A valid triangle, and an invalid athlete

These notes, from a textbook and lectures on understanding philosophy, first set out deduction and induction. A deductive argument is built so that the conclusion must follow from the given premises. If the premises are true, the conclusion cannot be false, and logical connection is an essential part of the structure. An inductive argument gathers particular cases, finds a feature that repeats among them, and extends it as a property of a wider class. The more numerous or representative the observed cases, the more the conclusion can be trusted, but one cannot decide that it must be true. Induction, in this telling, is an expanding inference: from limited information it draws a broader statement.

Deduction, by contrast, is treated as a way of arranging what was already contained in the premises. Structural validity can hold even apart from whether the premises are in fact true; the conclusion then follows from the form. The method, the notes say, does not so much create a new fact as show a logical consequence of information already at hand. Induction, working from experience, makes a conclusion that is only probable, and always allows that an exception may appear; it adds information the premises did not contain, and so cannot easily secure necessity.

In deduction, a general rule yields a conclusion about a particular case, and the key is logical validity. One case offered: if every triangle has three sides, and this figure is a triangle, then this figure has three sides — the conclusion must follow from the structure. By contrast, from “all athletes are fit” and “this person is fit,” the conclusion “this person is an athlete” is a structurally wrong argument. A sound deduction is complete only when that validity is joined by premises that are in fact true; the conclusion is then, the notes say, a truth beyond doubt. For induction to be in good order, the cases must be many and also representative across varied conditions.

Fish in season, and a city’s buses

An example of induction in the notes is this. In the past, people watched, over a number of years at some rivers, fish moving in groups at a particular time, and from that repeated experience they came to a knowledge that a pattern of movement forms with the seasons. The conclusion reaches beyond any single watching, yet it remains open to an exception.

A second example concerns punctuality. To survey how often the buses of a city run on time, checking only a few buses in a single day is not enough; if one observes widely for a month, by time of day and by route, a conclusion closer to the whole flow can be reached. Induction of this kind, the notes say, can raise the probability of the conclusion as far as it will go, and has a part in understanding and forecasting what actually happens. A simple generalization applies a shared feature of the cases to the whole; a statistical generalization estimates a share for the whole from collected figures, and then the representativeness of the sample becomes the central test.

If the sample is biased or too small, induction goes wrong; if a sufficient variety of cases is secured, trust in the conclusion rises. The inductive conclusion is to be read as a probabilistic statement, and left as a provisional judgment.

A mirror, a coherent system, and two later remarks

Correspondence theory, as the lectures set it out, holds that truth obtains when our judgment matches the actual world, point by point. Truth, in the image used in class, is a relation of agreement, as a mirror reflects the look of a thing; for that reason the view is often also called a copy theory, and truth is treated as a faithful reproduction of outside reality. In an account centered on the senses, what the eye sees and the hand touches, if it matches the judgment, is enough for truth, and the mind is treated like a camera or a mirror. The limit, the notes say, is that sense works differently from person to person, and can be distorted by illusion or hallucination; ideas such as freedom or justice cannot be checked by sense at all. An account centered on reason looks instead for a match between reason and the universal structure of things, past the instability of sense — yet reason itself is not wholly to be trusted, and not everyone has the same reason.

Coherence theory holds that truth obtains when several judgments connect without contradiction. It cares more for logical consistency among judgments than for a match with the outside world, and treats truth as content in harmony inside a system. The test is whether there is a contradiction, and whether the logical flow is natural; a new judgment may be called true if it sits well with judgments already taken as secure. The limit is plain in the same lectures: a fictional story, built without internal contradiction, can still be coherent, so coherence alone does not adequately secure a link to reality, and it is hard to explain why the first grounding proposition is true. The natural conclusion drawn in class is that the correspondence standard and the coherence standard should support each other; in the empirical sciences, observations gathered from many cases can give weight to the first proposition of a coherent system.

A later stretch of the same notes, after a discussion of necessity and chance, records two further remarks. Foucault, they say, held that the very idea of historical events arranged according to a particular purpose is itself a product of power. Daoist thought, they add, criticizes a moralism that stresses a fixed order, and values the flow of change and possibility. The same Korean report, at fuller length, is on CampusDown.

Sources

1. Student notes from a textbook and lectures on understanding philosophy, on deduction and induction, with a valid triangle case and an invalid athlete case.
2. Inductive examples of seasonal fish movement and of a survey of city-bus punctuality, left as the notes give them.
3. Correspondence theory, also called a copy theory, and coherence theory, with the limits named in class, and brief later remarks on Foucault and Daoist thought.

Last updated: 14 November 2026