After an initial approach to the very notion of formal logic and the main stages of its historical development, the course aims to examine the core concepts, terminology, and philosophical interpretations (ancient-medieval, modern rationalist, Kantian), as well as the most important forms of inference in traditional logic. A comprehensive final chapter on elementary mathematical logic (propositional and first-order) facilitates students' access to the conceptual and deductive changes brought about by contemporary mathematical logic.
UNIT 1: Introduction
Topic 1: General Introduction
1.0. Preliminary remarks: Syllabus. Bibliography. Exams. Assignments.
1.1. The concept of formal logic.
1.2. Formal logic and foundational research.
1.3. Major stages in the history of logic.
UNIT 2: Traditional Logic
Topic 2: Introduction to Traditional Logic
2.1. Logic, ontology (metaphysics), and epistemology.
2.2. Fundamental operations of the intellect.
2.3. Divisions of traditional logic.
2.4. The relationship of traditional logic with other branches of knowledge.
Topic 3: Logic of Concepts
3.1. Simple apprehension, concept (notion or idea), and term.
3.2. Concept, essence, and beings of reason.
3.3. Formation of concepts.
3.4. Concept and image.
3.5. Comprehension (intension) and extension of a concept.
3.6. Types of concepts.
3.7. The universality of concepts.
3.8. Term: meanings, use, and mention.
3.9. Analogy in terms and concepts (analogical meaning of terms and concepts).
3.10. Predicables or categorematic terms.
3.11. Predicaments or categories, and transcendentals.
3.12. Theory of definition.
3.13. Theory of division.
3.14. Correlations between concepts.
Topic 4: Logic of Judgments
4.1. Judgment, proposition, and statement.
4.2. Primary properties of judgments.
4.3. Structure of judgment.
4.4. Divisions of propositions.
4.5. Proposition correlations.
4.6. Obversion and conversion of propositions.
Topic 5: Logic of Reasoning
5.1. Reasoning, argument, argumentation.
5.2. Immediate inference.
5.3. Mediate inference: the syllogism.
5.4. Rules of the syllogism.
5.5. "Figures" and "modes" of the syllogism.
5.6. Reduction of syllogisms.
5.7. Indirect reduction (or "reduction to absurdity").
5.8. The question of the fourth figure.
5.9. Special forms of the categorical syllogism.
5.10. Invalid arguments.
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UNIT 3: Mathematical Logic
Topic 6: Elementary Mathematical Logic
6.1. Introduction. Key features of mathematical logic.
6.2. Propositional logic.
6.3. First-order logic (restricted predicate calculus).
Learning Activities:
1. In-person teaching and learning:
o Lectures by the professor.
o Student presentations.
o Debates.
o Final written exam.
2. Guided learning:
o Guided readings.
o One-on-one tutorials.
o Individual written assignment and in-class presentation.
3. Autonomous learning:
o Supplementary readings proposed by the professor.
o Personal study.
o Independent research and material gathering.
? Attendance, participation, and in-class exercises.
? Midterm written exam.
? Final written exam at the end of the semester.
? Attendance, participation, and in-class exercises: analytical and synthetic ability; knowledge and correct use of concepts; communication skills; deductive exercises: 10%
? Midterm written exam: analytical and synthetic ability; knowledge and correct use of concepts; communication skills; deductive exercises: 45%
? Final written exam: analytical and synthetic ability; knowledge and correct use of concepts; communication skills; deductive exercises: 45% for students who passed the midterm; 90% for those who failed it.
Alfredo Deaño, Introducción a la lógica formal, Madrid, Alianza, 1999.
José Luis Falguera y Concepción Martínez, Lógica clásica de primer orden: estrategias de deducción, formalización y evaluación semántica, 2 vols., Madrid, Trotta, 2004.
Carmen García Trevijano, El arte de la lógica, Madrid, Tecnos, 2008.
Manuel Garrido, Lógica simbólica, Madrid, Tecnos, 2001.
Manuel Sacristán, Introducción a la lógica y al análisis formal, Barcelona, Ariel, 1964.
Juan José Sanguinetti, Lógica, Pamplona, EUNSA, 1985.
