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General Information

Course ID (CB01A and CB01B)
PHILD007.
Course Title (CB02)
Deductive Logic
Course Credit Status
Credit - Degree Applicable
Effective Term
Fall 2023
Course Description
This course is a study of the concepts and methods of deductive logic, emphasizing formal proof techniques in sentential and predicate logic.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This course meets a general education requirement for °®¶¹´«Ã½ and CSU. This is a CSU and UC transferable course. This course belongs on the Liberal Arts degree program. This is °®¶¹´«Ã½'s only course that focuses specifically on the elements and methods of modern deductive logic. It is a required course in virtually all contemporary BA programs in philosophy in the US.

Foothill Equivalency

Does the course have a Foothill equivalent?
No
Foothill Course ID

Course Philosophy

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Letter Grade
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Transferable to both UC and CSU
°®¶¹´«Ã½ GEArea(s)StatusDetails
2GA3°®¶¹´«Ã½ GE Area A3 - Critical ThinkingApproved
CSU GEArea(s)StatusDetails
CGA3CSU GE Area A3 - Critical ThinkingApproved
C-IDArea(s)StatusDetails
PHILPhilosophyApprovedC-ID PHIL 110 C-ID PHIL 210

Units and Hours

Summary

Minimum Credit Units
4.0
Maximum Credit Units
4.0

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours4.08.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
48.0
Laboratory
0.0
Total
48.0
Course Out-of-Class Hours
Lecture
96.0
Laboratory
0.0
NA
0.0
Total
96.0

Prerequisite(s)

Corequisite(s)

Advisory(ies)

EWRT D001A or EWRT D01AH or ESL D005.

Limitation(s) on Enrollment

(Not open to students with credit in the Honors Program related course.)

Entrance Skill(s)

General Course Statement(s)

(See general education pages for the requirements this course meets.)

Methods of Instruction

Lecture and visual aids

Discussion of assigned reading

Discussion and problem solving performed in class

Quiz and examination review performed in class

Homework and extended projects

Collaborative learning and small group exercises

Collaborative projects

Assignments

  1. Reading
    1. Assigned reading from required and/or supplementary texts that introduce the nature, vocabulary, and techniques of propositional and predicate) logic.
    2. Assigned reading from required texts that demonstrate the relevance of formal logic to philosophical concerns in epistemology, metaphysics, and ethics. Readings will be be drawn from authors with diverse social, gender, and cultural perspectives and backgrounds.
    3. Assigned reading on the development and history of logic, giving students insight into the contributions to logic from a diverse set of logicians from across the globe.
  2. Writing
    1. Problem sets in sentential and predicate logic
    2. Analyzing paragraphs and/or essays for their deductive logical structure of reasoning
    3. Assigned translations of English texts into sentential and predicate logic

Methods of Evaluation

  1. Quizzes, midterm, and final exam comprised of translations, validity tests, proofs, and comprehension of technical vocabulary.
  2. Problem sets assigned to be completed both in class and as homework. Assigned problems will require students to translate English sentences into sentential or predicate logic, utilize methods of formal proof, and test the validity of arguments.
  3. Collaborative group work on proofs and translations in sentential and predicate logic, followed by a discussion in which students provide an accurate oral explanation of their work.
  4. Evaluation of readings demonstrating the relationship between philosophical problems in metaphysics, epistemology, ethics, and formal logic. Instructor will facilitate in-class discussions of readings, with the instructor assessing student comprehension of the philosophical implications of logic via informal quiz questions accompanying these discussions.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • None.
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
Allen, Colin and Hand, Michael. "Logic Primer". Cambridge, MA: MIT Press, 2001.
Copi, Irving and Carl Cohen, "Introduction to Logic", Fourteenth Edition, New York, NY: Routledge, 2013.
Hurley, Patrick, and Watson, Lori "A Concise Introduction to Logic", Thirteenth Edition. Boston, MA: Cengage, 2018.
Sider, Ted, "Logic for Philosophy". Oxford: Oxford University Press, 2010.
Bergmann, Moor, and Nelson, "The Logic Book," Sixth Edition, New York, McGraw-Hill Press, 2014.

