Reasoning

Plato distinguishes two modes of reasoning in the divided line. Mathematical reasoning (dianoia) starts from hypotheses and deduces consequences, but it never questions its own starting points. Dialectical reasoning (noesis) takes those same hypotheses as stepping stones and ascends to the unhypothetical first principle, the Form of the Good, from which it can then descend with full understanding. The difference is between reasoning within assumptions and reasoning that grounds its own assumptions.

In the Meno, Socrates demonstrates reasoning's power through the slave boy who, guided by questions, discovers geometric truths he was never taught. This is not instruction from outside but the recovery of knowledge the soul already possesses. Reasoning, for Plato, is essentially recollection (anamnesis): the mind's movement from confusion to clarity as it recognizes what it has always known. The Socratic method (elenchus) is reasoning in action, testing propositions by drawing out their consequences until contradictions expose false opinions and the truth stands clear.

Plato frames reasoning as both method and metaphysics: the mind does not merely calculate but ascends to reality. Aristotle will separate the methodological question (how valid inference works) from the metaphysical one (what the mind ultimately grasps) and give each its own treatment.

Aristotle formalizes reasoning. A syllogism is "a discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so." Given "All men are mortal" and "Socrates is a man," "Socrates is mortal" follows necessarily. The Prior Analytics catalogues the valid forms of syllogistic inference (the figures and moods) and shows which combinations of premises yield necessary conclusions. Aristotle distinguishes demonstrative reasoning (from true and necessary premises, yielding scientific knowledge) from dialectical reasoning (from probable premises, yielding opinion) and from sophistical reasoning (from premises that merely appear probable).

The Posterior Analytics treats demonstration, the form of reasoning proper to science. A demonstration must start from premises that are true, primary, immediate, more knowable than the conclusion, and causally related to it. This is reasoning that does not merely prove that something is the case but why it is the case. Aristotle also recognizes induction (epagoge), the movement from particulars to universals, but treats it as preparatory to demonstration rather than a form of strict reasoning in its own right.

Aristotle's syllogistic logic is the framework for Western reasoning for two thousand years. Aquinas adapts it for theology; Bacon attacks it in the name of induction; Mill rewrites it in empiricist terms. No one escapes the framework until Frege and modern logic.

Aquinas places reasoning within a hierarchy of intellects. God knows all things simultaneously in a single eternal act; angels know by grasping principles and their consequences at once; human beings must reason, moving step by step from what is known to what is not yet known. Reasoning (ratio) is not a separate faculty from intellect (intellectus) but a mode of its operation. The intellect grasps first principles directly; reason draws out what is implicit in those principles through the discursive movement of inference. A man who sees that all rational beings have dignity and then infers that this particular person has dignity is reasoning. An angel would see both truths simultaneously.

Human reasoning is therefore a sign of our intellectual weakness compared to higher minds, but it is also our distinctive cognitive power. Aquinas distinguishes two directions of reasoning: from causes to effects (propter quid, or reasoned demonstration) and from effects to causes (quia, or factual demonstration). Both are legitimate, but the first gives deeper knowledge because it reveals why things are as they are, not merely that they are.

Aquinas's view that reasoning is discursive (step-by-step) in contrast to the direct intuition of higher intellects becomes standard in Scholastic philosophy. Descartes tries to reduce the gap between human and angelic knowing by seeking intuitive certainty at every step.

Descartes finds Aristotelian syllogistics barren. The syllogism can organize what is already known but cannot discover new truths. In the Rules for the Direction of the Mind, he proposes two basic operations: intuition and deduction. Intuition is the mind's immediate, undoubting grasp of a clear and distinct truth (the Cogito, for instance). Deduction is the movement from one intuited truth to another through a continuous chain in which each link is as transparent as the first. The weakness of deduction is that long chains of reasoning strain the memory. At the end of a complex demonstration, the thinker may no longer hold the beginning clearly in mind.

Descartes's remedy is practice: by rehearsing chains of reasoning until each step is grasped intuitively, the whole chain can eventually be surveyed in a single act. His four rules of method (accept only what is clear and distinct, divide problems into parts, proceed from simple to complex, enumerate exhaustively) are designed to discipline reasoning and prevent error. The model is mathematics, where certainty accompanies every step. Descartes wants all reasoning to achieve this standard.

Descartes shifts the standard of reasoning from formal validity to intuitive certainty. This emphasis on clarity and distinctness at each step influences all subsequent epistemology and sets up the empiricist response from Locke and Hume.

Hobbes reduces reasoning to calculation. "When a man reasoneth, he does nothing else but conceive a sum total from addition of parcels, or conceive a remainder from subtraction of one sum from another." Just as arithmetic adds and subtracts numbers, reasoning adds and subtracts names. "Man" plus "living creature" yields "man is a living creature"; subtracting "rationality" from "man" yields "living creature without reason." The truth of reasoning depends entirely on the correctness of definitions. If the names are well defined, the reasoning is reliable; if the names are ambiguous, the reasoning goes wrong regardless of its form.