R. Verneaux, Introducción general y Lógica, Barcelona, Herder, 1980.
Aristóteles [1]: Tratados de lógica (2 vols.), Madrid, Gredos, 1988.
Aristóteles [2]: Metafísica, Madrid, Gredos, 1982.
Hans Urs von Balthasar, Teológica, 3 vols. (I-II: 1985, III: 1987), Madrid, Encuentro, 1997 (I-II),
1998 (III).
Joseph Gredt OSB, Elementa Philosophiae aristotelico-thomisticae (vol. I: Logica),
Barcelona, Herder, 1956.
Hegel [1812]: G.W.F.Hegel, Ciencia de la lógica (2 vols.), Buenos Aires, Solar, 1993.
Hegel [1817]: Lógica (Primera parte de la Enciclopedia) (2 vols.), Barcelona, Orbis, 1984.
Martin Heidegger, Lógica. La pregunta por la verdad, Madrid, Alianza, 2004.
Heidegger, Principios metafísicos de la lógica, Madrid, Síntesis, 2007.
Heidegger [1937/38]: Preguntas fundamentales de la filosofía, Granada, Comares, 2008.
Edmund Husserl, Philosophie de l'arithmétique, Paris, PUF, 1972.
Husserl, Investigaciones lógicas, 2 vols., Madrid, Alianza, 1982.
Husserl, Lógica formal y lógica trascendental, México, UNAM, 1962.
Immanuel Kant, Principios formales del mundo sensible y del inteligible (Disertación de 1770),
Madrid, CSIC, 1996.
Kant, Crítica de la razón pura, Madrid, Alfaguara, 1984.
Kant, Prolegòmens a tota metafísica futura que vulgui presentar-se com a ciència,
Barcelona, Laia, 1982.
Kant, Lógica (ed. Jäsche), Madrid, Akal, 2000.
Teodoro Lipps, Elementos de Lógica, Madrid, Daniel Jorro Editor, 1925.
Jan Lukasiewicz, La silogística de Aristóteles desde el punto de vista de la lógica formal
moderna, Madrid, Tecnos, 1977.
A. Pfänder, Lógica, Buenos Aires, Espasa-Calpe Argentina, 1938.
Helmut Seiffert, Introducción a la lógica, Barcelona, Herder, 1977.
Manuals de lògica matemàtica i temes connexos
Agazzi, E., La lógica simbólica, Barcelona, Herder, 1973.
Crossley, J. N., y otros, ¿Qué es la lógica matemática?, Madrid, Tecnos, 1983.
Dalla Chiara, M. L., Lógica, Barcelona, Labor, 1976.
Deaño, A., Las concepciones de la Lógica, Madrid, Taurus, 1980.
José Ferrater Mora y Hugues Leblanc, Lógica matemática, México, FCE, 1992.
David Hilbert y Wilhelm Ackermann, Elementos de lógica teórica, Madrid, Tecnos, 1975.
Richard C. Jeffrey, Lógica formal. Su alcance y sus límites, Pamplona, EUNSA, 1986.
Jean Ladrière, Limitaciones internas de los formalismos, Madrid, Tecnos, 1969.
Benson Mates, Lógica matemática elemental, Madrid, Tecnos, 1979.
Jesús Mosterín, Lógica de primer orden, Barcelona, Ariel, 1976.
Daniel Quesada, La Lógica y su Filosofía, Barcelona, Barcanova, 1985.
Willard V. O. Quine, Los métodos de la lógica, Barcelona, Ariel, 1981.
Patrick Suppes, Introducción a la Lógica Simbólica, México, Cía. Editora Continental, 1966.
Alfred Tarski, Introducción a la Lógica, Madrid, Espasa-Calpe, 1977.
Ernst Tugendhat y Ursula Wolf, Propedéutica lógico-semántica, Barna, Anthropos, 1997.
J. M. Bochensky, Historia de la lógica formal, Madrid, Gredos, 1985.
William y Martha Kneale, El desarrollo de la lógica, Madrid, Tecnos, 1980.
P.H. Nidditch, El desarrollo de la lógica matemática, Madrid, Cátedra, 1980.
Arthur N. Prior (y otros), Historia de la Lógica, Madrid, Tecnos, 1976.