Logic: Deductive and Inductive

Sec. 1. We have now reviewed Mill's five Canons of Inductive Proof. At bottom, as he observes, there are only two, namely, Agreement and Difference: since the Double Method, Var...

Sec. 1. A Fallacy is any failure to fulfil the conditions of proof. If we neglect or mistake the conditions of proof unintentionally, whether in our private meditations or in ad...

Sec. 1. Let me begin by borrowing an example from Bain (_Logic_: B. III. c. 6). The North-East wind is generally detested in this country: as long as it blows few people feel at...

Sec. 1. An Hypothesis, sometimes employed instead of a known law, as a premise in the deductive investigation of nature, is defined by Mill as "any supposition which we make (ei...

First, there are Axioms or Principles, that is real, universal, self-evident propositions. They are--(1) real propositions; not, like 'The whole is greater than any of its parts...

Sec. 1. Precision of thought needs precision of language for the recording of such thought and for communicating it to others. We can often remember with great vividness persons...

Sec. 1. Chance was once believed to be a distinct power in the world, disturbing the regularity of Nature; though, according to Aristotle, it was only operative in occurrences b...

(2) That one thing is a mark of another or constantly related to it, must be established by Induction; and the surest of all marks is a Cause. So that the application of the axi...

Sec. 1. Ordinary words may need definition, if in the course of exposition or argument their meaning is liable to be mistaken. But as definition cannot give one the sense of a p...

Sec. 1. Terms are next to be classified according to their Connotation--that is, according to what they imply as characteristic of the things denoted. We have seen that general...

Sec. 1. Classification, in its widest sense, is a mental grouping of facts or phenomena according to their resemblances and differences, so as best to serve some purpose. A "men...

As to Quantity, propositions are either Universal or Particular; that is to say, the predicate is affirmed or denied either of the whole subject or of a part of it--of _All_ or...

Sec. 1. Having now discussed Terms, Propositions, Immediate and Mediate Inferences, and investigated the conditions of formal truth or consistency, we have next to consider the...

Sec. 1. Logic is the science that explains what conditions must be fulfilled in order that a proposition may be proved, if it admits of proof. Not, indeed, every such propositio...

Sec. 1. Under the general title of Immediate Inference Logicians discuss three subjects, namely, Opposition, Conversion, and Obversion; to which some writers add other forms, su...

In this example, instead of P being predicated of M, M is predicated of P, and yet S is given as included not in P, but in M. The divergence of such a syllogism from the _Dictum...

Sec. 1. It is necessary to describe briefly the process of investigating laws of causation, not with the notion of teaching any one the Art of Discovery, which each man pursues...

Sec. 1. A Mediate Inference is a proposition that depends for proof upon two or more other propositions, so connected together by one or more terms (which the evidentiary propos...

Sec. 1. Since Logic discusses the proof or disproof, or (briefly) the testing of propositions, we must begin by explaining their nature. A proposition, then, may first be descri...

Sec. 1. Of the terms of a proposition which is the Subject and which the Predicate? In most of the exemplary propositions cited by Logicians it will be found that the subject is...

Sec. 1. The word Inference is used in two different senses, which are often confused but should be carefully distinguished. In the first sense, it means a process of thought or...

A Hypothetical Syllogism is one that consists of a Hypothetical Major Premise, a Categorical Minor Premise, and a Categorical Conclusion. Two Moods are usually recognised the _M...

Sec. 1. In treating of Deductive Logic it is usual to recognise three divisions of the subject: first, the doctrine of Terms, words, or other signs used as subjects or predicate...

Sec. 1. In ordinary discussion, whether oral or written, it is but rarely that the forms of Logic are closely adhered to. We often leave wide gaps in the structure of our argume...

Sec.1. The most important aspect of Uniformity in relation to Induction is Causation 174 Sec.2. Definition of "Cause" explained: five marks of Causation 175 Sec.3. How strictly...

Sec.1. Formal Consistency and Material Truth 159 Sec.2. Real General Propositions assert more than has been directly observed 160 Sec.3. Hence, formally, a Syllogism's Premises...

Sec.1. The Canon of Agreement 206 Negative Instances (p. 208); Plurality of Causes (p. 208) Agreement may show connection without direct Causation (p. 209) Sec.2. The Canon of A...

