introduction to logic
TRANSCRIPT
Introduction to Logic
A king moves one square in any direction.But, Solomon is a king.Therefore, Solomon moves one square in any direction.
Mr. Marcos is a billionaire.Mr. Marcos is a Filipino.Therefore, All Filipinos are billionaires.
Lost: the dog of a lady with a long tail
Recycle clothes and waste paper
God sees through everything.God sees through bathroom walls.God sees through bathrobes.
Why are you late?Because I’m not early.
Driver: Sir, do we turn left?Passenger: Right.
We have to be generous to others. Therefore, during examinations we have to share pur answers with our seatmate to show that we are generous.
The following statement is false.The preceding statement is true.
Logic is ...
• the study of the methods and principles used to distinguish correct from incorrect reasoning.
• the science and art of valid inferential reasoning
Logic is..
• only concerned with the “correctness” or the “validity” of reasoning (and not about truth)
• solely interested in the logical necessity (consequential relation) existing between the premises and the conclusion
Logic...
• Reasoning is valid if and when the conclusion is necessarily inferred from the premises.
(If X, then Y) and (If W, then Z)X or WTherefore, Y or Z
*logic is interested in the form of reasoning, its validity or correctness, irrespective of whether or not the premises of this reasoning agree with the facts.
Validity• True Premises, True Conclusion• • Valid: Lawyers are professionals.• Justices are lawyers.• Justices are professionals.• • Invalid: Lawyers are professionals.• Justices are professionals.• Justices are lawyers.• • True Premises, False Conclusions• • Invalid: Squares are polygons• Triangles are polygons• Triangles are squares
• • False Premises, True conclusion•
• Valid: Squares are three sided polygons• Triangles are squares• Triangles are three-sided polygons• • Invalid: Doctors are birds.• Surgeons are birds.• Surgeons are doctors.• • False Premises, False Conclusion• • Valid: Triangles are squares.• Circles are triangles.• Circles are squares.• • Invalid: Triangles are squares.• Circles are squares.• Circles are triangles.
Definition of Logic
• Etymological -> logike (gk.) – treatise on matters pertaining to thought (by Zeno of Elea)
• Real -> the science and art of valid inferential reasoning
Definition of Logic
• Logic is a science -> in as much as it follows certain scientific laws, patterns and principles in arriving at valid reasoning
• Logic is an art -> in as much as the mastery of its technique enables the mind to reason out in an easy, orderly and safe manner
Object of study
• Formal object-> inferential functions of concepts and propositions or logical relations of propositions (rules of eduction and syllogism, truth tables and validity)
• Material object -> concepts and conceptual structures (terms, propositions, syllogisms, informal fallacies, symbols)
Formal and Material Logic
• Formal Logic – discusses the conceptual patterns or structures needed for inference (main concern is validity and correctness of reasoning)
• Material Logic – discusses the kind of matter, that is the nature of terms and premises that are used in the different kinds of demonstration given in the latter part of logic (its concern involves truth, correspondence to facts)
Importance of Studying Logic
• It helps one to reason out validly• It makes us more critical and analytical• It helps us think systematically• It helps us detect fallacies and errors in reasoning • It helps us to distinguish valid from invalid
reasoning • It enables us to persuade people • It develops in us self-confidence
Divisions of Logic and Acts of the Intellect
Acts of the Intellect Mental Product External Sign Logical Issue
Simple Apprehension
Idea (s) Term (s) Predicability
Judgment Enunciation Proposition Predication
Reasoning Argumentation Syllogism Inference
Three Acts of the Intellect
• 1. Simple Apprehension – the first act of the intellect wherein the mind mentally grasps a thing without affirming or denying anything about it.
• Product: idea• External Sign: term• Example: book, everybody, conventional
Three Acts of the Intellect
• 2. Judgment – the second act of the intellect wherein we join two understood terms obtained in simple apprehension by affirmation or decompose the two terms by negation.
• Product: Enunciation• External Sign: Panda is a meat eater.
Some musicians are also painters.
Three Acts of the Intellect
• 3. Reasoning – is the third act of the intellect wherein we draw a conclusion from a given set of validly joined premises.
• Product: Argumentation • External Sign: Syllogism• Example: A square is a four sided polygon.
But a circle is not a four sided polygon.Therefore, a circle is not a square.
Development of Logic
• A. Pre-Aristotelian Logic in Greek -used logic to argue against each other
and defend their ideas
• ELEATICS – Zeno of Elea• SOPHISTS- Gorgias, Thrasymachus• MEGARICS - Euclides
Development of Logic
• B. Aristotelian Logic - Aristotle formalized a systematic study of logic (Oganon)
• Aristotle combined*Socrates’ idea of universal definition, *Zeno’s reductio ad absurdum, *Parmenides’ and Plato’s claims about propositional structure and negation *the argumentative techniques found in legal reasoning and geometrical proofs
Development of Logic
• C. Post-Aristotelian Logic in Greece-continuation and further development
of Aristotle’s Organon and the search for a criterion of truth (beginnings of Epistemology)
• Theophrastus – hypothetical syllogism• Eudemus, - responsible for incorporating logic
into philosophy
Development of Logic
• D. The Greek and Latin Commentators-the handing down of knowledge from the Greek to the Romans
Alexander of Aprhodisias and St. John of Damascus on the problem of universals
Galen – 4th syllogistic figure and the fallacies of DictionAndronicus of Rhodes – compiled and organized
Aristotle’s worksCicero – wrote the 1st logical treatise in Latin
Development of Logic
• E. The Scholastics and the Crusaders-improvement of Aristotelian logic and
the incorporation of logic into the sciences Marciannus Capella – De Nuptiis Mercurii et
PhilologiaeBoethius – translated Aristotle’s works into LatinPeter Abelard – composed an independent
treatise on logic
Development of Logic
• F. Modern Logic -aims at escaping the ambiguity of
language-development of the inductive method
way of reasoning and symbolic logic
Gottfried Wilhelm Leibniz – envisioned the development of a universal language to be specified with mathematical precision
Development of Logic
• 3 Overlapping Traditions in the Development of Logic1. Algebraic School – focus on the relationship between
correct reasoning and operations like addition ad multiplication
2. Logicist School – aimed to codify The underlying logic of all rational, scientific discourse into a single system
3. Mathematical School – axiomatization of particular branches of mathematics like geometry, arithmetic, analysis and set theory.
An Invitation to Logic• Protagoras was a Sophist who lived in Greece during the 5th century B.C. He taught many subjects but specialized in
the art of pleading before juries. Eulathus wanted to become a lawyer but not being able to pay the required tuition, he made an arrangement according to which Protagoras would teach him but not receive payment until Eulathus won his first case. When Eulathus finished his course of study, he delayed going into practice. Tired of waiting for the money due him, Protagoras brought suit against his former pupil for the fee that was owed. Unmindful of the adage that the lawyer who tries his own case has a fool for client, Eulathus decided to plead his own case in court, when trial began, Protagoras presented his side of the case in a crashing dilemma:
• If Eulathus loses this case, then he must pay me (by the judgment of the court).• If he wins this case, then he must pay me (by the terms of the contract).• But, he must either win or lose this case;• Therefore, Eulathus must pay me
• Eulathus rebutted the dilemma showing that he had learned to argue effectively under the tutelage of Protagoras:
• If I win this case, I shall not pay Protagoras (by the judgment of the court)• If I lose this case, I shall not pay Protagoras (by the terms of the contract)• But , I must either win or lose;• Therefore, I do not have to pay Protagoras.
Were you the judge how would you handle the case?