Japan was an assumption for the proof (Q or not Q). But the assertion from the reality was John is in Paris, which proves John is not in Japan.

This is such a simple logic, but you are worrying about whether John is in any other part of Japan, which is irrelevant for the proof.

Anyhow, this was a sideline thought for proving the PSR is not valid. It is not related directly to the OP. Hence we better stop at here. If you feel that this is a worthy of a separate OP, please go and start one. I don't think it is worth for a new OP with this topic, because it is such a simple and basic stuff.
But if you feel so, do so. Thank you for your feedback. Good luck.

I am unclear on what you mean by "natural" vs "super-natural". How do you define those two terms? — A Christian Philosophy

Roughly, natural explanations do not introduce anything outside the natural world. It rejects the idea that the world is contingent and requires a necessary cause, that is, a super or supra-natural cause that is above or beyond the limits of the natural world and on which the world is dependent.

Ok. It's official. You do not know what you're talking about. Too bad, because sometimes that kind of ignorance can be a block to learning. Modus ponens, Modus tollens, as basic to basic logic as 2+2=4 to arithmetic. Learn them.

If the PSR is true - and you think it is - then you can't just say that something is fundamental or basic. Such a status is precisely what the PSR denies.

The PSR says that everything - everything - has an explanation. So what's the explanation of it?

To me, "essence" suggests a set of necessary and sufficient properties that uniquely identify an existing, individual object. [...] Perhaps you mean something else. If so, explain what you mean, and why anyone should accept such a metaphysical framework. — Relativist

Essence is the same as identity, metaphysically speaking. As per the law of identity, everything has an identity. But sometimes a thing supervenes on more fundamental parts such that it gets its identity not from the whole but from the parts. E.g. a rock supervenes on fundamental physical elements like matter and energy, and so the rock does not have its own identity but gets its from its fundamental physical elements. Since the fundamental physical elements do not supervene on anything more fundamental (by definition of being fundamental), then their properties are essential to their identity.

Existence isn't a property; that would imply there are objects in the world that lack it - which is absurd. All objects in the world exist. — Relativist

Some objects lack existence. Otherwise, the following propositions would not make sense, but they do.

• Before I existed, I did not exist; and after death, I might cease to exist.
• Horses exist but unicorns do not.
• There will be a solar eclipse during this date in the future; but the event does not exist yet.

In contrast, the proposition "a being, whose essence is to have existence, does not exist" would not make sense. (Of course, we would need to defend why a being has that essence before claiming that such a being exists).

Essence is the same as identity, metaphysically speaking. — A Christian Philosophy

It's not a synonym. I think you're saying that an identity has a unique essence. But that still leaves "essence" undefined. You later said, "a being, whose essence is to have existence". This suggests "existing" is an essence (part of an essence?).

Suppose there is a fundamental layer of reality, for example: 20-dimensional strings. Everything is composed of them, and they are not composed of anything deeper. These strings exist at all times and locations. Does this fit your paradigm of having "existence" as part of its "essence"?

Some objects lack existence. Otherwise, the following propositions would not make sense, but they do.
Before I existed, I did not exist; and after death, I might cease to exist.
Horses exist but unicorns do not.
There will be a solar eclipse during this date in the future; but the event does not exist yet. — A Christian Philosophy

Events aren't objects; they are points (or intervals) in time. By "object", I'm refering to ontological objects- things that exist. You're conflating concepts (or definitions) with "objects".

We can refer to objects in the past, present, or future. But when we refer to unicorns, we aren't refering to objects that ever have, or ever will, exist - they are merely concepts -words with no referents to anything in time or space. You again seem to be treating a definition as a thing's essence (as you did with triangles).

You said. "a rock supervenes on fundamental physical elements like matter and energy, and so the rock does not have its own identity but gets its from its fundamental physical elements. "
If physicalism is true, the same thing can be said about you and me, as you say about the rock. This suggests you're assuming physicalism is false. Is that correct? If so, then your paradigm can't be used to show some form of immaterialism is true- because that's a premise.

What is the reason for the existence of logic? — RussellA

As per the OP section "Argument in defence of the PSR", logic (and the PSR) are first principles of metaphysics. This means they exist in all possibe worlds, which means they have necessary existence. Thus, logic and the PSR exist necessarily or inherently. This is an internal reason which is valid under the PSR.

