Argument Patterns and Valid Inference

ArguPre-Aristotelian evidence for reflection on argument forms and valid inference are harder to come by. Both Zeno of Elea (born c. 490 BCE) and Socrates (470–399) were famous for the ways in which they refuted an opponent's view. Their methods display similarities with reductio ad absurdum, but neither of them seems to have theorized about their logical procedures. Zeno produced arguments (logoi) that manifest variations of the pattern ‘this (i.e. the opponent's view) only if that. But that is impossible. So this is impossible’. Socratic refutation was an exchange of questions and answers in which the opponents would be led, on the basis of their answers, to a conclusion incompatible with their original claim. Plato institutionalized such disputations into structured, rule-governed verbal contests that became known as dialectical argument. The development of a basic logical vocabulary for such contests indicates some reflection upon the patterns of argumentation.

The 5th and early to mid-4th centuries BCE also see great interest in fallacies and logical paradoxes. Besides the Liar, Eubulides is said to have been the originator of several other logical paradoxes, including the Sorites. Plato's Euthydemus contains a large collection of contemporary fallacies. In attempts to solve such logical puzzles, a logical terminology develops here, too, and the focus on the difference between valid and invalid arguments sets the scene for the search for a criterion of valid inference. Finally, it is possible that the shaping of deduction and proof in Greek mathematics that begins in the later 5th century BCE served as an inspiration for Aristotle's syllogistic.

2. Aristotle

(For a more detailed account see the entry on Aristotle's Logic in this encyclopedia.) Aristotle is the first great logician in the history of logic. His logic was taught by and large without rival from the 4th to the 19th centuries CE. Aristotle's logical works were collected and put in a systematic order by later Peripatetics, who entitled them the Organon or ‘tool’, because they considered logic not a part but rather an instrument of philosophy. The Organon contains, in traditional order, the Categories, De Interpretatione, Prior Analytics, Posterior Analytics, Topics andSophistical Refutations. In addition, Metaphysics Γ is a logical treatise that discusses the principle of non-contradiction, and some further logical insights are found scattered throughout Aristotle's other works, such as the Poetics, Rhetoric, De Anima, Metaphysics Δ and Θ, and some of the biological works. Some parts of the Categories and Posterior Analytics would today be regarded as metaphysics, epistemology or philosophy of science rather than logic. The traditional arrangement of works in the Organon is neither chronological nor Aristotle's own. The original chronology cannot be fully recovered since Aristotle seems often to have inserted supplements into earlier writings at a later time. However, by using logical advances as a criterion, we can conjecture that most of the Topics, Sophistical Refutations, Categories andMetaphysics Γ predate the De Interpretatione, which in turn predates the Prior Analytics and parts of the Posterior Analytics.

2.1 Dialectics

The Topics provide a manual for participants in the contests of dialectical argument as instituted in the Academy by Plato. Books 2–7 provide general procedures or rules (topoi) about how to find an argument to establish or refute a given thesis. The descriptions of these procedures—some of which are so general that they resemble logical laws—clearly presuppose a notion of logical form, and Aristotle's Topics may thus count as the earliest surviving logical treatise. TheSophistical Refutations are the first systematic classification of fallacies, sorted by what logical flaw each type manifests (e.g. equivocation, begging the question, affirming the consequent,secundum quid) and how to expose them.

2.2 Sub-sentential Classifications

Aristotle distinguishes things that have sentential unity through a combination of expressions (‘a horse runs’) from those that do not (‘horse’, ‘runs’); the latter are dealt with in the Categories(the title really means ‘predications’[1]). They have no truth-value and signify one of the following: substance (ousia), quantity (poson), quality (poion), relation (pros ti), location (pou), time (pote), position (keisthai), possession (echein), doing (poiein) and undergoing (paschein). It is unclear whether Aristotle considers this classification to be one of linguistic expressions that can be predicated of something else; or of kinds of predication; or of highest genera. InTopics 1 Aristotle distinguishes four relationships a predicate may have to the subject: it may give its definition, genus, unique property, or accidental property. These are known as predicables.

