We have causality in the world, in the sense that for every event we can always find preceding events that contributed to the outcome. But some events involve an irreducible randomness or chance. They are unpredictable, uncertain, and indeterministic. We can describe such events with the ancient concept of the uncaused cause or causa sui.

Although almost all philosophers became language philosophers in the twentieth century, they have been notoriously sloppy with definitions of philosophical terminology. They have been especially confused when they attempt to prove things with logic and language about the world.

For example, they like to say that if determinism is false, indeterminism is true. This is of course logically correct. Strict causal determinism with a causal chain of necessary events back to an Aristotelian first cause is indeed false, and modern philosophers know it, though most hold out hope that the quantum mechanical basis of such indeterminism will be disproved someday and declare themselves agnostic.

These agnostic philosophers go on to argue that the principle of bivalence requires that since determinism and indeterminism are logical contradictories, only one of them can be true. The law of the excluded middle allows no third possibility. Now since neither determinism nor indeterminism allow the kind of free will that supports moral responsibility, they claim that free will is unintelligible or an illusion. This is the standard argument against free will.

Finally, despite their claim that professional philosophers are better equipped than scientists to make conceptual distinctions and evaluate the cogency of arguments, they have confounded the concepts of "free" and "will" into the muddled term "free will" despite the clear warnings from John Locke that this would lead to confusion. Locke said very clearly, as had some ancients like Lucretius, it is not the will that is free (in the sense of undetermined), it is the mind.

The practical empirical situation is much more complex than such simple black and white logical linguistic thinking can comprehend. Despite quantum uncertainty, there is clearly adequate determinism in the world, enough to permit the near-perfect predictions of celestial motions, and good enough to send men to the moon and back. But this "near" (Honderich) or "almost" (Fischer) determinism is neither absolute nor required in any way by logical necessity, as Aristotle himself first argued against the determinist atomists.

The core idea of causality is closely related to the idea of determinism. But we can have causality without determinism. We call it "soft" causality. The departure from strict causality is very slight compared to the miraculous ideas usually associated with the "causa sui" (self-caused cause) of the ancients.

Causality is a rhetorical tool, It is ad hoc reasoning to identify preceding events that contributed to a current event. We can always find a reason (λόγος) or reasons for events, leading to the ancient dictum "every event has a cause."

And certainty, necessity, and predictability are all closely related to determinism, but they have their main applicability in slightly different fields - mathematics, logic, and physics - which gives rise to ambiguity when used outside those fields.

Certainty is a powerful idea that has mesmerized philosophers, and especially religious leaders, throughout the ages. Belief in absolute and certain truth has all too often justified the most inhumane behavior toward those not sharing that truth and that belief.

Certainty is the case of a mathematical probability equal to one.

Necessity is often opposed to chance. In a necessary world there is no chance. Everything that happens is necessitated. In our real physical world nothing is necessary. There is nothing logically true of the world.

Necessity is just a useful tool as part of our deductive reasoning in logic, where chance is theoretically non-existent.

Predictability is a characteristic of law-governed phenomena. When the laws are expressible as mathematical functions of time, knowledge of the initial conditions at some time allows us to predict the conditions at all later (and retrospectively earlier) times.

Predictability in like circumstances is the key to the hypothetical-deductive method of experimental science.