Ancient Philosophy Handout #1: Logic Overview I. Stoic Logic A. Proposition types Affirmative P P Negative not P ~P Conjunction P and Q P Q Hypothetical (or Conditional) if P, then Q Disjunction P or Q P Q Negated Conjunction not both P and Q B. Basic Syllogistic Forms Mode Ponendo Ponens Ponendo Tollens Tollendo Ponens Common Modus Ponens Conjuctive Syllogism Disjunctive Syllogism P Q P Q P Q ~P Q Example If the fight against al-qaeda in Iraq meets all the criteria of the Just-War Theory, then there is no moral objection to fighting it. It does meet those criteria. So, there s no moral objection to fighting it. He cannot have passed every test and still failed the course. He did pass every test. So, he did not fail the course He either passed the placement examination or he took logic at another school before coming here. He did not take logic at another school. So, he passed the placement examination.
2 Mode Tollendo Tollens Common Modus Tollens ~Q ~P Example If my theory is correct, then these two chemicals should turn yellow when mixed. They do not turn yellow when mixed. So, my theory is not correct. C. Other Argument Forms Common Chain Argument Constructive Dilemma Destructive Dilemma Q R P R R S P R Q S P S ~Q ~S ~P ~P] Example If guns are outlawed only outlaws will have guns. If only outlaws have guns, our country will be a more dangerous place to live. So, if guns are outlawed, our country will be a more dangerous place to live. (St. Thomas More:) If I swear that the Act of Succession in declaring the King head of the Church in England is legal, I will be guilty of perjury & lose my soul. If I swear that the Act is illegal, I will be charged with treason & lose my life. I have only two choices: swearing that the Act is legal or swearing that it is illegal. [In fact, he found a third alternative.] So, either I will lose my soul or I will lose my life. (Plato in the Republic:) If Homer speaks the truth then the heroes are the sons of the gods and if he speaks the truth then they did many wicked things. But either they are not the sons of gods or they did not to many wicked things. So, Homer does not speak the truth.
3 II. Aristotelian Logic A. Proposition types Type Universal Affirmative All S are P Asp Particular Affirmative Some S are P Isp Particular Negative Some S are not P Osp Universal Negative No S are P Esp B. Opposition & Conversion 1. Contradictory Opposition: The members of a contradictory pair have opposite truth-value (one must be true; the other must be false) All S are P & Some S are not P No S are P & Some S are P (Asp & Osp) (Esp & Isp) 2. Contrary Opposition: Universal propositions are contrary to one another. They cannot both be true. All S are P & No S are P (Asp & Esp) 3. Conversion: Conversion is the interchange of subject & predicate. It is valid for E & I propositions and for A propositions when the predicate is a definition. No S are P. So, No P are S. (Esp. Eps) Some S are P. So, Some P are S. (Isp. Ips) All S are P (defn). So, All P are S. (Asp (defn). Αps)
4 C. Concepts necessary to distinguishing Categorical Syllogisms The names of terms major term minor term middle term The names of premises major premise minor premise The mood of a syllogism The figure of a syllogism 1st Figure 2nd Figure 3rd Figure Definition Isp Osp Omp Osp the predicate of the conclusion p p p the subject of the conclusion s s s the term which occurs in both premises, but not in the conclusion the premise containing the predicate of the conclusion (the major term) the premise containing the subject of the conclusion (the minor term) the list of the forms of proposition in this order: major minor conclusion the specification of now the middle term is related to the end terms the figure in which the middle term is subject of one end term & predicated of the other the figure in which the middle term is predicated of both end terms the figure in which the middle term is subject of both end terms m m m Omp AII EIO OAO 1 2 3
5 D. Valid Syllogistic Forms Premise Pair (at least one Universal; at least one Affirmative) 1st Figure (Univ. Major; Aff. Minor; Any Conclusion) 2nd Figure (Univ. Major; Any Minor; Neg. Conclusion) 3rd Figure (Any Major; Aff. Minor; Part. Concl.) AA Asm Asp EA Asm Esp Asm Esp AE Apm Esm Esp AI Ims IA Imp Isp EI Ims AO Apm Osm OA Omp
6 1st Figure Schema Example Barbara Amb Adm Adb All wars that inflict more harm than good are unjust. All nuclear wars inflict more harm than good. So, all nuclear wars are unjust. Celarent Darii Ferio Emb Adm Edb No military action whose harmful effects cannot be controlled is morally permissible. All military uses of biological weapons are military actions whose harmful effects cannot be controlled. So, no military uses of biological weapons are morally permissible. All wars that inflict more harm than good are unjust. Some wars in defense of a good cause inflict more harm than good. So, some wars in defense of a good cause are unjust. No military actions that intentionally kill the innocent are just. Some US military actions in WWII intentionally kill[ed] the innocent. So, some US military actions in WWII were not just.
7 2nd Figure Schema Example Cesare Asm Esp No computers are capable of common sense. All human beings are capable of common sense. So, no human beings are computers. Camestres Festino Baroco Apm Esm Esp Apm Osm All persons are capable of language use. No computers are capable of language use. So, no computers are persons. No punishments that are not essential to the fight against crime are justified. Some contemporary executions are punishments not essential to the fight against crime. So, some contemporary executions are not justified. All animals have the power of sensation. Some living things do not have the power of sensation. So, some living things are not animals.
8 3rd Figure Schema Example Darapti All lemons are sour. All lemons are fruits. Some fruits are sour. Disamis Datisi Felapton Bocardo Ferison Imp Ims Omp Ims Some human beings do stupid things. All human beings are rational. So, some rational beings do stupid things. All human beings are rational. Some human beings do stupid things. So, some beings that do stupid things are rational beings. No lemons are sweet. All lemons are fruits. So, some fruits are not sweet. Some citrus fruits are not sweet. All citrus fruits are fruit. So, some fruits are not sweet. No living beings capable of local motion are plants. Some living beings capable of local motion are onecelled organisms. So, some one-celled organisms are not plants.