Traditional Logic: Introduction to Formal Logic

1. Traditional Logic:Introduction to Formal Logic Martin Cothran

2. Introduction

3. Logic: The Basics (1) • Logic: The science of right thinking. • German philosopher Immanuel Kant called Aristotle “the father of logic.” • Formal logic has changed little since Aristotle.

4. Two Branches of Logic (2) • 1.) Material “major”: concerned with the content of argumentation. • Deals with the truth of the terms and propositions in an argument. • 2.) Formal “minor”: interested in the form of the structure of reasoning. • Truth is a secondary consideration; concerned with the method of deriving one truth from another.

5. G. K. Chesterton (2) “Logic and truth… have very little to do with each other. Logic is concerned merely with fidelity and accuracy with which a certain process is performed, a process which can be performed with any materials, with any assumption. You can be as logical about griffins and basilisks as about sheep and pigs… Logic, then, is not necessarily an instrument for finding out truth; on the contrary, truth is a necessary instrument for using logic—for using it, that is, for the discovery of further truth… Briefly, you can only find truth with logic if you have already found truth without it.”

6. This means what? (2) • We should refer to statements as true or false, not logical or illogical. • Likewise, arguments are not true or false, but valid or invalid. • Validity: helps describe if an argument is logical. • Truth: the correspondence of a statement to reality.

7. Argument Anatomy (3) • Expect your arguments to take on the general structure:

8. Mental Act vs. Verbal Expression

9. Mental Acts (3-4) • Simple Apprehension: occurs when we first form in our mind a concept of something. • EX: thinking of your logic book • Judgment: to affirm or deny • You think: “This book is boring.” • Deductive Inference: when we make the logical connections in our mind between the terms in the argument in a way that shows us that the conclusion either follows or does not follow from the premises; i.e., when we make progress

10. Verbal Expression (4) • Term: the verbal expression of a simple apprehension • Proposition: the verbal expression of a statement • Syllogism: the verbal expression of a deductive inference

11. Drawing everything together… (5) • Imagine moving from one room to another. • Moving your foot -> Simple Apprehension • Taking steps -> Performing judgment • Everything together -> Deductive inference

12. Chapter 1What is Simple Apprehension?

13. What is Simple Apprehension? (9) • The introduction said Simple Apprehension occurred when we first form in our mind a concept of something. • Example: Looking at a chair • 1. We perceive it with our senses • 2. We form an image of it with our minds • 3. We conceive of its meaning

14. 1. Sense Perception (9) • “Sense perception” is common vocabulary in all branches of philosophy • Definition: The act of seeing or hearing or smelling or tasting or touching.

15. 1. Sense Perception (9) • We have sense perception while we are in contact with objects • Your sense perception of a chair ends when you stop looking at the chair, etc. • The sense perception of “chair” is different than the chair itself because it is in your mind

16. 2. Mental Image (9-10) • Definition: The image of an object formed in the mind as a result of a sense perception of that object. • Occurs when an image continues after sense perception ceases • Different than both the chair itself, and the sense perception that it creates

17. 3. Concept (10-11) • Understanding without a mental image or sense perception. • “When you grasp the concept of something, like a chair, you understand what a chair is.” • “Simple apprehension is an act by which the mind grasps the concept of general meaning of an object without affirming or denying anything about it.”

18. Other Terms (11) • Essence: the meaning of a thing • Abstraction: The process by which a simple apprehension is derived from a sense perception and a mental image • Helps raise a chair from the senses to the intellect • To affirm or deny a Simple Apprehension is to engage in judgment • However, thinking merely “chair” is Simple Apprehension

19. Chapter 2Comprehension and Extension

20. First things… (15) • This chapter will discuss the properties of Simple Apprehension. • Definitions explain what something is. • Properties distinguish objects from each other. • The two properties of Simple Apprehension • Comprehension: tells the essence of a thing • Extension: tells us the things to which that essence applies

21. Comprehension (15) • Defined as “the completely articulated sum of the intelligible aspects, or elements (or notes) represented by a concept.” • Note this is NOT the definition you grew up with. Welcome to life. • Not all concepts are simple. • Plato’s definition of man: a “featherless biped” • Plato later said man is a “rational animal”

22. What is an animal? (16) • Animals break into four simple concepts: • Substance: something rather than nothing • Material: to have a non-spiritual body • Living (self-explanatory) • Sentient: to have senses • These concepts are called “notes,” or intelligible aspects represented by a concept. • See explanation of “Comprehension.” • A chair has four notes.

23. What is a man? (16) • “Man” breaks into five concepts or notes: • Substance • Material • Living • Sentient • Rational • Comprehension of man, then, equals the sum of said five notes.

24. The Porphyrian Tree (17) • Invented by third-century logician Porphyry • Helps us break down complex concepts into simple concepts • Comparable to our “Ladder of Abstraction” in terms of specificity

25. Porphyrian Categories (17) • Substance: material or nonmaterial • Unicorns have no substance yet chairs do. Do you know why? • Body: living or nonliving (mineral) • Organism: sentient or nonsentient (plant) • Animal: rational or nonrational (brute) • Logical species: man

26. Extension (19) • Extensions tells us the things to which that essence applies. Think “example!” • What is the extension of man? • All the men who have ever lived, who are now living, and who will live in the future • The greater number of notes a concept has, the less extension it has. • Man has five notes while animals have four. • “Man” is more specific than “animals” • There are more animals than man.

