|Protreptikos, Vol. 1, no. 2, a publication of Introduction to Philosophy|
Simple Apprehension is the grasp of a concept. A concept is also called an idea, a species, an intelligible form, and a mental word. A concept has an extension, which is the group of things included under the concept. A singular concept is the concept of one individual, for example, your concept of President Abraham Lincoln. A universal concept extends to a whole class of things. The more features (or notes) included in a universal concept, the narrower its extension. A transcendental concept is one that applies to anything that exists, for example being, thing, unit, distinct, good, true, beautiful. A concept by itself is not true or false, just as a single word is not true or false. A concept is a sign of a thing, just as a spoken word is a sign of a concept, and through the concept the spoken word is a sign of the thing. A concept is not merely a sensation stored in the mind, but is an immaterial act of understanding.
Our grasp of concepts is made precise by definition, and by logical division.
|The classical example of logical division and essential definition is known as the tree of Porphyry (a logician who wrote a commentary on Aristotle's Categories). It is like the mental technique developed by Tony Buzan called a mind map (nothing new under the sun!). To find Tony Buzan’s products to help create and use mind maps, visit: http://www.imindmap.com/|
|Tony Buzan developed has developed a number of memory techniques, on of which is the Mind Map. Our memory for spatial relations is better than our verbal memory, and so if we can draw a map-like diagram to represent ideas and their relations, we will retain more in our memory. Buzan's rules for drawing a mind-map are as follows: 1. A coloured image is in the centre; 2. Main ideas branch off the center; 3. Main Ideas should be in larger letters than secondary ideas; 4. Words should always be single (phrases can be broken down into a number of small branches on which there are single key-words); 5. Words should always be printed; 6. Words should always be printed on the lines (this gives your brain a clearer image to remember); 7. Lines should always be connected (this helps your memory to associate); 8. Use as many images as possible (this helps develop a whole-brained approach, as well as making it much easier for your memory to picture it; a picture is, in this sense, worth a thousand words); 9. Use dimension wherever possible (things outstanding are easier to remember); 10. Use numbers to code or put things in order; 11. For coding and connecting use arrows, symbols, numbers, letters, images, colours, dimension.|
A Judgment is expressed in a complete sentence or proposition. Judgements are either attributive, when we say "A is B", where A is a subject and B is a predicate, or existential, as when we say "A exists". Affirmation or affirmative judgment is called composition, because we are putting two concepts together. Negation is called division, because we are taking two concepts apart. A judgment is either true or false.
Reasoning involves three terms or concepts, and two judgments.. The major term is the most broad, the minor term is the most narrow, and the middle term is between the two, included in the meaning of the major term, and including in itself the meaning of the minor term. An example is given in the table below (The Structure of a Syllogism).
|Structure of a Syllogism|
|Major Premise||Every man is mortal||Mortal = major term|
Man = middle term
Philip = minor term
|Minor Premise||Philip is a man|
|Conclusion||Philip is mortal|
A syllogism is the verbal expression of an act of reasoning. In a syllogism or perfect argumentation, where one thing is given, another thing necessarily follows. Other forms of argumentation give lesser degrees of certainty. A perfect syllogism employes deduction, which is reasoning that starts from general truths, and then applies them in a particular instance.
A sophism is something that may appear to be a correct reasoning, but is not. Sophisms may be divided into two kinds:
Induction is reasoning from particular cases to a general truth. When it is based on a knowledge of every case, then it is called complete induction, and it is then infallible. Most often, even in the physical sciences, induction is based on a sample of cases, but not all possible cases, and then it is incomplete induction. It is always probable and fallible, and never certain, although for practical purposes, we may treat some inductive conclusions as certain.
Induction has some other specialized meanings in philosophical tradition. Karol Wojty»a (now Pope), mentions a sort of induction that comes naturally, called "stabilization", where particular sense qualities converge into the knowledge of one individual being.1. This is common to all animals, since animals can recognize individuals. Thomas Aquinas taught that we know first principles by induction.2. .
|1. Wojtyla, Karol The Acting Person, Reidel Publishing, Holland, 1979, p. 6 & 14.|
2. Aquinas, Summa Theologica I, 17, 3 c. in The Pocket Aquinas, p. 29-31.
Formal Logic is concerned with correct form in reasoning. Material Logic is concerned with truth in reasoning. In material logic, we look at the evidence and validity of the premises upon which our reasoning is based. If our reasoning is based on necessary premises, that is, statements which have irrefutable evidence, the expression of our reasoning is called a demonstration. Demonstration is a syllogism that produces science, or in more detail, it is a syllogism that contains premises that are true, primary, immediate, better known than, and causes of the conclusion. 1. Science, in the classical sense, is a kind of knowledge whereby we know the cause of a thing, a certain knowledge through causes.2. Ultimately every demonstration must reason on self-evident premises, which require no other proof. These are called principles. 3.
|1. cf. Oesterle, John A., Logic, the Art of Defining and Reasoning, Prentice-Hall, 1963, p. 327-250.|
2. Aquinas, Summa Theologica, I-II, q. 57, a. 2 in The Pocket Aquinas, p. 28-29. Another view of science was expressed by Auguste Comte(1798-1857), the founder of sociology, that science is not concerned with knowing causal relations, but merely with perceiving predictable statistical relations.
3. cf. Aquinas, Exposition of Aristotle's Posterior Analytics, I, lect. 5, in The Pocket Aquinas, p. 31.
If our reasoning is based on probable matter, which have strong but not irrefutable evidence, the expression of our reasoning is called dialectics. In dialectical argument, the truth or falsehood of a statement is tested by exploring its implications, and a statement may be disproved by showing that it leads to an absurdity. This method of reasoning is called reductio ad absurdum. Plato's dialogues offer many instances of dialectical reasoning. One example is the short dialogue Euthyphro In this dialogue we see the participants looking at a problem in several different ways, with examples and examinations of the logical consequences of various positions.
|cf. Plato, Euthyphro, in Stumpf's Elements of Philosophy, p. 5-11.|
Demonstration and dialectics are used as tools for obtaining knowledge. Rhetoric is argumentation used to convince others by any means. Rhetoric does have a legitimate role. Imagine a basketball coach, who would dispassionately construct rigorous logical argumnents for why the team should try to win. Poetic argument is the use of literature, fiction and myth to make a point about human existence.