Hobbes thereby eliminates any appeal to intellectual intuition or innate principles. Reasoning is a mechanical operation performed on conventional signs. It is powerful because it allows us to move from known consequences to unknown ones, but it is also fallible because it depends on memory and correct use of words. This is a flat, deflationary account, as far from Plato's dialectical ascent as one can get. Hobbes anticipates the modern view that reasoning is formal manipulation of symbols according to rules, without metaphysical freight.

Hobbes's computational view of reasoning opens the path toward formal logic and artificial intelligence. Locke rejects the identification of reasoning with linguistic computation but accepts the emphasis on clear definitions. Leibniz will dream of a universal calculus that formalizes Hobbes's insight.

Locke treats reasoning as the faculty by which the mind discovers the agreement or disagreement of ideas that are not immediately compared. Intuitive knowledge perceives agreement directly (I see that white is not black). Demonstrative knowledge perceives it through a chain of intermediate ideas, each step itself intuitive. Reasoning is this chain-building process. But Locke adds a third category, sensitive knowledge of the existence of particular external things, which falls short of demonstration yet exceeds mere opinion.

The important practical domain of reasoning operates below certainty, in the realm of probability. Most of our beliefs about the natural world, about history, about the reliability of testimony, are probable rather than certain. Locke devotes careful attention to the degrees of assent appropriate to different levels of evidence. Reasoning well is largely a matter of managing evidence: not over-committing where evidence is thin, not under-committing where it is strong. Locke is suspicious of syllogistic logic as a tool for discovery; it organizes results already obtained but does not generate new knowledge.

Locke's account of reasoning as the management of evidence and probability feeds directly into Hume's analysis of belief and into the broader development of probabilistic and inductive reasoning.

Hume divides all reasoning into two kinds. Reasoning about relations of ideas (mathematics, logic) is demonstrative and certain. Reasoning about matters of fact is experimental and probable. All experimental reasoning depends on the relation of cause and effect: I infer fire from smoke, death from poison, fraud from certain patterns of behavior. But what justifies causal inference? Not reason, for the contrary of any causal claim is always conceivable. Not experience alone, for experience only shows constant conjunction (A followed by B) and never necessary connection.

The missing link is habit. After repeated experience of A followed by B, the mind forms a propensity to expect B on perceiving A. This propensity is belief, and belief is the foundation of all reasoning about matters of fact. Hume is careful to note that this is not a defect. Custom is "the great guide of human life," and without it we could not function. But the philosopher who asks for a rational foundation of inductive reasoning will find none. Reasoning about the world rests on a non-rational ground.

Hume's analysis of experimental reasoning as resting on habit rather than logic is the most influential challenge to rationalist accounts of reasoning. It provokes Kant's critical philosophy and Mill's attempt to justify induction empirically.

Kant distinguishes understanding (Verstand) from reason (Vernunft). Understanding applies concepts to experience, producing judgments. Reason seeks to unify those judgments under ever more general principles, pursuing the unconditioned ground of every conditioned thing. This drive produces the syllogistic chain: if every judgment rests on a more general one, reason pushes toward a first judgment that rests on nothing further. In the Transcendental Analytic, Kant shows that understanding's categories (substance, cause, reciprocity) structure experience a priori.

In the Transcendental Dialectic, he shows that reason's drive for the unconditioned produces ideas (soul, world-totality, God) that outstrip experience and generate antinomies: contradictions that arise when reason tries to determine what lies beyond possible experience. Reasoning is therefore both indispensable and dangerous. Its analytic function (unifying knowledge under principles) is the engine of science. Its dialectical function (seeking the unconditioned) is the source of metaphysical illusion. Kant's project is to preserve the legitimate uses of reason while exposing the illegitimate ones.

Kant's distinction between legitimate and illegitimate uses of reason sets the terms for all subsequent debate. Hegel tries to overcome the limits Kant imposed; Mill insists that reasoning is empirical through and through. The tension between these positions persists.

Mill challenges the primacy of deductive reasoning. The syllogism, he argues, is not a genuine form of inference at all. When we say "All men are mortal; Socrates is a man; therefore Socrates is mortal," the conclusion is already contained in the major premise. The real inferential work was done earlier, when we generalized from observed cases of human mortality to "all men are mortal." That generalization was an induction, and induction is the fundamental form of reasoning. All reasoning, Mill insists, is "from particulars to particulars." We observe that certain men have died and infer that this particular man will also die. The universal proposition is a convenient way of registering and recalling the results of past inductions, but it adds nothing to the inference.

Mill is aware of the circularity: induction presupposes the uniformity of nature, which is itself an induction. He accepts this and argues that the principle of uniformity is justified by its success. Against Kant, Mill denies that any reasoning is a priori. The axioms of geometry, the principle of causation, and the rules of arithmetic are all empirical generalizations, no different in kind from the generalization that all swans so far observed have been white.

Mill's empiricist theory of reasoning, with induction as the master form, represents one pole of the debate that Aristotle began. The difficulty he cannot resolve is the one Hume named: induction is justified only by appeal to the uniformity of nature, which is itself an induction. Mill accepts the circularity and calls it self-confirming, but this means his account of reasoning ultimately rests on a habit, not on a principle — which is exactly where Hume left it.