The Trivium, Chapter 1: The Liberal Arts
“For both the utilitarian arts and the fine arts are transitive activities, whereas the essential characteristic of the liberal arts is that they are immanent or intransitive activities”
The liberal arts are studied for their own sake. For ourselves, to educate ourselves, and to create a mind in which we wish to live in.
Facio liberos ex liberis libris libraque “I make free men of children by means of books and a balance.”
Liberal arts are both an art and a science. Music, for instance, is the perfect example.
“The function of the trivium is the training of the mid for the study of matter and spirit, which together constitute the sum of reality.”
There are two types of studies, normative and speculative. The former, seeks to regulate, bring into conformity with a norm or standard. Grammar or ethics for example. The latter seeks to know and know only. Astronomy for example. Since we can only know but not influence over how the planets move.
The Trivium, Chapter 2: The Nature and Function of Language
The function of language is to communicate thought, volition, and emotion. Only humans have language, in the proper sense of the word. We communicate either by imitation (i.e. pictures, pantomimes) or by symbol, arbitrary sensible signs that have meaning imposed by convention. The spoken language is the original and fundamental system of symbols for which all other signs are merely substituted. This distinction between imitation and symbols made me wonder where would graphic design fit, specially that of portraying, for example, a cloud raining to convey the message of rainy weather (?).
A word, like any other physical reality, is constituted of matter and form. Orthography and phonetics, is matter. Semantics is form. The form of language is meaning. Words can symbolize individuality or essence, symbolizing a particular chair in the former and symbolizing all chairs in the latter. Only human beings have the power of intellectual abstraction, that is, understanding the essence of things and consequently being able to form a general or universal concept.
In P. 22 she stated that animals are incapable of progress because “they lack the rational powers (intellect, intellectual memory, free will)” (!=).
The logical dimension of a word is its thought content. In rhetoric this is called the denotation of a word. The psychological dimension of language is in its emotional content. In rhetoric this is called the connotation of a word.
“A sensitive awareness of the subtleties of language, particularly in its psychological dimension, enables one to recognize good style in the speech and writing of others and to cultivate good style in one’s own composition.” (=) P. 29.
The emotional effect (idiom) of a word is often a by-product of its historical context. Allusions are passing references. Pompous style is displeasing (!=). The psychological dimension of words is especially affected by their combinations (=). It’s important to make a distinction between logical and poetic understanding, especially when it comes to metaphors. Since words are symbols, whose meaning is not intrinsic but imposed on, ambiguity is a natural consequence. Ambiguity can arise from imposition and intention, from the nature of the phantasm, and even on purpose (irony and metaphors).
Aristotle, Cicero, and Renaissance rhetoricians held puns in esteem (!). To Aristotle metaphors were a compressed proportion a:c of a:b::c:d. An example would be the moon is a boat (a:c), because the moon (a) moves through the sky (b) as a boat (c) sails over the sea (d).
Cognition, appetition, and emotion, are the powers of the mind. Logic is concerned only with operations of the intellect. Grammar gives expression to all states of mind or soul. Rhetoric judges which one of a number of equivalent grammatical symbols for one idea is best for communication given the circumstance.
“Logic may function without rhetoric or poetry, but these without logic are shallow. Grammar is requisite to all.” Formal knowledge of the trivium is valuable because we should know why certain reasonings and expressions are correct or effective, and others just the opposite.
The Trivium, Chapter 3: General Grammar
“General grammar is concerned with the relation of words to ideas and to realities.”
I have always loved language, and by that I mean special grammar (incorrectly). Although I knew most of the content of this chapter from when I was in school, not because we all learned it in class but because of my special interest in it due to poetry and songwriting, I had lost most of the technicalities of this science. However, I had learned special grammar, which is that one specific to a language, unlike general grammar. I enjoyed revisiting this topic and actually got to engage it from a completely different perspective, which turned out to be very nourishing.
In general grammar the essential distinction between words is that between categorematic words, those which symbolize some form of being and can be categorized into either substantives and attributives. Syncategorematic words are those which have meaning only along with other words, they are mere grammatical cement and can be categorized into definitives and connectives.
