The Indian numerals discussed in our article Indian numerals form the basis of the European number systems which are now widely used. However they were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe.
By Gail Jefferson
This report is a preliminary examination of lists occurring in natural conversation. It focuses upon the work which list-construction, as a task, allots to speakers, and some uses to which list-construction, as a resource, can be put by speakers.
The presence of three-part lists are first noted. Speakers and hearers orient to their three-part nature. The completed list can then constitute a turn at talk and the hearer can monitor the third component as a sign of turn completion. Lists can thereby’ be a conversational sequential resource.
By virtue of the three-part structure of some lists, members can orient to such matters as a “weak,” “absent,” or “missing” third part. Third items can be used to accomplish particular interactional work, such as topic-shifting and offense avoidance.
Further, a list can be constructed by more than one speaker. This feature may be used for a range of activities, including the achievement of interactional accord in situations of impending discord.
Read report here – List construction
9. Triadism and the Universal Categories
Merely to say that Peirce was extremely fond of placing things into groups of three, of trichotomies, and of triadic relations, would fail miserably to do justice to the overwhelming obtrusiveness in his philosophy of the number three.
Indeed, he made the most fundamental categories of all “things” of any sort whatsoever the categories of “Firstness,” “Secondness,” and “Thirdness,” and he often described “things” as being “firsts” or “seconds” or “thirds.”
For example, with regard to the trichotomy “possibility,” “actuality,” and “necessity,” possibility he called a first, actuality he called a second, and necessity he called a third. Again: quality was a first, fact was a second, and habit (or rule or law) was a third. Again: entity was a first, relation was a second, and representation was a third. Again: rheme (by which Peirce meant a relation of arbitrary adicity or arity) was a first, proposition was a second, and argument was a third.
The list goes on and on. Let us refer to Peirce’s penchant for describing things in terms of trichotomies and triadic relations as Peirce’s “triadism.”
Logic (Deduction and Induction) is one of the three roads from the Trivium.
The Subject of Logic: “Syllogisms”
All Aristotle’s logic revolves around one notion: the deduction (sullogismos). A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory. What, then, is a deduction? Aristotle says:
A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. (Prior Analytics I.2, 24b18-20)
Each of the “things supposed” is a premise (protasis) of the argument, and what “results of necessity” is the conclusion (sumperasma).
The core of this definition is the notion of “resulting of necessity” (ex anankês sumbainein). This corresponds to a modern notion of logical consequence: X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true. We could therefore take this to be a general definition of “valid argument”.
When arguing with someone in an attempt to get at an answer or an explanation, you may come across a person who makes logical fallacies. Such discussions may prove futile. You might try asking for evidence and independent confirmation or provide other hypotheses that give a better or simpler explanation. If this fails, try to pinpoint the problem of your arguer’s position. You might spot the problem of logic that prevents further exploration and attempt to inform your arguer about his fallacy. The following briefly describes some of the most common fallacies:
Ethos, Pathos, Logos
Within the Trivium the goal of argumentative writing is to persuade your audience that your ideas are valid, or more valid than someone else’s. The Greek philosopher Aristotle divided the means of persuasion, appeals, into three categories–Ethos, Pathos, Logos.
Ethos (Credibility), or ethical appeal, means convincing by the character of the author. We tend to believe people whom we respect. One of the central problems of argumentation is to project an impression to the reader that you are someone worth listening to, in other words making yourself as author into an authority on the subject of the paper, as well as someone who is likable and worthy of respect.