The Trivium

The Trivium describes the first three liberal arts of seven, which are LOGIC, GRAMMAR and RETHORIC. This book is probably the most important book we will read at the MPC becuase it absoluteley describes everything that surrounds us and how we percieve it. It speaks of the beginnings of language and how everything is described in a certain way and why.

Logic is based only on the intellect but without any cognition and/or emtions.

Grammar gives expression to all states of mind. Grammar works with short sentences unlike logic and rhetoric which work with more extended paragraphs of thoughts.

FOUR CASES OF SUBSTANTIVES

- Nominative: The subject, it is necessary in every sentence.

- Genitive: names the possesor

- Dative: names the term to which the action proceeds.

- Accusative: names the object that recieves the action.

Syllogism

"The syllogism is the act of reasoning by which the mind percieves that from the relation of two propositions (called premises) having one term in common there necessarily emerges a new, third proposition (called the conclusion) in which the common term, called the middle term does not appear"

- The Liberal Arts.

- Liberal arts is divided into seven different branches, all contained in the Trivium and in the Quadrivium. The Trivium relates to the aspects of the mind (logic, grammar and rhetoric) and the Quadrivium to the aspects of matter (arithmetic, music, geometry and astronomy).

- Liberal arts teach one to live, to train faculties and bring them to perfection.

The Nature and Function of Language.

- The main function of language is to communicate thought, volition and emotion through symbols. There are two means of communication: imitation (artificial likeness) and symbols (meanings imposed by convention). Words are symbols of ideas about reality.

- Form of language

– essence

– species

– genus

– aggregate.

Ambiguity:
History of words
Imposition and intention
Nature of the Phantasm (image of the word, common nature, common and proper names)
Deliberate ambiguity (irony, pun, metaphor)

Importance of grammar:
Grammar gives expression to all the states of mind or soul. It is also a prerequisite for logic and rhetoric

General Grammar

General grammar is concerned with the relation of words to ideas and to realities. Special grammar is the relation of words between words (English and Latin grammar).
General grammar is divided into two: categorematic and syncategorematic. These two make up the 4 parts of speech:
Substantives (noun, pronoun)
Attributes (verbs, adjectives, adverbs)
Definitive (articles, pronomials)
Connectives (prepositions, conjunctions)

The noun is categorized into: concrete or abstract- number – gender – person – case(nominative, genitive, dative, accusative)

The functions of the verb express an attribute along with the notion of time, it also indicates the tense, expresses a mood and asserts.

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Terms and Their Grammatical Equivalents: Definition and Division.

A term is a concept communicated through a symbol (when words are used to communicate a concept of reality).
A logical term is a complete symbol, which must be either a proper name, a general description, an empirical description or a common name.

Terms are divided into 5:
Empiciral and general
Contradictory (+-)
Concrete and abstract
Absolute and relative
Collective and distributive

A definition is a perfect general description which can be divided into logical, casual and descriptive or distinctive.

Propositions and Their Grammatical Expression.

A proposition asserts the relation of terms. It consists of subject, copula and predicate. It divides into modal, categorica, simple and compound.
Modal: asserts mode. If it asserts a relationchip it is necessary metaphysical, physical, moral or logical.
Categorical: does not asser mode
Simple: relation of two terms
Compound: Relation of at least 3 terms.

Characteristics of propositions
Reference to reality (general or empirical)
Quantity (total or partial)
Quality (affirmative or negative)
Modality (necessary or contingent)
Value (true or false)

Symbolized propositional content is divided into a simple declarative sentence, a complez declarative sentence, a compound declarative sentence or a non-sentence.

Relations of Simple Propositions

The relations of propositions can be divided into four:
Conjunction: joining two or more propositions (implicit/explicit) (bare/material)
Opposition: the square opposition
Eduction: obversion, conversion, added determinants, omitted determinants, converse relation.
Syllogism: simple, hypothetical, disjunctive, the dilemma.

In this chapter of the book is where logic is starting to make sense. It is where we work a little harder to find the logic of the relationships.

The Simple Syllogism

A syllogism is an act of reasoning by which the mind perceives that from the relation of two propositions (premises) having one term in common there necessariliy emerges a new, third proposition (conclusion) in which the common term, called the middle term (M) does not appear.
The formula for reasoning is either valid or invalid.

Matter of syllogism: three propositions relating its three terms. (S – minor, P – mayor, M – middle).

Figure: determined by the position of the middle term in the premises.

Enthymeme: a syllogism logically abridged by the omission of one proposition.
Because, for, since introduce a premise.
Therefore, consequently, accordingly introduces a conclusion.
And/but connects two premises and indicates that the preposition omitted is the conclusion.

Sorities: chains of enthymemes or abridged syllogisms.
Conclusion turns into the mayor premise of the next.
Conclusion turns into minor premise of the next (Aristotelian, Goctenian)

Epicheirema: abridged polysyllogism combining any figures, at least one of the premises in an enthymeme.

Mediated opposition: is the opposition between two propositions which together contain 3 terms, one being common to both.

Reduction: demonstrate the validity of an imperfect figure as a formal process of reasoning by showing that an argument carried according to the rules of an imperfect figure is valid in the perfect figure.

What we don’t realize is that in this chapter Sister Miriam is actually describing part of our daily lives, like the use of the enthymeme. We might not notice but we are constantly using the grammar and logic used in this chapter, with this in mind we can come to think that grammar is the basics to knowing anything.

Relations of Hypothetical and Disjunctive Propositions.

A hypothetical proposition is one that asserts the dependence of one proposition on another

Fallacies

A fallacy is a violation of a logical principle disguised under an appearance of validity; an error in process. A “erroneous relation of proposicions”.
Falsity: an error in fact. A erroneous relation of terms”.

Fallacies in diction (6): ambiguity of language
Equivocation: ambiguity of words.
Amphiboly: ambiguity of grammatical structure.
Composition: Parts are illicitly predicated of the whole.
Division: the whole is illicitly predicated into parts.
Accent: different meaning conveyed through emphasis.
Verbal form: similarity in language = similarity in meaning.

Fallacies in extradictionem: false assumption.
Accident: shifting usage of the same term (intention, imposition)
Confusion of absolute and qualifies statements: true in one case is assumed to be true in another.
Fallacy of consequent: assumption that a proposition is convertible simple –
Arguing besides the point: ignoring the issue (argumentum ad hamen, ad populum, ad misericordiam, ad baculum, ad ignoratiam.
False cause: something that is not a cause is held for a cause.
Begging the question: assuming the proposition to be proved (tautological, shuttle, question-begging, and epithet).
Complex question: divide a question and answer it by parts.

A Brief Summary of Induction

Logic seeks truth. The requirements for truth are:
What is thought must represent what is.
Thoughts must be consisted among themselves.

Knowledge is whatever the information the mind possesses.

Induction: every proposition is derived directly or ultimately from induction. It could be enumerative, intuitive or dialectical.
Induction is concerned with the investigation of causes:
Cause: makes the thing what is
Condition: enables the cause to act in producing effects.
Determining agent: conditional that sets in motion causative factors.

Aristotle’s 4 metaphysical causes: explain every material effect.
Efficient cause
Final cause
Material cause
Formal cause
Scientific induction: discovery of thruth
Observation
Analogy
Hypothesis
Sifting of data (joint method, residues, concomitant variations, method of agreement, method if difference)
Verification of hypothesis (elimination, intuitive induction, application and demonstration by deduction).