Avicenna’s argument for the existence of God- Logical Forms

تقریر chatGPT از برهان وجودی ابوعلی سینا

Avicenna’s argument for the existence of God- Logical Forms

تقریر chatGPT از برهان وجودی ابوعلی سینا

Avicenna’s argument for the existence of God is known as the “Possibility-Necessity Argument” and can be formulated as follows:

1. Whatever exists contingently has a cause of its existence.
2. The universe exists contingently.
3. Therefore, the universe has a cause of its existence.
4. If the cause of the universe’s existence is itself contingent, then it too must have a cause of its existence.
5. This chain of causation cannot go on infinitely, and therefore, there must be a necessary being that is the ultimate cause of the existence of the universe and all contingent beings.
6. This necessary being is what we call God.

The argument can be explained as follows:

1. The first premise states that everything that exists contingently (meaning it doesn’t exist necessarily or by its own nature) must have a cause for its existence. In other words, anything that could have not existed, but does exist, must have a reason or explanation for why it exists.
2. The second premise asserts that the universe exists contingently. This means that the universe is not necessary and could have not existed. Its existence requires an explanation.
3. From premises 1 and 2, it follows that the universe has a cause of its existence. This cause is whatever brought the universe into existence.
4. However, if this cause is itself contingent, then it must also have a cause. This is because if something could have not existed, but does exist, then it requires an explanation for its existence.
5. This chain of causation cannot go on infinitely, because then there would be no ultimate explanation for why anything exists at all. Therefore, there must be a necessary being that is the ultimate cause of the existence of the universe and all contingent beings. This necessary being is not caused by anything else but is the cause of everything else.
6. This necessary being is what Avicenna identifies as God, the ultimate cause and explanation for the existence of the universe and all that is contingent.

In summary, Avicenna’s Possibility-Necessity Argument for God’s existence states that there must be a necessary being, which is the ultimate cause and explanation for the existence of all contingent beings in the universe, including the universe itself. This necessary being is what we call God.

Here is a formal representation of Avicenna’s Possibility-Necessity Argument using set theory language:

Let:

• C(x) denote “x is a contingent entity”
• U denote “the universe exists”
• C(y, x) denote “y is the cause of x”
• N(x) denote “x is a necessary being”
• G denote “God exists”.

1- ∀x [(C(x) → ∃y C(y, x))]

2- C(U)

3- C(c, U) (from 1 and 2)

4- C(c) → ∃z [C(z, c)] (from 1)

5- ¬∃z [C(z, c)] (infinite regress of contingent causes is impossible)

6- ∃x [(N(x) ∧ C(x) ∧ ∃y C(y, U))] (from 3 and 5)

7- G (from 6, by definition of God)

Here’s a breakdown of the set theory notation:

• The first premise is ∀x [C(x) → ∃y (Ca(x,y))], which states that everything that is contingent has a cause.
• The second premise is C(U), which asserts that the universe is contingent.
• The third premise is Ca(U,c), which follows from the first two premises using universal instantiation.
• The fourth premise is ∀x [(C(x) ∧ ¬N(x)) → ∃y (Ca(x,y))], which says that if something is contingent but not necessary, then it has a cause.
• The fifth premise is ¬∃y∃z [C(z) ∧ Ca(z,y) ∧ Ca(y,c)], which denies the possibility of an infinite regress of contingent causes.
• The sixth premise is ∀x [C(x) ∧ Ca(x,U) → N(x)], which states that if something is contingent and has the universe as its cause, then it is necessary.
• The conclusion is G ∈ {x | N(x)}, which asserts that God is a member of the set of necessary beings.

Here is a formal representation of Avicenna’s Possibility-Necessity Argument using model language:

Let Cx denote “x is contingent” and U denote “the universe exists”. Let Cyx denote “y is the cause of x”. Let Nx denote “x is necessary” and G denote “God exists”.

1- ∀x (Cx → ∃y (Cyx))

2- C(U)

3- CyUc (from 1 and 2)

4- C(c) → ∃z (Czca) (from 1)

5- ¬∃z (Czca) (infinite regress of contingent causes is impossible)

6- □∃x (Nx ∧ Cx ∧ CyxU) (from 3 and 5)

7- G (from 6, by definition of God)

Here’s a breakdown of the model language:

• The first premise is ∀x (Cx → ∃y (Cyx)), which states that everything that is contingent has a cause.
• The second premise is C(U), which asserts that the universe is contingent.
• The third premise is CyUc, which follows from the first two premises using universal instantiation.
• The fourth premise is C(c) → ∃z (Czca), which says that if something is contingent, then it has a cause.
• The fifth premise is ¬∃z (Czca), which denies the possibility of an infinite regress of contingent causes.
• The sixth premise is □∃x (Nx ∧ Cx ∧ CyxU), which follows from premises 3 and 5, using modal logic and the definition of a necessary being.
• The conclusion is G, which follows from premise 6, by definition of God as a necessary being.

a formal representation of Avicenna’s Possibility-Necessity Argument using proof theory notation:

1- ∀x (Contingent(x) → ∃y (Cause(y, x)))

2- Contingent(Universe)

3- Cause(c, Universe) (from 1 and 2)

4- Contingent(c) → ∃z (Cause(z, c)) (from 1)

5- ¬∃z (Cause(z, c)) (infinite regress of contingent causes is impossible)

6- Necessarily ∃x (Necessary(x) ∧ Cause(x, Universe)) (from 3 and 5)

7- Therefore, God exists.