2.3 Syntax and Semantics of Sentences

When writing the De Interpretatione, Aristotle had worked out the following theory of simple sentences: a (declarative) sentence (apophantikos logos) or declaration (apophansis) is delimited from other pieces of discourse like prayer, command and question by its having a truth-value. The truth-bearers that feature in Aristotle's logic are thus linguistic items. They are spoken sentences that directly signify thoughts (shared by all humans) and through these, indirectly, things. Written sentences in turn signify spoken ones. (Simple) sentences are constructed from two signifying expressions which stand in subject-predicate relation to each other: a name and a verb (‘Callias walks’) or two names connected by the copula ‘is’, which co-signifies the connection (‘Pleasure is good’) (Int. 3). Names are either singular terms or common nouns (An. Pr. I 27). Both can be empty (Cat. 10, Int. 1). Singular terms can only take subject position. Verbs co-signify time. A name-verb sentence can be rephrased with the copula (‘Callias is (a) walking (thing)’) (Int. 12). As to their quality, a (declarative) sentence is either an affirmation or a negation, depending on whether it affirms or negates its predicate of its subject. The negation particle in a negation has wide scope (Cat. 10). Aristotle defined truth separately for affirmations and negations: An affirmation is true if it says of that which is that it is; a negation is true if it says of that which is not that it is not (Met. Γ.7 1011b25ff). These formulations, or in any case their Greek counterparts, can be interpreted as expressing either a correspondence or a deflationist conception of truth. Either way, truth is a property that belongs to a sentence at a given time. As to their quantity, sentences are singular, universal, particular or indefinite. Thus Aristotle obtains eight types of sentences, which are later dubbed ‘categorical sentences’. The following are examples, paired by quality:

اقتباس :

Singular:	Callias is just.	Callias is not just.
Universal:	Every human is just.	No human is just.
Particular:	Some human is just.	Some human is not just.
Indefinite:	(A) human is just.	(A) human is not just.

Universal and particular sentences contain a quantifier and both universal and particular affirmatives were taken to have existential import. (See entry The Traditional Square of Opposition). The logical status of the indefinites is ambiguous and controversial (Int. 6–7).
Aristotle distinguishes between two types of sentential opposition: contraries and contradictories. A contradictory pair of sentences (an antiphasis) consists of an affirmation and its negation (i.e. the negation that negates of the subject what the affirmation affirms of it). Aristotle assumes that—normally—one of these must be true, the other false. Contrary sentences are such that they cannot both be true. The contradictory of a universal affirmative is the corresponding particular negative; that of the universal negative the corresponding particular affirmative. A universal affirmative and its corresponding universal negative are contraries. Aristotle thus has captured the basic logical relations between monadic quantifiers (Int. 7).

Since Aristotle regards tense as part of the truth-bearer (as opposed to merely a grammatical feature), he detects a problem regarding future tense sentences about contingent matters: Does the principle that of an affirmation and its negation one must be false, the other true, apply to these? What, for example, is the truth-value now of the sentence ‘There will be a sea-battle tomorrow’? Aristotle may have suggested that the sentence has no truth-value now, and that bivalence thus does not hold—despite the fact that it is necessary for there either to be or not to be a sea-battle tomorrow, so that the principle of excluded middle is preserved (Int. 9).ment Patterns and Valid Inference

» The Modal Argument
» . The Argument From Skepticism
» The Argument from Hallucination
» The Chinese Room Argument
» St. Anselm's Ontological Argument

Argument Patterns and Valid Inference

2. Aristotle

2.1 Dialectics

2.2 Sub-sentential Classifications

2.3 Syntax and Semantics of Sentences

Argument Patterns and Valid Inference :: تعاليق

Argument Patterns and Valid Inference

مواضيع مماثلة

مواضيع مماثلة