“The human ability to abstract one aspect of reality and to make it the object of thought has been the indispensable means whereby the limited human mind has been able to advance in the search for truth. As human civilization advances, the proportion of abstract substantives in the language increases” (!)
Substantives (nouns and pronouns) symbolize either individuals, species, or genus. They have number, gender, person, and case. Cases include nominative, genitive, dative, and accusative, at least.
Verbs express an attribute along with the notion of time, time being the measure of change. Time is indispensable to verbs, however, tense is not. The mode or mood asserts the manner in which the subject and predicate are related as certain, possible, conditional, etc. Moods include indicative, potential, interrogative, and volitive (e.g. thou shall not steal). Verbs can be transitive or intransitive, depending if the action ends in the subject or if it ‘goes across’ to others.
Copulas are words that link an attributive or a substantive to the subject. There are two types of copulative verbs: true copulas and pseudocopulas. They differ in the sense that the latter expresses sense-perception (e.g The apple tastes sour).
There are two types of attributives, verbs and adjectives, they express an attribute to the subject. There are three classes of verbals: the infinitive, the participle, the gerund. Secondary attributives are adverbs function as attributes of attributes (e.g The man walks swiftly).
Syncategorematic parts of speech refer to words which are only significant with other words. Definitives are capable of singling out an individual or a group of individuals from the whole class designated by the common name. They include articles, indefinite and definite. Connectives include prepositions, conjunctions (explicit or implicit), and the pure copula (which connects the subject and predicate e.g the sun is shining).
The Trivium, Chapter 4: terms and their grammatical equivalents: Definition and division
Words are symbols creates to represent reality. A term is a concept communicated through a symbol. Once words are used to communicate a concept of reality, they become terms.
Terms can either be empirical or general, Concrete or abstract, absolute or relative, Collective and distributive. Terms have extension and intention, the former is the total set of objects which the term can be applied to, the latter is the essence of the term, the qualities that define it. As a term increases in intention it decreases in extension.
The summum genus is the largest genus, the infima species is the smallest species. The Tree of Porphyry illustrates the full relationship.
Definitions can be logical or distinctive. A distinctive definition is a definition by property, that is a definition by the characteristics that make something unique.
Logical division is the analysis of the extension of the term. Logical division includes three elements: the logical whole, the basis of the division and the dividing members.
Chapter 5: Propositions and their Grammatical Expression
Propositions can be labeled A, E, I, or O. Euler’s circles illustrates the differences between this concepts. A is total inclusion of S in P, all roses are flowers. E is total exclusion of P from S, No roses are flowers. I Inclusion of part of S in part of P, some roses are flowers. O Exclusion of all P from part of S, Some roses are not flowers.
Chapter 6: Relations of Simple Propositions
Invention is the art of finding material for reasoning or discourse, and disposition is the art of properly relating or ordering the material. The relations of propositions are four: conjunction (and), opposition (A E I O), eduction , and syllogism. Conjunction is a material relation, the others are formal relations (a process of either mediate or immediate inference).
Chapter 7: The Simple Syllogism
The syllogism is the act of reasoning by which the mind perceives 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 (M), does not appear. A syllogism is composed of three terms: Minor (S), which is the object of the conclusion. Major (P), the predicate of the conclusion. And Middle (M). A syllogism is composed of a minor premise (SM) and a major premise (PM).
To find the mood of a syllogism note the A E I O form of each of the premises. To find the figure, note the position of the middle term.
An enthymeme is a syllogism logically abridged by the omission of one proposition. Sorites are chains of enthymemes, where the conclusion of one becomes a premise of the next. An epicheirema is like a sorite but the movement of thought is partly backward and partly forward.
Analogical inferences are based on similitude and their conclusion can only be probable, if it ceases to be probable, it ceases to be an analogy.
Chapter 8: Relations of Hypothetical and Disjunctive Propositions
I made a lot of connections between this chapter and computer science or programming, since many of the language used for programming is the same or directly based from this types of propositions.
Hypothetical propositions express a conditional relationship of dependence between propositions, they’re composed of an antecedent and a consequent. They can either have three or four terms: If you study, you will learn. If she comes, I will go. A hypothetical proposition is true when the nexus holds in the real order and false when it does not.
