Is the principle of sufficient reason false?

[AlNg]

Does everything have a sufficient reason? For everything [p] which is true, is there another truth [q] which explains why that [p] is true. Suppose yes, then call that the principle of sufficient reason: SR.

Suppose you are a skeptic and you think that there are some things which don’t have sufficient reasons, i.e., there is no explanation for them.

So, being a skeptic, you try to prove that SR is false. So you give a statement A which says that there is no explanation for A, i.e., for itself. So A says it does not have a sufficient reason. Now A is either true or it is false.

Let us suppose that A is true. Then there is a statement which does not have a sufficient reason. So SR is false.

Now let us suppose that A is false. Since A is false, it does have a sufficient reason; i.e., there is an explanation showing that A is true. So A is true after all, and then we have constructed a statement without a sufficient reason, i.e., without an explanation. Therefore SR is false.

In either case, whether A is true or whether A is false, it necessarily logically follows that the principle of sufficient reason is false. So the skeptic is right after all and there are some things which do not have an explanation as to why they are true.

 

[Neithan]

Whether statement A is true or false, the sufficient reason for statement A is the skeptic. It doesn’t demonstrate anything else.

 

[AlNg]

By SR here is meant an explanation showing that something is true. So if A has SR, it means that there is an explanation showing that it is true. But A says that there is no explanation for A. So since A is true, there is no explanation for A and therefore SR is false since there is a statement with no explanation.

 

[Gorgias]

Does everything have a sufficient reason? For everything [p] which is true, is there another truth [q] which explains why that [p] is true. Suppose yes, then call that the principle of sufficient reason: SR.

Suppose you are a skeptic and you think that there are some things which don’t have sufficient reasons, i.e., there is no explanation for them.

So, being a skeptic, you try to prove that SR is false. So you give a statement A which says that there is no explanation for A, i.e., for itself.

Hang on a second, though. These two statements aren’t identical! Just because you don’t know the sufficient reason for A doesn’t mean that a sufficient reason doesn’t exist! Conflating “sufficient reason” and “knowledge of a sufficient reason” is an invalid approach, no?

Unless you’re saying that everything has a manifest sufficient reason, which is a completely different kind of assertion!

 

[Wesrock]

Hang on a second, there are different types of brute facts. It’s ontological brute facts, the being and state of an actually existent entity, for example, that generally is required to have sufficient reason. And a strong form of the PSR (there are weaker ones) isn’t that all things are explained by another, it’s something like “all things have a sufficient reason for their existence, either from itself or from another.”

Contradictory logic phrases also don’t serve as proof. There more so just nonsense. The use of logic and the belief that logic follows and the mind tracks reason and that logic is supposed to be a reason for believing something generally presupposes the PSR in itself, too.

 

[Dovekin]

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system.

This if from Wikipedia on Gödel’s incompleteness theorems.. It applies to a tightly defined situation, but the point is “true but unprovable.” True but unprovable is not the same as lacking a sufficient reason but I think it comes close enough to look at it in this context. The main issue I would think is if sufficient reason is limited to a particular type of answer, which it generally is not.

 

[o_mlly]

Does everything have a sufficient reason?

Yes, every concrete thing that exists has sufficient reason to exist. This is the self-evident first principle which underlies all science.

“… there is a sufficient reason or adequate necessary objective explanation for the being of whatever is and for all attributes of any being” (Bernard Wuellner, Dictionary of Scholastic Philosophy , p. 15).

Suppose you are a skeptic and you think that there are some things which don’t have sufficient reasons, i.e., there is no explanation for them.

I would have to be a radical skeptic to think so. And, being a radical skeptic, there would be no point in arguing with me as I would still be arguing with myself that what I claim is also not true.

So if A has SR, it means that there is an explanation showing that it is true.

If A is a concrete thing that exists then A has SR to exist.

It is also self-evidently true that A cannot be greater than the cause(s) which explain A’s existence, i.e., the principle of proportionate causality.

 

[Rhubarb]

I’ve never understood why the principle of sufficient reason must be true, except as an unproven axiom itself.

 

[AlNg]

I’ve never understood why the principle of sufficient reason must be true, except as an unproven axiom itself.

Looking at this somewhat differently suppose that S is as follows - S: everything has a sufficient reason.
Suppose that there is an axiom which says that S is true. then what is the sufficient reason to accept that axiom. Suppose that A is the sufficient reason to accept that the axiom is true. Then what is the sufficient reason to accept A. Suppose it is B. then what is the sufficient reason to accept B? Suppose it is C. And so on, which places you in a repugnant infinite regress. Then what is the sufficient reason for the infinite regress? And so on. Continuing in this manner it is impossible to construct a sufficient reason for everything in an algorithmic manner. So whether there is a sufficient reason for everything or not is undecidable.