27. Important! (19) • The greater the comprehension a concept has, the less extension it has; and the more extension it has, the less comprehension. • Example: Man has five notes while animals have four. Thus, man is more specific and applies to less things. • The higher on the tree, the more to which the object applies. The lower, the less.

28. Simple Apprehension Wrap Up • Processes of Simple Apprehension • Sense Perception, Mental Image, Concept • Two properties of Simple Apprehension • Comprehension: a description plus categories • Extension: describes the things to which the concept applies • Next week we will have our last real vocabulary lesson!

29. Chapter 3: Signification and Supposition

30. Overview • Term: a word or group of words which verbally expresses a concept (23). • There are two properties of “terms” • Signification: defined by if the term is univocal, equivocal, or analogous (23) • Supposition: refers to types of existence, such as verbal, mental, or real (25)

31. Univocal Terms • Definition: have exactly the same meaning no matter when or how they are used (23) • Latin: “unus” (one) + “vox” (voice) • EX: photosynthesis, table saw, Phillips head screwdriver, drill bit

32. Equivocal Terms (24) • Definition: although spelled and pronounced exactly alike, have entirely different and unrelated meanings • Latin: “aequus” (equal) + “vox” (voice) • Example: plane, jar, hang • “We must all hang together, or assuredly we will all hang separately.” (Ben Franklin)

33. Analogous Terms (24) • Definition: applied to different things but have related terms • Unlike equivocal terms, their differing meanings are related • Example: “set of wheels” • Means both “car” and “new tires”

34. Why does this matter? (24) • Logic requires an accurate and consistent use of the terms • The English language has many equivocal and analogous terms • In real life, language confusion is the source of many arguments

35. Example Argument (25) • All NBA basketball players are men • Dennis Rodman is a good NBA basketball player • Therefore, Dennis Rodman is a good man • This argument is invalid because “good” is used analogously • This problem will be explained more in detail in later lessons

36. Supposition (25) • Verbal existence: refers to material supposition • EX: “Man” is a three-letter word • Mental existence: logical supposition • EX: “Man” has five notes • Real existence: real supposition • EX: censored

37. Summary of Chapters 1-3 (26) • Three aspects of logic: simple apprehension, judgment, deductive inference • Verbally expressed by terms, propositions, and syllogisms • In future chapters we will discuss terms in propositions, then syllogisms (arguments)

38. Chapter 4: What is Judgment? Chapter 5: The Four Statements of Logic

39. Judgment (31) • From the outset, Judgment (Mental Act) aligns with Proposition (Verbal Expression) • Judgment: the act by which the intellect unites by affirming, or separates by denying • EX: Man is an animal. • We are joining “Man” and “animal”

40. Uniting Concepts in Judgments (31) • Judgments are made of subjects and predicates • Subjects: that about which we are saying something; the concept which we are affirming or denying • Predicates: what we are saying about the subject; what we are affirming or denying about

41. The Proposition (32) • Definitions: (1) the verbal expression of a judgment; (2) a sentence or statement which expresses truth or falsity • Not all sentences are propositions (such as questions, commands, exclamations, etc.) • Examples • It is raining today. • There is a fly in my soup.

42. Elements of Proposition (32) • There are three elements to any proposition: • The subject-term (S), verbal expression of subject of a judgment • The predicate-term (P), verbal expression of a predicate of a judgment • The copula (C), the word that connects or relates the subject to the predicate; a form of “to be” such as “is” or “are”

43. Examples of Propositions (32) • Man (S) is (c) an animal (P). • The little brown-haired boy is very loud. • Subject: little brown-haired boy • Predicate: very loud • Notice how this is similar to algebraic statements, such as X = Y. • Modern logic takes this to an extreme, whereas Classical Logic does not.

44. Logical Sentence Form (33) • Sentences must be placed into a proper form to be handled logically. • EX 1: “The little brown-haired boy screams very loudly” is not in logical form. • We need to rework the predicate portion • EX 2: “The little brown-haired boy is a child who screams very loudly.”

45. The Four Statements of Logic (39) • Formal Logic has four basic categorical forms: • A: All S is P. • I: Some S is P. • E: No S is P. • O: Some S is not P. • The letters come from the Latin “affirmo” and “nego,” or “to affirm” and “to deny.” • Note: Non-categorical propositions will not be covered in this curriculum.

46. To Affirm or Deny? (40) • Affirmo • A: All S is P. (EX: All men are mortal) • I: Some S is P. (EX: Some men are mortal.) • Nego • E: No S is P. (EX: No men are mortal.) • O: Some S is not P. (EX: Some men are not mortal.) • Notice the pattern?

47. The Quantifier (40-41) • Quantifiers tell us quality and quantity • Four kinds: All, Some, No, Some… not. • Quality: affirmative or negative? • EX: “All men are mortal” affirms about “All men.” • Quantity: universal or particular? • Universal: refers to all, not some • Particular: refers to some, not all

48. Distinguishing Universals (41) • When there is no quantifier, we must determine whether they are universal or particular. • EX: “Frogs are ugly”  “All frogs are ugly” • General rule: All is intended unless some is clearly indicated. • EX: Men have gone to the North Pole. • Does not mean “all.” • “Some men have gone to the North Pole.”

49. Closing Thoughts • Universal/Particular cont.: In “Socrates is a man,” statement is singular (41). • We can summarize quality-quantity like this: • A: Affirmative-Universal • I: Affirmative-Particular • E: Negative-Universal • O: Negative-Particular (42)

50. Chapter 6: Contradictory and Contrary StatementsChapter 7: Subcontraries and Subalterns