A disjunctive proposition is one which asserts that of two or more suppositions, one is true. It is an either … or proposition.
Sine qua non means that the item labeled is essential.
This chapter served as well as an introduction to fallacies when using mixed hypothetical and simple syllogisms, dilemmas, and trilemmas.
Chapter 9: Fallacies
Since logic is concerned with truth, and a fallacy is a false argument disguised as valid, logic is concerned with fallacies. A fallacy is either formal (from the violation of rules governing the formal relations of propositions), material (have their root in the matter in which the idea is communicated), or both.
Fallacies In Dictione arise from the ambiguity of language. FallaciesExtra Dictionem are a hidden false assumption not warranted by the language in which the ideas are expressed.
The fallacies of arguing beside the point or ignorato elenchi include argumentum ad hominem, ad populum, ad misericordiam, ad baculum, ad ignorantiam, ad verecundiam. In rhetoric ethos means establishing the speaker or writer as one worthy of making an argument, pathos means that a speaker or writer tries to establish empathy with the audience. The post hoc ergo propter hoc inductive fallacy, which happens to be my all-time favorite, was discussed in this chapter as well.
Chapter 10: A Brief Summary of Induction
Logic deals with all that is thought in its most general aspect – truth. The norm of conception and induction is ‘What is thought must represent what is’. Knowledge is derived either from human powers (sense or intellectual) or from faith (all that one knows from the testimony of another).
Induction is not a form of inference, it is a form of intuition. Induction is a mental act, preliminary to inference; it is an intuition of truth, either general or empirical. There are three types of induction: Enumerative induction in which the assertion of a numerically definite plural empirical proposition as a result of observing facts and counting instances. Intuitive induction, the psychological act of asserting a self-evident proposition as true. Dialectical or problematic induction, the psychological act of asserting a proposition, whether general or empirical, as a possibility, without any calculation of its probability. Induction is the legitimate derivation of general propositions from individual stances. It is a method for the discovery of truth, not a process of proof or reasoning about truth.
It is also necessary to understand causality. A cause is that which has a positive influence in making a thing be what it is. A condition is that which in any way enables a cause to act in producing the effect. A determining agent is a condition which sets in motion the causative factors. And then we have the four metaphysical causes (the efficient, the final, the material, and the formal), which explain every material effect according to Aristotle.
(Page 216, interesting paragraph on free will of humans and free will of the universe (miracles).)
Philosophy in the field of knowledge. Progress towards unity goes like this: experience, science, philosophy, unity of the perfect truth. Philosophy’s primary function is to discover ultimate causes, it accepts the findings of the special sciences as its data and treats of the ultimate principles and characteristics which constitute the order or the universe as a whole.
Chapter 11: Composition and Reading
Aristotle systematised rhetoric and made it an instrument of truth, rhetoric was created as a tool of persuasion. It, alongside logic, are concerned with communicating truth from the mind of the author to the mind of the listener.
Aristotle defined it as the art of finding in any given subject matter the available means of persuasion, which is achieved by pathos, logos, and ethos. Logos requires one to convince the minds of the listeners or readers by proving the truth of what one is saying. Pathos requires on to put the listeners into a frame of mind favorable to one’s purpose, principally by working on the emotions. Ethos requires one to inspire in the audience, by courtesy and other qualities, confidence in one’s character, competence, good sense, good moral character, and good will. Style (good diction, grammatical structure, good rhythm, clear and appropriate language, etc.) and arrangement (the order of parts: introduction, statement and proof, conclusion) are also fundamental.
Poetic (narrative), as Aristotle understands it is imitation, imitation of life, in which the author does not speak to the reader directly but only through his characters. Poetry, on the other hand, uses rhythm and language and expresses things which cannot be expressed in any other way. Music uses rhythm and harmony. The book finishes with brief introductions of essays and expository writing.
This chapter was a very interesting way to finish the book because it very indirectly connected logic, grammar, and rhetoric through the different types of writing. I realized the importance of Aristotle and the many contributions he made to the trivium, and incremented the appreciation I have for poetry, since when regarded from a logical standpoint it was evident that it retained its irrational/unique edge.