In this paper, I will first explain the difference between a deductive argument and an inductive argument. I will compare two arguments which both explain the existence of theistic God, the cosmological argument and the argument from design. I will show that the former is deductive; while the latter is inductive. However, I will argue that the cosmological argument also rests on inductive reasoning.

The difference between a deductive argument and an inductive argument rests on whether the argument has a truth preserving logical structure and whether it creates new knowledge.

A deductively valid argument has a truth preserving logical structure, in other words, if its premises are true, its conclusion must be true. For example:

  1. All men are moral (premise);
  2. Socrates is a man (premise);
  3. Socrates is moral (conclusion).

However, a deductively invalid argument is an argument that its premises do not form the logical necessity to give its conclusion. For example:

  1. Poison can kill people (premise);
  2. Daniel was killed (premise);
  3. Daniel had taken poison (conclusion).

This argument is invalid, as experience tells us that many reasons can cause death, so the conclusion cannot be deduced from the premises.

Furthermore, deductive reasoning does not grant new knowledge, as it draws specific conclusion based on the prior knowledge of its premises, of which the conclusion is merely a subset of existing knowledge.

The cosmological argument is a deductive argument. It states that “(1) every being is a dependent being or an independent being, and (2) not every being can be a dependent being, therefore, (3) there exists a self-existent being”, which can be represented by the following formal logical  structure:

  1. P or Q (premise);
  2. P is not true (premise);
  3. Q holds (conclusion).

We can verify its deductive validity via an intuitive example: an integer is either even or odd, so if an integer is not odd, then it must be even. The conclusion of this argument must be true if the two premises are true.

To the contrary, an inductive argument does not guarantee the truth of its conclusion. It draws general inferences from specific instances, and the truth of its premises provides a reason for accepting the conclusion with some level of probability. For example:

  1. The sun has risen every day in the past (premise);
  2. The sun will rise in the future (conclusion).

Although there is an infinitesimal possibility that the sun could explode tomorrow, this is unlikely to happen by our current knowledge, so the conclusion has high probability to be true.

Since inductive argument give generalizations of current knowledge, the generalized conclusion can then be applied to other new specific conditions with some confidence level. In this way, the inductive argument makes prediction and thus produces new knowledge.

The argument from design rests on inductive reasoning. It proceeds by Inference to the Best Explanation from the complexity, diversity and the appearance of purposes of design in the realm of living things to the existence of a divine designer, namely the theistic God. It is called “best explanation” because alternative explanations such as magic and randomness seem far less plausible by intuition. For example, the human body is a complex biological machine such that each system functions appropriately for a purpose and harmonious cooperate to carry out vital activities, which is unlikely to be caused by some random or magic power. Therefore, among all the alternatives the argument from design is its only probable explanation.

I will argue that cosmological argument (CA) indeed rests on inductive reasoning, because its premises rest on the Principle of Sufficient Reason (PSR), and PSR is an inductive argument.

First, CA(1) rests on PSRa. CA(1) states that “every being is a dependent being or an independent being”, with “dependence” defined as “can be caused by others or composed of others”, and “independence” defined as “can be caused by itself or composed of itself”. In other words, CA(1) proposes that every being can be explained by its causes or its components, and the cause or component can either be some other being or itself. This is based on PSRa. PSRa states that “there must be an explanation of the existence of any being”, which denies the existence of any unexplained being, implying every being must be either explained by others or explained by itself.

Second, CA(2) rests on PSRb. PSRb states that “there must be an explanation of any positive fact whatever”, which requires an explanation of the existence of the collection of all the dependent beings. The collection is either explained by itself, for which implies it is independent, or explained by others, for which the “other” being must be independent. Therefore, PSRb necessitates the existence of at least one independent being, so CA(2) holds.

Finally, PSR is inductive. It comes from the following reasoning:

  1. We observe many beings/facts have had an explanation in the past (premise).
  2. Therefore, every being/fact has and will have an explanation (conclusion).

The conclusion, however, does not exclude the possibility, albeit small, of no explanation. For example, the movement of sub-atomic particles whose cause has not fully explored by scientists might not have explanations. In sum, PSR which cosmological argument rests on is inductive.