Note, I am away for the next couple of days. I will read and respond to subsequent comments early next week.

Thank you for the definition; however I am still unclear because I am not sure what "natural world" means. Does "natural" only mean things in the world that we already know of, and "super-natural" means things that we don't know of yet? To me, both a necessary cause and contingent causes would be part of the same world or reality. The only difference is that the necessary cause has not been observed yet; although it can be deduced.

Note, I am away for the next couple of days. I will read and respond to subsequent comments early next week.

If the PSR is true - and you think it is - then you can't just say that something is fundamental or basic. Such a status is precisely what the PSR denies. The PSR says that everything - everything - has an explanation. So what's the explanation of it? — Clearbury

Something that is fundamental or basic can still meet the PSR as long as it has necessary existence. This would be an internal reason which is valid under the PSR. Now, we said that the PSR is a first principle of metaphysics. This means it exists in all possible worlds, which means it has necessary existence.

Note, I am away for the next couple of days. I will read and respond to subsequent comments early next week.

Does "natural" only mean things in the world that we already know of, and "super-natural" means things that we don't know of yet? — A Christian Philosophy

No. When you say:

We could entertain that the laws of nature are caused by prior laws, but this only pushes the problem one step back. To avoid the risk of infinite regress, a fundamental laws must be explained by something that requires an explanation but not a cause. — A Christian Philosophy

that is an indication that you know the difference. What is natural means what can be explained, to the extent it can be explained, by the laws of nature. It is because you accept the idea that everything must have a cause and reject the idea that the laws of nature are self-caused that you "deduce" that there must be something that causes the laws of nature. Rather than questioning the principle that there must be a cause you simply posit the existence of one because you believe that there must be one.

Rather than the problem of an infinite regress, the problem is one of the limits of human reason.

As per the OP section "Argument in defence of the PSR", logic (and the PSR) are first principles of metaphysics. This means they exist in all possibe worlds, which means they have necessary existence. Thus, logic and the PSR exist necessarily or inherently. This is an internal reason which is valid under the PSR. — A Christian Philosophy

There are many different type of logic, suggesting that no one logic exists necessarily. For example, there is Propositional Logic, First Order Logic, Second order logic , Higher order logic, Fuzzy logic, Modal logic, Intuitionistic Logic, Dialetheism, etc.

Logical systems also change, also suggesting that no one logical system is necessary. For example, today few would maintain that Aristotle's logic doesn't have serious limitations.

The Law of Identity "A is A" is one of the three Laws of Thought.

The Laws of Thought are axiomatic rules, taken to be true to serve as a premise or starting point for further reasoning and argument. In other words, taken to be true but not necessarily true.

The Law of Identity was described as fundamental by Aristotle, as primitive by Leibniz and to a certain extent arbitrary by George Boole.

"A is A" exists as a convenient axiom, not as a necessity.

The PSR states that everything has a sufficient reason. It is true that we use the Law of Identity "A is A" for a reason, but this is an external reason, in that it is convenient for further reasoning and argument. This is not a "sufficient reason" in terms of the PSR

We use the Law of Identity as an axiom as a convenience not because it has any internal necessity.

The Law of Identity, as an example of logic, is used for the external reason that it is convenient in further reasoning, not from any reason of internal necessity.

I forgot to say, I am away for the next couple of days. I will read and respond to your comment early next week.

The PSR is logically incompatible with there being necessary existences.

A necessary existence is something that exists and can't not. That is just a description of what one would be, not an explanation of its existence.

Therein lies the problem. The PSR says everything has an explanation. Not some things and not others. Not contingent existences but not necessary existences. Everything.

Labelling something a necessary existence does nothing to explain it. THus, any necessary existence you posit has itself to be given an explanation.

Labelling something 'a thing that needs no explanation' or 'a thing that has its explanation in itself' is no explanation of why those things exist.

Here is a different way to make the same point. Let's just posit a necessary existence. And let's suppose that there is a necessarily existing light source behind this necessary existence. Well, now there is also a necessary shadow being cast by the interaction between the necessarily existing object and the necessarily existing light source.

But note that the shadow, though it exists of necessity, is explained by the light and the object. Thus, one cannot treat 'exists necessarily' as synonymous with 'needs no explanation'. The shadow exists of necessity, yet it clearly needs - and has - an explanation.

Well, that now applies to the object and the light source too and to any other necessary existent you care to posit.