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One variation of principle of sufficient reason that Thomists use is:

Everything that exists must exist by something.

How do they prove such a statement? In particular, why can not something just exist (de facto) and not by anything else?

Edit.

I meant to use variation of sufficent reason which says: Whatever is, has that whereby it is.

This was used by Jacques Maritain in his Preface to Metaphyscis:

We have thus brought out the notion of sufficient reason. It is that in virtue of which an object is. We must, therefore, enunciate the principle of sufficient reason in one of the two following ways: Everything which is, to the extent to which it is, possesses a sufficient reason for its beings that is to say, is grounded in being, so that, to put it in another way, it is capable of explaining itself to the intellect, though not necessarily to our intellect; whatever is, is intelligibly determined; whatever is, has that whereby it is. Both these formulas must be taken in the most general sense.

Later he tries to reduce it to the principle of non-contradiction:

At a later stage we can reduce, or rather logically attach, the principle of sufficient reason to the principle of identity, by a reductio ad absurdum. This is a reflex operation which may, for example, be described compendiously as follows. The expression in virtue of whichy when we say that in virtue of which an object is, must have a meaning or be meaningless. If it is meaningless philosophy is futile, for philosophers look for a sufficient ground of things. If, on the other hand, it has a meaning it is evident that in virtue of the principle of non-contradiction it is identical with the meaning of the phrase that without which an object is not. If, therefore, anything exists which has no sufficient reason for its existence, that is to say which has neither in itself nor in something else, that in virtue of which it is, this object exists and does not exist at the same time. It does not exist because it lacks that without which it does not exist. This reductio ad absurdum proves that to deny the principle of sufficient reason is to deny the principle of identity.

To this I would respond that to deny of PSR is the same as to deny the PNC or accept that philosophy is futile, as Maritain says above.

Why (do Thomists) not accept that philosophy is futile (ie. accept that world at its core is not intelligible)? Why (do Thomists) accept that the world is intelligible rather than that it is not?

Edit 2.

As Mark Andrews noted in the comment Maritain quote needs to add italic to better understand his point. I have no time to do that so feel free to use the link on his book to read it with italics and all that.

As for the answer to my question, I think that Réginald Garrigou-Lagrange, O.P., answers my question in God: His Existence and His Nature vol. 1 (link to it is in Geremia answer, so I will accept his answer). Other answers also add some important points so I am thankful for those too.

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    They do not prove it, they postulate it. One can support it by empirical induction or by a priori arguments that identify explanations with causes, see Leibniz's versions, for example. – Conifold May 27 at 22:56
  • @Conifold: that is incorrect. Not only do they not postulate it, they explicitly deny it. Your link to an explanation of Leibniz's PSR seems unobjectionable though. – Jayson Virissimo May 28 at 3:08
  • @JaysonVirissimo If you are talking about existing by itself that is included in the shorthand motto. – Conifold May 28 at 3:10
  • @Conifold perhaps you are right, but given the final question asked by Thom, I think it more likely that they misunderstand the proposition, rather than are just using an abbreviated form of it. – Jayson Virissimo May 28 at 3:22
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    The Maritain quotes need a little work. Maritain’s use of italics adds a lot to understanding his point, but the quotes above do not include these. – Mark Andrews May 28 at 22:58
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Thomists affirm theism, but God would be a counterexample to your proposition as stated: God is something "that exists" in Himself; He does not "exist by something [else]".

Thomists' principle of sufficient reason (PSR)

A more accurate statement of Thomists' version of PSR is (Philosophical Axiom 7.1):

Everything has sufficient reason of being either in itself or in another.

Omne ens habet rationem sufficientem sui essendi in se aut in alio.

PSR is indemonstrable.

PSR, like other metaphysical principles* such as the principle of non-contradiction (PNC), is true but not directly demonstrable.

As Réginald Garrigou-Lagrange, O.P., explains in God: His Existence and His Nature vol. 1, §24, pp. 181-191 (PDF pp. 98-103), PSR can be reduced to PNC indirectly, via a reductio ad absurdum.

Discussing PNC, St. Thomas writes (Summa Theologica I-II q. 94 a. 2 co.): "on this principle all others are based" ("super hoc principio omnia alia fundantur").


