I've heard that 'God' is the only exception to the law of Cause and Effect which means that He is not dependent in His existence on anything. Can it be philosophically true? If we accepted this exception how could we make sure that the law would not be broken once again? Can we even call it a philosophical law with this exception?
There is some debate if causation exists at all. One of the founders of that debate was Hume. He observed, that one thing we don't observe is causation. We see
A happening, afterwards we see
B happening, and sometimes we say "
B happened because of
A". But the one thing we don't perceive is
B, just a succession of events. The causing is invisible. Kant agreed to a degree and proposed, that causes are not "out there" but are the way we structure the world. Nagel was convinced, that causality is just a maxim to scientific work; but it has no empirical content.
The history of the philosophical notion of causality might started with Aristotle. He proposed, that there are for types of causation: Form, Material, Final and Effect. Now in 17th century it became common sense, that the first three are metaphysical, only the last one (the classical "cause and effect") has any scientific value. This was still not the notion of causation we have today: When Kepler developed his theory of planetary movement, he was very concerned that there was nothing in it, causing the movement of the planets. So he invented sun-entities that push the planets, causing them to move. When Newton proposed his theory, he was quite uncertain that it is causal, because a given celestial body (e.g. the sun) causes an effect where it is not (e.g. at the earth). He himself thought it as preposterously violating the laws of cause and effect.
So the notion was changed again, stating that a certain state
A must guarantee that a different state
B will occur*. So we are down to "causality as determinism". No mechanism was required any more that somehow turns
A only needed to ensure
B. With the rise of the quantum mechanics, there was a lot of head-shaking, that now causality is broken. So they changed the notion again: A state A must increase the probability of state B to occur. But now we are far away from any harsh law of nature when we talk about causality. It is just defined as something that increases the chances of one thing to happen if a different thing happens. Some even say, that causation is is no part of physics at all - it is nothing but "folk science"..
Tl:dr; God (if he exists) was not the only exception to causation. And we do have to expect, that such violation will happen again (regardless if god exists or not).
*What they did not realize, is that already Newtons theory was not deterministic: Take a bowl and turn it upside down. Now take a ball and push it with the exact amount of speed it requires to stop at the highest point of the bowl. That is compatible with Newton, right? But since to the laws of Newton are invariant to the direction of time, it is also compatible with Newton, that if we position a ball at that exact spot, it will roll down again. In an uncertain direction, at a uncertain time, without a cause. Newton does not say, it will do that. He allows it. It is no deterministic theory. More on this you will find under "The Damn Dome".
I've heard that 'God' is the only exception to the law of Cause and Effect which means that He is not dependent in His existence on anything.
In both Islamic and Christian theology this is correct; but note that one might also say that he is His own cause and effect; which then leaves no exceptions to the law as you've described.
Can it be philosophically true?
The philosophy and literature on causation is huge; Aristotle for example already identifies four kinds of causes.
If we accepted this exception how could we make sure that the law would not be broken once again?
The laws of nature are not in our hands to fix; possibly you mean that how do we refine our notion of causality so that it doesn't admit exceptions - see comment above.
Can we even call it a philosophical law with this exception?
Zero was understood for a long time as not a number, for precisely the fact it referred to 'nothing'. It was an exception; now we can't get along without it.
I take it the question at hand asked in a pre-Quantum Mechanics (QM) world is this:
Rule of cause and effect = for every effect, there must be a necessary and prior cause sufficient to its causation.
This matters for Aquinas's Five Ways (proofs of the existence of God) and Aristotle's proof from which it is derived. The argument is precisely that there cannot be an endless chain of causes and that this un-caused cause would be God.
I'm not a medievalist but I gather there are several types of objections available:
Deny causality as A → B. This has grown more popular with QM. But I'm not so sure it's as wonderful as some imagine. For starters, this depends on some interpretations of QM (it is not settled that this is what happens). Second, it is not clear even if reverse causality is happening that it would happen out side of an h-bar (if you don't know what an h-bar is, then you're not qualified to dispute that).
Accept a real infinite regress of causes. Many of the Greeks did accept this as do some contemporary philosophers. For instance, the Stoics thought everything repeated after the great Conflagration.
