A guaranteed conclusion, and a mushroom told apart by harm

Human knowledge, in this telling, has been built by two kinds of inference. Deduction is an argument in which universal premises guarantee the truth of the conclusion. A valid argument is a form from which the conclusion must follow; an invalid argument is a form in which the premises may be true and the conclusion still fail. The strength of deduction is that it secures necessity, and so can give knowledge that holds. Its limit is that the conclusion is already contained in the premises, and so does not add information beyond them. Restating a proposition, though, can still help a person understand it newly.

Induction generalises, from a finite number of sample cases, to a property of a whole group. If the sample is not representative, the induction is a poor one; if the sample is representative, the induction is a better one. When the cases are many, or truly representative, the conclusion can be trusted, though only as probability: the chance may be high, but an exception cannot be ruled out. A large part of what people know has been formed this way. People once learned to tell a poisonous mushroom from an edible one after illness and death had followed the same meal more than once. The conclusion, in induction, goes beyond the premises, and so new information is added, at the price of necessity.

Two styles of inductive generalisation are distinguished. Simple generalisation takes a common feature in a limited number of cases and treats it as holding, without exception, for the whole group. One example given is of two products from company A that both broke within a week, from which a person concludes that every product made by company B will be of poor quality — a jump in which the quantitative condition has been left out. Statistical generalisation estimates a property of a whole population from a ratio or a probability in a sample, and depends on how well the sample represents the whole. In a factory example, 1,000 phone batteries are drawn at random and tested for life, and 5 per cent fall short of a defect standard; about 5 per cent of the whole line is then likely to be defective. That 5 per cent is left with the example.

A mirror, and a system that fits itself

Correspondence is the view that truth is a precise fit between an object and a judgment, between what is real and an idea, or between a thing and the intellect. Because it is like a mirror copying a thing as it is, it is also called a copy theory. The fit is then split in two. A sensory copy theory holds that a truth is established when the look of the outer world, as the senses take it in — as if one were seeing with the eyes and touching with the hands — matches a judgment perfectly. The mind is to work like a camera. A statement is true only if it can be shown to match each fact through sensory experience and observation, and the basic standard is how accurately a physical fact of the experienced world is reflected. The main criticisms are that the senses are subjective, so that the same phenomenon can be taken differently and a universally valid truth is hard to fix; that universal truths which outrun experience, as in mathematics, logic, or ethics, cannot be copied by the senses; and that illusion or hallucination can appear, so that a sensory match cannot, by itself, guarantee truth.

A rational copy theory holds that truth is established when human reason matches the underlying law or structure of a thing, which is a different work from copying a particular object. It cares about a universally valid truth — a mathematical axiom, or a metaphysical proposition — corresponding to what pure reason thinks. Reason, in this view, goes past the outer thing to the essence, and completes truth as a clear and certain knowledge beyond the limit of the senses. The difficulties named are that placing the ground of truth too heavily in rational ideas can ignore the outer world and slide into a subjective idealism; that a higher concept such as an essential principle cannot itself be proved by experience, so it is hard to show objectively that a rational judgment has matched its object; and that the view is relatively weak at settling the truth of empirical, scientific knowledge built from particular facts.

Coherence starts from the limits of correspondence. So long as knowledge appears in the realm of judgment, it argues, the standard of a universal truth should be sought not in a fit between what is real and an idea, but in a fit among ideas, and among judgments. A particular judgment is true or false according to whether it is consistent with already clear judgments — that is, whether it contradicts them or not. The law of non-contradiction, and the rules of deduction, decide that consistency. The decision is logical, not sensory, and so, in this telling, leaves no room for disagreement, and can serve as a basis for the systematic character of every field of study. The problems are as sharp as the claim. More than one knowledge system can be internally consistent and still contradict another; a work of fiction can be coherent in itself and still not be a truth of the world. Coherence alone makes it hard to tell a truth about the real world. The weakest standard — mere absence of contradiction — could count even unrelated propositions as coherent and true. And to judge coherence, a first proposition is needed; coherence by itself cannot say why that first proposition is true, and some other standard has to be brought in.