*Réginald Garrigou-Lagrange, O.P., lists the following metaphysical first principles in his Reality: A Synthesis of Thomistic Thought Chapter 56: Realism And First Principles:
metaphysical principles: The principle of contradiction or identity,1380 that of sufficient reason,1381 that of efficient causality,1382 and that of finality.1383 These principles, we say, are true, because it is evident that they are primary laws, not only of our mind but of all reality. They are not merely existential judgments, but express objective and universal impossibilities. Never and nowhere can a thing simultaneously exist and not exist, can a thing be without its raison d’etre, can a non-necessary thing exist without cause, can a thing act without any purpose. Metaphysical principles admit no exception.
1380. Being is being, non-being is non-being, or, being is not non-being.
1381. Everything that exists has its raison d’etre, intrinsic or extrinsic.
1382. Every contingent being depends on an efficient cause.
1383. Every agent, including natural agents not endowed with cognition, acts for an end.

  • I meant to say: whatever is, has that whereby it is. If I accept the principle of non-contradiction, what would be wrong with saying: "whatever is, just de facto exists and that's all"? Where would in that case contradiction arise (if it would)? – Thom May 27 at 23:11
  • @Thom "whatever is, just de facto exists and that's all" This statement seems to imply that everything is a self-subsisting being. That's different from the principle of non-contradiction, which can be expressed "Being is" or "Whatever is, is". – Geremia May 28 at 15:18
  • Why does it seem to you that it implies that everything is a self-subsisting being? If we have some self-subsisting being, then that being exists by itself and that is different than saying that some being just de facto exists (ie. that it exists by no-thing). – Thom May 28 at 17:03
  • @Thom I don't see the difference. What do you mean by "no-thing", exactly? Also, study the Thomistic Thesis #1: "Potentiality and actuality so divide being that whatsoever exists either is a Pure Actuality [God], or is necessarily composed of potentiality and actuality, as to its primordial and intrinsic principles." – Geremia May 28 at 17:29
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    Let us continue this discussion in chat. – Geremia May 28 at 23:48
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There isn't really a ubiquitous reading of the principle of sufficient reason (PSR), so I think it's worth going over some distinctions and different formulations.

There are at least two major formulations of the PSR, and several sub-formulations of each of the two major formulations (my six below are by no means exhaustive). The first major formulation is in terms of explanation and the second is in terms of causation. Edward Feser, a contemporary Thomist, discusses both in Scholastic Metaphysics. In his terminology, he calls the explanatory version the PSR and the causal version the principle of causality (PC). I'll do the same, and I think it may be the PC that Thomists in particular are interested in.

The PSR comes in several sub-formulations, in terms of true propositions, beings, and events (and not everyone who accepts one formulation will accept the others):

  1. For any true proposition, p, there is a sufficient explanation for the truth of p
  2. For any existing being, b, there is a sufficient explanation for why b exists
  3. For any event, e, there is a sufficient explanation for why e occurs

The PC comes in several sub-formulations too:

  1. Whatever is a compound of act and potency (i.e. has actual properties, but also has properties that it could potentially have, but does not actually have), has an external, already actual cause for why some properties become actualized, and some merely remain as potential properties. (See Edward Feser's Five Proofs for the Existence of God, chapter titled The Aristotelian Proof, and his book Scholastic Metaphysics, the section titled 2.3 The Principle of Causality for more on this.)

  2. Whatever has its existence distinct from its essence, must have been caused to exist by something external to it. (See Edward Feser's Five Proofs for the Existence of God, the chapter titled The Thomistic Proof.)

  3. Whatever begins to exist, must have an external cause of its coming into existence. (This is from William Lane Craig's Kalam cosmological argument.)

There are two noteworthy differences between the two version:

  1. In the PC not everything has a cause; only things that are compounds of act and potency, essence and existence, or that begin to exist have a cause. In the explanatory PSR, yes everything (true propositions, beings, events) does indeed have an explanation.

  2. In the PC, causes are always external to the thing being caused, since the idea of something being self-causing is absurd. But in the explanatory PSR, things can indeed be self-explaining (such as necessary beings, or beings for which there exists a successful ontological argument).