Hume's objection: you only have proved a cause sufficient for the effect — not an infinite cause or something we can identify with the Christian or Aristotelian God.
I don't recall having read it raised (but I also don't remember the Thomistic response) -- but you can also claim there are multiple un-caused causes each capable of having originated things.
Teleology. In Aristotelian thought, the final "cause" is a metaphysical concept that implies, what I liked to call "backwards" causality. In other words, the effect precedes the cause. But I believe the more common view on the final cause is a "things" essence, hence Greek τέλος, telos (root: τελε-, "end, purpose"
For what it's worth, I speak as someone trained as a Quantum Physicist. I have a Ph.D. in particle physics. I say this to make it clear that when I speak of Quantum Mechanics, I'm not just quoting something I read by Deepak Chopra, but am basing it upon established science and research performed by me and also by actually well-known scientists.
There are boundless exceptions to the Law of Cause and Effect. Every time a radioactive particle decays, it is an effect which has no cause.
One of the most interesting things about QM is that this theory enables us to differentiate between "information we do not know and cannot get" from "information that does not exist." Data that we do not know and cannot get are called "hidden variables." Experiments have demonstrated that theories that rely on hidden variables to explain quantum phenomena make predictions about these phenomena that are inconsistent with observed results.
In more succinct terms: Any theory that allows you to predict specifically when a particular radioactive particle will decay is a theory that does not describe the universe in which we live. Literally, the information on when the particle will decay does not exist until the time when the particle decays. This has been demonstrated irrefutably, numerous times.
There is no way to logically assign a cause to such an event.
So, you might ask, do we really need to care about when tiny particles decay? We're talking issues regarding massive humans. Where's the connection?
If a radioactive particle decays, emitting an electron, and that electron crosses the junction between two neurons, the event could trigger one of the neurons to fire. One neuron firing often causes a cascade of neurons to fire. If this happened to occur in the part of your brain responsible for memory of scents, you might get a sudden flash of the smell of cooking meat flitting across your consciousness. If you're on your way home from work, you might decide to stop for a burger, rather than continuing home and having leftover pasta.
In this scenario, what you have for dinner that night would depend on whether the particle decayed while you were on the way home. In other words, the information on what you will have for dinner literally does not exist until partway through your drive home. The cause-effect chain for your decision on what to eat would not go back any farther than that moment on your drive home.
Might, might, might. How often does this sort of thing actually occur? Well, considering the amount of C14 in the environment, the amount of carbon in your brain, and the half-life of C14, that comes to about 50 decays inside your brain per second. I don't know of any research into how many of these events trigger decisions, but I doubt the number could be absolutely zero.
I guess that by the definition of the word 'law', as the scientist would use it, ideas around cause and effect do not succumb.
The classic notion has been that eternal things escape the need for a cause in the same way they escape the idea of being created by their nature of being eternal.
If I do take a chance at reading between the lines I would say you operate under a wide spread misunderstanding about how causality works under Christian Theism.
Christian Theism has not claimed that everything has a cause. To claim that an eternal thing has a cause is somewhat of a contradiction in terms.
Rather it claims that everything with a BEGINNING has a cause, that is, non eternal things.
Now I can easily see myself hearing from the critic that to build my defense of the inerrancy of causality and then to claim that it vanishes when it suits me is intellectually dishonest.
To this I would just like to add that the idea of eternal objects escaping causality is hardly held only by theism.
In the early 20th century a great deal of Enstein-ish agnosticism was based on the idea of an eternal universe needing no cause (God).
So at least if a non believer can withhold belief of a cause of the universe on the premise of it being eternal, a religious person can withhold belief of the idea that an eternal deity needs a cause.
Comments about eternal causes not pointing to a so called godless cause is based on inaccurate assumptions. First even if god was the cause, it is an assumption on faith, not proof, and then scientific reason would be more Aristotle proof. However, the proof will never be understood as rational unless we logically come to a parallel part of cause that God subordinated himself to all causes of will and non will. That he is outside of this subordinate function by the vary cause of creation, he is in eternity. We exist in time, and mother deity is our womb. So space is a continuum, but a chronisity of time is like a finger snap in time that is where god lay can not be in time but in eternity, he knows the end before the beginning of causes so to speak.