Inference

Inference is the mental process of deriving a proposition from observation and/or other propositions. Inferences can be either deductive or inductive. Deductive inference is the application of the general to the particular (or to the less general). While inductive inference the process of generalizing from particulars (or from the less general). Where deduction applies the more general to the less general, induction moves from the less general to the more general. ^[1]

Inferences can only be drawn from something known, none—no thought whatsoever—can be drawn from the arbitrary.

Proof is a process of inference — deductive or inductive inference. In either form, inference is a process of moving in thought from something known to something else logically related to it. An inference is made from something, not from nothing. Consequently, there must be a starting point. The starting point of any valid chain of proofs, however long, is the information given in direct awareness — i.e., the self-evident.^[2]

The conclusion of a deductive inference is implicitly contained within the general premise. The most elementary act of deduction is the Syllogism, which is the “atom” of deductions. In the syllogism "All men are mortal; Socrates is a man; therefore, Socrates is mortal," the conclusion (Socrates is mortal) is drawn from the generalization about men and the particular instance of Socrates being a man. Deductive reasoning is used to make implicit knowledge explicit, bringing specific implications of general knowledge into conscious awareness.

Almost all of everyday reasoning is deductive. Deduction is the process used when one goes from “It is raining” to “I should take an umbrella” (using the suppressed premise: “When it rains, I should take an umbrella”). [...] Even the act of making a simple statement, like “That is a dog,” is deductive, at least in pattern, because it applies a general term (dog) to its subject.^[3]

Induction is the primary means of acquiring new conceptual knowledge. Observing that fire burns paper, focusing sunlight with a magnifying glass burns paper, and placing paper in a hot oven burns it, one can induce the general principle that high heat burns paper. Induction is fundamental to forming general premises upon which deductive inferences rely. Without induction, there would be no general knowledge for deduction to apply.

Since all inferences either are inductions or require inductively reached premises, the attack on induction is an attack on all inference — which is self-refuting, since the attacks themselves require making and applying generalizations reached by induction. In other words, the statement “Induction is invalid” commits the fallacy of self-exclusion. The same is true of milder attacks, such as “Induction cannot give certainty” which is itself a claim to certainty about a generalization.

Though there is no “problem of induction,” there are legitimate questions regarding how induction works and what is required for an inductive generalization to be valid. (In the same way, there never was any “problem of deduction,” but Aristotle’s discovery of the principles of deduction marked an historic advance.)^[4]

For a proposition derived by inference to be true, it must be logically valid and sound. All valid inferences begin with self-evident perceptual data. Proofs and logical processes connect ideas back to these self-evident facts. Inferences must adhere to The Law of Non Contradiction, to make sure that propositions do not assert contradictory claims. Logic, the art of non-contradictory identification, governs the process of inference.

Inference is a crucial component of human cognition, enabling the transition from observation and known propositions to new knowledge. Concepts are the tools of reason, and it is by means of concepts that man stores and accesses his knowledge. The ability to form concepts is what enables human cognition to grasp the vast array of facts about reality, and inference is the method by which these concepts are applied to reach new conclusions. This hierarchical progression from perception to concepts, to propositions, and finally to inferences, illustrates the structured nature of human knowledge. Through inference, whether deductive or inductive, we validate and expand our understanding of reality.