Sec.1. Hypothesis defined and distinguished from Theory 266 Sec.2. An Hypothesis must be verifiable 268 Sec.3. Proof of Hypotheses 270 (1) Must an hypothetical agent be directly...

Sec.1. Axioms; Primary Laws; Secondary Laws, Derivative or Empirical; Facts 288 Sec.2. Secondary Laws either Invariable or Approximate Generalisations 292 Sec.3. Secondary Laws...

Sec.1. Meaning of Chance and Probability 310 Sec.2. Probability as a fraction or proportion 312 Sec.3. Probability depends upon experience and statistics 313 Sec.4. It is a kind...

Sec.1. Illustrations of the Syllogism 121 Sec.2. Of Figures 122 Sec.3. Of Moods 123 Sec.4. How valid Moods are determined 124 Sec.5. Special Canons of the Four Figures 126 Sec.6...

Sec.1. Nature of Mediate Inference and Syllogism 107 Sec.2. General Canons of the Syllogism 108 Definitions of Categorical Syllogism; Middle Term; Minor Term; Major Term; Minor...

Sec.1. Precise thinking needs precise language 348 Sec.2. Nomenclature and Terminology 349 Sec.3. Definition 352 Sec.4. Rules for testing a Definition 352 Sec.5. Every Definitio...

Sec.1. Connotation of General Names 37 Sec.2. Question of Proper Names 38 other Singular Names (p. 40) Sec.3. Question of Abstract Terms 40 Sec.4. Univocal and Equivocal Terms 4...

Sec.1. Outline of Inductive investigation 192 Sec.2. Induction defined 196 Sec.3. "Perfect Induction" 196 Sec.4. Imperfect Induction methodical or immethodical 197 Sec.5. Observ...

Sec.1. Classification, scientific, special and popular 330 Sec.2. Uses of classification 332 Sec.3. Classification, Deductive and Inductive 334 Sec.4. Division, or Deductive Cla...

Sec.1. Deductive character of Formal Induction 236 Sec.2. Further complication of Deduction with Induction 238 Sec.3. The Direct Deductive (or Physical) Method 240 Sec.4. Opport...

Sec.1. Fallacy defined and divided 385 Sec.2. Formal Fallacies of Deduction 385 Sec.3. Formal Fallacies of Induction 388 Sec.4. Material Fallacies classified 394 Sec.5. Fallacie...

Sec.1. As to Quantity 53 Quantity of the Predicate (p. 56) Sec.2. As to Quality 57 Infinite Propositions (p. 57) Sec.3. A. I. E. O. 58 Sec.4. As to Relation 59 Change of Relatio...

Sec.1. The rigour of scientific method must be qualified 369 Sec.2. Still, Language comprises the Nomenclature of an imperfect Classification, to which every Definition is relat...

Sec.1. Plan of the Chapter 79 Sec.2. Subalternation 79 Sec.3. Connotative Subalternation 80 Sec.4. Conversion 82 Reciprocality (p. 84) Sec.5. Obversion 85 Sec.6. Contrary Opposi...

Sec.1. Definition of Logic 1 Sec.2. General character of proof 2 Sec.3. Division of the subject 5 Sec.4. Uses of Logic 6 Sec.5. Relation of Logic to other sciences 8 to Mathemat...

Sec.1. Propositions and Sentences 16 Sec.2. Subject, Predicate and Copula 17 Sec.3. Compound Propositions 17 Sec.4. Import of Propositions 19 Sec.5. Form and Matter 22 Sec.6. Fo...

Sec.1. Some Account of Language necessary 27 Sec.2. Logic, Grammar and Rhetoric 28 Sec.3. Words are Categorematic or Syncategorematic 29 Sec.4. Terms Concrete or Abstract 30 Sec...

Sec.1. Meaning of Inference 69 Sec.2. Immediate and Mediate Inference 70 Sec.3. The Laws of Thought 72 Sec.4. Identity 73 Sec.5. Contradiction and Excluded Middle 74 Sec.6. The...

Sec.1. Popular Arguments Informal 138 Sec.2. The Enthymeme 139 Sec.3. Monosyllogism, Polysyllogism, Prosyllogism, Episyllogism 141 Sec.4. The Epicheirema 142 Sec.5. The Sorites...