 

[Dovekin]

This is like most “infinite” regress. It ends with God, the uncaused cause, the uncreated creator, the gratuitous giver who exists for no reason except to exist.

Looking at Gödel yesterday, I was reminded of the Liar paradox. This is the argument you used against sufficient reason yesterday. The Liar says “I am lying.” Is he telling the truth=lying, or lying=telling the truth?

 

[Gorgias]

Looking at this somewhat differently suppose that S is as follows - S: everything has a sufficient reason.
Suppose that there is an axiom which says that S is true. then what is the sufficient reason to accept that axiom.

Hang on a second. Are you trying to say that, in the set of all statements, then for every statement which is true, there exists some statement that substantiates that statement, but this isn’t itself sufficient? I’m not seeing how that holds up.

If I were trying to formalize it, I’d say that you’re first saying that:

for all si in S = {s1… sn}, iff (si v 0) then ∃ sj, s.t. sj → si.

Right?

However, since sj → si, then we’re good, right? The fact that there’s another sk s.t. sk → sj doesn’t imply “regress” any more than any other inductive proof, no?

 

[Neithan]

I was trying to think what kind of semantic content this statement could possibly have, or if it’s just an imaginary but analytic impossibility, like 'pataphysics.

I think you first have to demonstrate that such a statement has any metaphysical or epistemological value. Otherwise it doesn’t really have anything to do with sufficient reasons for reality, it’s just a word puzzle.

 

[EndTimes]

Does everything have a sufficient reason?

Such as for examples?

 

[AlNg]

Such as for examples?

Such as for example the axiom:
SR: Everything has a sufficient reason.

 

[rom]

Does everything have a sufficient reason?

Yes, everything has a sufficient reason. But you need to understand and state the principle correctly.

The principle of sufficient reason can be stated ontologically and epistemologically.

Ontologically, the principle of sufficient reason states that everything that exists must have a reason for its existence. It does not mean that everything depends on a cause, or that there must always be something outside itself that explains its existence. Not at all. Everything that exists must, indeed, have a reason for its existence, but the reason could also be something within itself, its essential perfection, rather than some cause outside itself that explains its existence.

Epistemologically, the principle of sufficient reason states that every proposition that is true must have some evidence that manifests its truth. It does not mean that every proposition [p] depends on the truth of another proposition [q] to manifest its truth. Not at all. Every proposition [p] that is true must, indeed, have evidence manifesting its truth, but that evidence could also be within itself, in the fact that it is self-evident as soon as the terms are understood, rather than in some exterior evidence supplied by another proposition.

For everything [p] which is true, is there another truth [q] which explains why that [p] is true.

Not always. If a true proposition [p] is self-evident, such as the axioms of mathematics, they do not require another proposition [q] to manifest its truth. The truth of [p] becomes clear as soon as its terms are understood, and the principle of sufficient reason is epistemologically satisfied. There is no need to find a proof for axioms.

The statement, “For everything [p] which is true, there is another truth [q] which explains why [p] is true” is NOT the principle of sufficient reason. To correctly state the principle of sufficient reason epistemologically, we should say, “For everything [p] which is true, there must be evidence that manifests its truth.” But that evidence does not have to come from another proposition [q]. The evidence can be manifest, as in the case of axioms and self-evident propositions, from the very meaning of the terms of the proposition. So, to show why [p] is true, all that is required is not to prove it, but to explain the meaning of the terms of the proposition. Thus, the axiom, “Every number is equal to itself,” does not have to be proved. But to someone not familiar with the terms, you may need to explain what a number is, and what equality is, etc. Once the terms are understood, the truth of the proposition immediately manifests itself.

 

[rom]

By SR here is meant an explanation showing that something is true. So if A has SR, it means that there is an explanation showing that it is true. But A says that there is no explanation for A. So since A is true, there is no explanation for A and therefore SR is false since there is a statement with no explanation.

If a proposition is true, then by the principle of sufficient reason the evidence is either found in itself or in another proposition. If in another proposition, then the evidence for that proposition is again found either in itself or in another, and so on. This cannot regress to infinity, or else nothing would be known as true. Therefore, if a proposition is known to be true, it is because at the end of the line there is a proposition whose evidence is within itself, and whose truth provides evidence for all other propositions that depend on it.

The above is talking epistemologically. Ontologically, a similar line of reasoning is often used to prove the existence of God. Thus, if something exists, then by the principle of sufficient reason the reason for its existence is either found within itself, or in another. If in another being, then the reason for this being’s existence is again either found in itself, or in another, and so on. This cannot regress to infinity, or else nothing would exist. Therefore, if something exists, you will reach a Being whose reason for its existence is found in itself, or in its own perfection, and nowhere else. This we call God. Therefore, God exists.

 

[EndTimes]

Everything has a sufficient reason.

Sufficient Reason means nothing?