These two points are important to keep in mind because in your question you phrase the PSR as "Everything that exists must exist by something". If we're talking about the causal PC, then as Geremia says, no Thomist would accept this because God is something which is uncaused. If we're talking about the explanatory PSR, then "Everything that exists must exist by something" is true, but that is because we're taking about explanation and some things can be self explaining, namely God (but he's certainly not self-causing).

Getting back to your actual question...

In Scholastic Metaphyics, Feser considers four arguments for the (act-potency version of the) PC: appeals to self-evidence, empirical arguments, arguments from the PNC (principle of non-contradiction), and arguments from the PSR (the explanatory version). The arguments from self-evidence and empirical arguments are basically as you would expect. As for the argument from the PNC, he agrees with you that the PNC does not imply the PC, and writes "Some Thomists explicitly reject attempts to argue from PNC to PC." He notes that there doesn't seem to be an explicit contradiction in negating the PC, and attempts to derive a contradiction can be defended against, by the very act-potency distinction that Thomists want to embrace. Feser writes:

Now if we think of causation as essentially a matter of there first being a moment when a thing in no way has being, and then a later moment when it has being, then it is indeed hard to see any outright contradiction in the idea that this transition might lack a cause. But for the Scholastic that is the wrong way to characterize the situation. We should think instead of a thing’s potency for existence (which is not nothing even if it is not actual) being actualized at any particular instant it exists (and not merely by a temporally precedent cause).

Now seen in this light it may not seem so clear that denying PC does not involve a contradiction. For if the critic of PC is saying that a thing’s potential for existence can be actualized at a given instant without there being anything that does the actualizing, does that not entail that he is saying that the thing is at that instant both potential and actual with respect to its existence? And is that not a contradiction?

But that inference too would be too quick. For of course, the Scholastic himself says that a thing is at any instant both potential and actual. There is no contradiction here, because a thing is potential and actual in different respects. It is in potency with respect to its essence, but in act with respect to its existence. Now the critic of PC, it seems, can appeal to this very difference in order to defend himself against the charge of contradiction.

Finally, he offers an argument for the PC from the explanatory PSR. (Note, that Feser himself rejects the true-proposition version of the PSR, and where explanation is understood as implication so that the explanans logically imply the explanandum. He understands explanation as "making something intelligible") He writes:

So the argument from PNC to PC appears to fail. However, a more popular approach among Scholastic writers to demonstrating PC is to appeal to the principle of sufficient reason. (Cf. Gardeil 1967, pp. 22728; Phillips 1950, pp. 235-37; Renard 1946, p. 125-27) PSR states that “everything is intelligible” (Garrigou-Lagrange 1939, p. 181), and that “there is a sufficient reason or adequate necessary objective explanation for the being of whatever is and for all attributes of any being” (Wuellner 1956b, p. 15). But if PC were false -- if the actualization of a potency, the existence of a contingent thing, or something’s changing or coming into being could lack a cause — then these phenomena would not be intelligible, would lack a sufficient reason or adequate explanation. Hence if PSR is true, PC must be true. PC is an application of PSR to things that are mixtures of act and potency and essence and existence, and which therefore – unlike God, who as pure actuality and subsistent being itself has the sufficient reason or adequate explanation for his existence within himself – require an explanation by reference to something outside them.

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In mediaeval philosophy, the verb " existing" is sometimes used in its strict sense.

Strictly speaking " existing" means " standing out of its causes".

The verb existing in this sense does not apply to God. For only an (1) actual being ( not a being "in potentia") (2) that is finite, in other words, that has a cause can be said to " exist".

If "existing" is taken in this strict sense, then the proposition " everything that exists has a cause" cannot be proved, since it is a tautology.

References :

Etienne Gilson, Being and some philosophers.

Etienne Gilson, History of Mediaeval philosophy.

Maritain on "existence " : https://books.google.fr/books?id=edXRIxIyc3wC&pg=PA88&lpg=PA88&dq=maritain,+being+existere,+outside+of+its+causes&source=bl&ots=jgt6xrWKQY&sig=ACfU3U1UFU_xBiAQHTCrN-M1zu6ZQxLCrw&hl=en&sa=X&ved=2ahUKEwiJ-ff40L3iAhXk0eAKHTEHCDYQ6AEwAHoECAcQAQ#v=onepage&q=maritain%2C%20being%20existere%2C%20outside%20of%20its%20causes&f=false

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