A first proposition, and a rain that reason cannot settle

The criticisms are then gathered, and a complement is offered. The trouble with a sensory copy is that the senses can be caught in illusion or hallucination, and that the truth or falsity of a concept that cannot be experienced — freedom, or justice — is hard to explain. The trouble with a rational copy is that reasoning can err, that not everyone has the same kind of reason, and that a clear empirical fact such as “it is raining now” cannot be settled by reason alone. The trouble with coherence is that several fictional systems with no inner contradiction, a novel among them, would all come out true; that its hold on the real is weak; and that it cannot guarantee the first proposition on which coherence itself stands.

For coherence to become a more universal view of truth, the highest judgment needs a way of confirming its content: by the senses, or by rational intuition. That is a way of saying that coherence needs help from correspondence. In an empirical-scientific system, the highest judgment is supplemented by a sensory copy: the proposition “every living thing dies” is possible as an inductive generalisation from the experience of many living things dying. In a theoretical-scientific system, the highest judgment is secured not by a sensory copy but by a rational one, through an intuition that is clear and evident. Logical and mathematical truth is guaranteed by an evident intuition of axioms and by deduction from them; geometry and mathematics, built from such axioms and deduced propositions, are treated here as among the most universal systems people have made. In short, the limit of coherence is to be met, in empirical work, with the help of induction, and in a pure theoretical system such as geometry or mathematics, with the help of deduction. Correspondence and coherence, with the induction and the deduction they involve, are read as mutually complementary theories of scientific truth.

Existence is then also looked at under necessity, possibility, and actuality — a work the account calls modal analysis. Necessity means “cannot be otherwise,” “must be.” Ideal necessity is the inward, social trust that a value or a belief, once taken in, is the only natural way; real necessity is an objective physical fact that must appear under a natural law or a causal rule. If the causal principle “everything has a cause” is granted, absolute chance cannot stand: what we call chance is only a crossing of causal relations we have not fully grasped, a name we use when we cannot see every cause. Even a determinist or a fatalist, until the causal chain is known, meets the event as chance. World-views sit past proof, in metaphysics; determinism and indeterminism are treated here as a matter of how a life is understood, not simply of right and wrong. The same human affair can be read as chance or as necessity, depending on the point of view. All human affairs are settled, in this telling, but only known at the end, so that an unlucky chance may be taken boldly as the sign of a later good, and a stroke of luck watched carefully as the seed of harm. A balanced stance among world-views is named as the inner aim of this kind of thinking. The possible is what may be or may not be: ideal possibility is what the mind allows when there is no logical contradiction, whether or not it can be realised; real possibility also has to pass the natural laws and physical conditions of the world.

Why the mushroom, the battery, and the first proposition sit together

A conclusion that is already in the premises, a conclusion that goes a little past them, a mirror, and a system that fits itself, all have a limit. The useful work, here, is to know which limit one is near, and to borrow what the other side still has. The same Korean report, at fuller length, is on CampusDown.

Sources

1. Summary of deduction and induction, correspondence and coherence and a critical complement, and necessity, chance, possibility and actuality, following a course in the understanding of philosophy (Korean source page).
2. Lee Jeong-ho and others, Understanding Philosophy, Korea National Open University Press, 2016, as the textbook cited for chapters 13, 14, and 15.
3. Examples as given: telling a poisonous mushroom from an edible one after repeated harm; two products from company A that broke within a week, wrongly generalised to company B; 1,000 phone batteries drawn at random, of which 5 per cent fell short of a defect standard.
4. The 2016 textbook is left as the cited edition. The assignment framing of a 2025 common liberal-arts paper is not used as a source of philosophical claims.

Last updated: 14 November 2026