(A) All S is P (or Every S is P) (E) No S is P (I) Some S is P In pursuing the aims of logic, it has been fruitful to proceed systematically, that is, to construct formal axiomatic sys-tems of various kinds. Aristotelian (Categorical) Logic •Aristotle identified four very common sentence forms, i.e. Also recall that usually in an argument the premises are offered to support or justify the conclusions. Argument vs. A SHORTCUT FORMAL METHOD: REDUCTIO AD ABSURDUM TESTS 315 Summary 320 6 MODAL PROPOSITIONAL LOGIC 323 1. MODAL OPERATORS 323 Non-truth-functionality 323 Modal and nonmodal propositions; modalized and non- modalized formulae 324 The interdefinability of the monadic and dyadic modal operators 327 3. the aim of logic proper is to develop methods for the logi-cal appraisal of reasoning,1 and the aim of metalogic is to develop methods for the appraisal of logical methods. –Some arguments can be shown to be valid by examining the forms of the premises and the conclusion. 5 It -may happen that F contains a member Xi and an infinite sub-class Fi, not includinlf sucg xh that the ^-combinationx tos consistin- g of x gether with any p—1 members of F], all belong to C\. Explanation •Arguments and explanations often have a similar structure. Recall that an argument is a collection of statements (declarative sentences), one of which is designated as the conclusion, and the remainder of which are designated as the premises. Descartes for one recognized this in his Rules for the Direction of the Mind (1628), where he writes: RULE 4: There is need of a method for investigating the truth about things. … (PDF partial edition with an added Appendix, 2014) A Modern Formal Logic Primer Previously published by Pearson Education, Inc. ... sively to formal logic, need only purchase Volume I1 to build on the foun- dation already laid. They might both take the form: Since , we have , or: , because . Formal Logic. Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous. Argument vs. Explanation •In an argument, the basis is the premises, which are already believed. patterns or structures. RULE 5:... we shall be Logical reasoning is vital to philosophy. •They both have what we might (vaguely) call a basis and a result. The Primer incorporates a number of unusual features. TRUTH-FUNCTIONAL PROPOSITIONAL LOGIC 313 10. Logic investigates inferences in terms of the arguments that represent them. Chapters 1, 3, and 4 emphasize the concept of a truth function. INTRODUCTION 323 2. The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an intro-ductory formal logic course). ON A PROBLE 26M OF FORMAL LOGIC.