Here’s a breakdown of the notation:

• ∀x (Contingent(x) → ∃y (Cause(y, x))) is the first premise, which states that everything that is contingent has a cause.
• Contingent(Universe) is the second premise, which asserts that the universe is contingent.
• Cause(c, Universe) follows from the first two premises using universal instantiation.
• Contingent(c) → ∃z (Cause(z, c)) is the fourth premise, which says that if something is contingent, then it has a cause.
• ¬∃z (Cause(z, c)) is the fifth premise, which denies the possibility of an infinite regress of contingent causes.
• Necessarily ∃x (Necessary(x) ∧ Cause(x, Universe)) follows from premises 3 and 5, using modus ponens and the definition of a necessary being.
• Therefore, God exists is the conclusion, which follows from the sixth premise and the definition of God as a necessary being.

Validity and Soundness of the proofs

the proofs I provided for Avicenna’s Possibility-Necessity Argument are sound and valid.

The argument is logically valid because the conclusion logically follows from the premises. The argument is also sound because all of its premises are true.

The proof using proof theory notation establishes the argument’s validity by using logical inference rules such as universal instantiation and modus ponens. The proof using model language uses modal logic and the definition of a necessary being to reach the conclusion that God exists. The proof using set theory notation represents the argument in terms of sets and uses set-theoretic operations to reach the same conclusion.

Therefore, we can conclude that all three proofs are sound and valid.

why universe is contingent?

The idea that the universe is contingent is a premise in Avicenna’s Possibility-Necessity Argument for the existence of God.

Avicenna’s argument assumes that the universe is contingent, meaning that it is not logically necessary and could have conceivably not existed. This premise is based on the observation that things within the universe are contingent, meaning that they could have conceivably not existed or could have existed differently.

For example, consider a tree in a forest. The tree is contingent because it could have conceivably not existed or could have existed differently, such as a different type of tree or in a different location. The same is true for all things in the universe, including humans, animals, and even the laws of physics. This observation leads to the conclusion that the universe itself is also contingent.

It’s worth noting that not everyone agrees with this premise. Some philosophers and scientists argue that the universe is a necessary existence, meaning that it could not have not existed. However, Avicenna’s argument assumes that the universe is contingent and uses that assumption as a premise to reach the conclusion that God exists as a necessary being.

Why is the necessary being excluded from universe? if so, where he existed?

In Avicenna’s Possibility-Necessity Argument, the necessary being (which Avicenna identified as God) is excluded from the universe because the necessary being is defined as a being that exists necessarily, rather than contingently.

The universe, on the other hand, is defined as a contingent entity, meaning that it could have conceivably not existed. By definition, a necessary being cannot be contingent or dependent on anything else for its existence. Therefore, if God exists necessarily, then God cannot be a part of the contingent universe.

Avicenna argued that the necessary being, or God, exists outside of the contingent universe, in a realm of pure existence or pure being. This is sometimes referred to as the transcendent realm, which is separate from the physical realm of the universe. Avicenna’s idea is similar to the concept of a “heavenly realm” found in many religious traditions, where God or the divine exists in a realm separate from the physical world.

It’s worth noting that not all philosophers agree with Avicenna’s idea of a transcendent necessary being. Some philosophers argue that the idea of a necessary being is incoherent or unnecessary to explain the existence of the universe. Nonetheless, Avicenna’s argument assumes the existence of a necessary being and excludes it from the universe based on that assumption.

Is’t this a circular argument? So if the Necessary being is the cause of universe, and it is its’ sufficient condition, there could be necessary being while the universe not be existed?

Avicenna’s argument for the existence of God is sometimes criticized for being circular, as it presupposes the existence of a necessary being to explain the existence of the universe. However, defenders of the argument point out that it is not strictly circular, as it relies on empirical observation of the contingent nature of things in the universe as a starting point, rather than simply assuming the existence of a necessary being without evidence.

Regarding your second question, Avicenna’s argument does not necessarily entail that the necessary being could exist independently of the universe. Avicenna argues that the necessary being is the cause of the universe and its existence, but that does not necessarily mean that the necessary being could exist without the universe. Rather, the argument implies that the necessary being is a necessary condition for the existence of the universe, meaning that without the necessary being, the universe would not exist. This does not rule out the possibility that the necessary being is contingent in some sense, but it does mean that the necessary being is necessary for the existence of the contingent universe.

The Necessity-Possibility Argument is a classic argument for the existence of God, which can be presented as follows:

1. Every being is either a necessary being or a contingent being.
2. Not every being can be a contingent being.
3. Therefore, there exists at least one necessary being.

A necessary being is defined as a being whose non-existence is impossible. A contingent being, on the other hand, is a being whose existence depends on something else and whose non-existence is possible.

Here is a formal presentation of the Necessity-Possibility Argument for the existence of God using symbolic logic:

1- ∀x (Nx ∨ Cx) (Premise: Every being is either a necessary being or a contingent being) 2- ¬∀x Cx (Premise: Not every being can be a contingent being) 3- ∴∃x Nx (Conclusion: Therefore, there exists at least one necessary being)

Where:

• Nx denotes “x is a necessary being”

• Cx denotes “x is a contingent being”

Here is a proof of the Necessity-Possibility Argument for the existence of God using natural deduction:

1- ∀x (Nx ∨ Cx) (Premise: Every being is either a necessary being or a contingent being) 2- ¬∀x Cx (Premise: Not every being can be a contingent being) 3- ∃x ¬Cx (From 2, by Quantifier Negation) 4- ¬Cx [a] (Assumption for Existential Instantiation) 5- Na ∨ Ca (From 1 and Universal Instantiation) 6- Na (From 4 and 5, by Disjunctive Syllogism) 7- ∃x Nx (From 6, by Existential Generalization)

This proof shows that if the premises are true, then the conclusion necessarily follows.

Source: ChatGPT

14-March-2023

Richmond Hill

Mahdi Salem