Protreptikos, Vol. 1, no. 2, a publication of Introduction to Philosophy

return to Intro page
first page

Philosophy and Method

The Art of Logic - an Instrument of Philosophy

• Simple Apprehension: the act by which the intellect knows an essence (what a thing is), and produces a concept;
• Judgment: the act by which the intellect affirms or denies the truth of something, putting together or dividing apart concepts;
• Reasoning: the act whereby the intellect compares two concepts with one third concept, and perceives whether the two concepts go together.

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.

• A Definition is an expression that sets forth the nature of a thing or the meaning of a term. Every definition has two terms:
  1. the genus, or broad group;
  2. the specific difference, or what sets the thing apart from another thing.
• Definitions apply to groups of things. An individual cannot be defined, only described.
• A nominal definition does not show the nature of a thing directly, but either explains the word by etymology (e.g. philosophy is from two words that mean "love of wisdom") or by using a better known word (e.g. Canis domesticus is another term for dog).
• A real definition shows what the thing is. The best definition shows the essence of thing, but often this is impossible, and we have to use properties, or show how the thing is made.
• Laws of Definition:
  1. The definition must be interchangeable with the thing defined, i.e. you could substitute the word for the definition in a sentence without changing the meaning;
  2. The definition should be clearer than the thing defined;
  3. An essential definition is made up of the proximate genus and the specific difference.
  4. The thing that is defined should not enter into the definition, otherwise it is a "circular definition" (e.g. a dog is an animal that looks and sounds like a dog;
  5. A definition should not be negative;
  6. A definition should not be too long. It should not include anything unnecessary.
• A logical division is an expression that distributes a class of things into its parts. The following are rules for logical division:
  1. A logical division must have one foundation or criterion (animals are divided according to habitat, or according to the way they produce offspring, but not both at the same time);
  2. The whole and the members of the division are equal (no member is left out, nothing that is not part of the subdivisions is included);
  3. The division should be as simple as possible;
  4. A logical division should be orderly; a genus should be divided into the species immediately subordinate to it — we divide animals into vertebrates and invertebrates, and divide verterbrates immediately into amphibians, reptiles, birds, and mammals; we don't start by dividing animals into aardvarks, antelopes, ants... etc.

• 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).

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.

Errors in Logical Reasoning

A sophism is something that may appear to be a correct reasoning, but is not. Sophisms may be divided into two kinds:

1. Fallacies in Speech
2. Fallacies apart from Speech

Fallacies in Speech

1. Equivocation is when the middle term has two different meanings in each of the premises, but is taken in the same meaning;
2. Amphiboly arises from an ambiguous grammatical construction.

Fallacies apart from Speech

1. Fallacy of the Complex Question: what appears to be one question requiring one answer of yes or no, is actually two or more questions: e.g. "Have you stopped beating your wife?".
2. Begging the Question: someone tries to prove something by restating the thing that he intends to prove: e.g. "Thomas is the father of James, because James is the son of Thomas". If this goes through several steps, it is called a circular argument, or vicious circle.
3. Not to the Point: when one evades the question, supporting the argument by something irrelevant. This can be done in various ways:
   1. argument based on popularity : e.g. "everyone is doing it, so it can't be wrong";
   2. argument based on force: might makes right.
   3. argument based on false authority: many examples come to mind, actors voicing their opinions on matters of state, cartoon characters extolling the virtues of vitamins.
   4. argument based on character: where instead of looking at the strength of an argument, one tries to destroy the argument by attacking the character of the opponent.
   Where these types of argument are not strictly logical, they may sometimes be used properly in dialectic and rhetoric. There are many situations where we must make decisions and judgements in the face of some uncertainty. For example, the character of the witness should be established before we believe his testimony, and a defense lawyer may show that a witness has a history of deception. A policeman does not have to argue fine points of constitutional law every time he encounters someone in the commission of a crime. Logic textbooks often overlook this.
4. Fallacy of the Relative to the Absolute: something said in a qualified sense is applied in a general sense: e.g. "he is a good surgeon, so he is good, and he will be a good administrator". Perhaps this is the fallacy found in the "Peter Principle", that a person will be promoted in an organization until he is in a post where he is incompetent, and there he will remain. The people promoting him are constantly making the same error, thinking if he is good at one task, he will be good at another.
5. Fallacy of the Accident: what is said of an accident (a secondary feature) is applied in an absolute sense: e.g. My dog is big. Big is a word. Therefore my dog is a word. I don't think you will find this sort of argument except in universities and comedies such as Monty Python's Flying Circus. However, some philosophers, such as Kant, seem to have built their whole system upon

Laws of Reasoning

1. A true conclusion will always follow from a true premise, but a true conclusion may sometimes follow from a false premise.
2. The conclusion always follows the weaker part:if a premise is negative or not universal, so the conclusion will be merely negative or not universal. (A universal statement is one that states something about all the members of a class or group: e.g. "All men are mortal"). This is because the premises are the causes of the conclusion, and so the effect cannot be greater than the cause.

Ways of Reasoning: Induction, Deduction, and Analogy

1. Deduction is the ideal form of logical reasoning. A perfect formal reasoning starts from a general and universal premise, and concludes with a particular statement. This process of reasoning from general to particular is called deduction.

2. 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.

3. Reasoning by Analogy is the recognition of a similar pattern in otherwise dissimilar cases. It provides very little certainty or even probability, but is useful in forming hypotheses.

Argumentation: Science and Demonstration, Dialectic, Rhetoric, Poetic Argument

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.