Examples of Supporting Texts and References

AuthorTitlePublisher
Aristotle, Analytica Priora, in Richard McKeon (ed.), "The Basic Works of Aristotle", New York, NY: Random House, 1941.
Beaney, M. (ed.), "The Frege Reader", Oxford, UK: Blackwell Publishers, 1997.
Church, Alonzo, "Introduction to Mathematical Logic", Reprint Edition, Princeton, NJ: Princeton University Press, 1996.
Marcus, Ruth Barcan, "Modalities: Philosophical Essays", Oxford: Oxford University Press, 1995.
Russel, Bertrand. "On Denoting". In Mind (New Series) vol 14, no. 56 (Oct. 1905).
Kneale, William and Martha Kneale, "The Development of Logic", Oxford, UK: Clarendon Press, 1991.
Mates, Benson, "Stoic Logic". Berkeley and Los Angeles, CA: University of California Press, 1961.
Nye, Andrea. Words of Power: "A feminist Reading of the History of Logic", New York: Routledge, 1990.
Matilal, Bimal Krishna, "The Character of Logic in India". Albany: SUNY Press, 1998
Zhuangzi, "The Complete Works of Zhuangzi", trans. Burton Watson. New York: Columbia University Press, 2013.
Russell, Bertrand. And Alfred N. Whitehead, "Principia Mathematica to *56". Cambridge, UK: Cambridge University Press, 1967.
Strawson, P.F., "Introduction to Logical Theory", Methuen & Co. Ltd., 1967.
Mills, Charles W., "The Racial Contract", Ithaca: Cornell University Press, 1999.
Appiah, Kwame Anthony, "As If: Idealization and Ideals", Cambridge, MA: Harvard University Press, 2019.
Paul, L.A., "Transformative Experience", Oxford: Oxford University Press, 2015.

Learning Outcomes and Objectives

Course Objectives

  • Develop and formulate a conceptual and methodological understanding of deductive logic, including investigation of: the nature of deductive reasoning; practical and philosophical applications of formal logic; the limitations of logic.
  • Analyze basic elements of deductive reasoning, using the technical vocabulary of formal logic.
  • Apply the techniques of sentential logic.
  • Employ the techniques of predicate logic, and demonstrate a grasp of the differences between sentential and predicate logic

CSLOs

  • Translate English sentences into the languages of propositional and predicate logic.

  • Distinguish between valid and invalid deductive arguments.

  • Complete multi-step deductive proofs, employing primitive rules of proof for propositional and predicate logic.

Outline

  1. Develop and formulate a conceptual and methodological understanding of deductive logic, including investigation of: the nature of deductive reasoning; practical and philosophical applications of formal logic; the limitations of logic.
    1. Uses for inductive and deductive logic.
    2. Philosophical applications of logic in epistemology, metaphysics, and ethics.
    3. Logical symbolization as fundamental motif of written, verbal, and numerical communications in all human languages and quantitative reasoning
    4. Distinction of deductive and inductive argument forms and their correlative relations
    5. The development of logic from Aristotle, late antiquity, the European middle ages, and Frege's revolution in the "Begriffschrift", and the post-Fregean developments. Later developments will include work done by logicians in the United States, Europe, India, and Asia. These will also include contributions to logic by women, such as Ada Lovelace and Ruth Barcan Marcus.
  2. Analyze basic elements of deductive reasoning, using the technical vocabulary of formal logic.
    1. Argument definition, identification, and the contexts of discovery and justification
    2. Argument form and the distinction between sentences and propositions
    3. Truth, validity, entailment, and soundness in deductive arguments
  3. Apply the techniques of sentential logic.
    1. Distinction of atomic and compound sentences, variables and constants, and sentences and sentence forms
    2. Symbolic notation for conjunctions, disjunction, material implication, material equivalence, and negation
    3. Structure and function of truth table analysis and/or truth trees
    4. Identification of tautological, contradictory, and contingent sentences
    5. Symbolization of compound sentences
    6. Structuring arguments in ordinary language into their proper argument form
    7. Differentiating argument form and argument validity (formal vs. non-formal validity)
    8. Constructing standard proofs using valid argument forms
    9. Principles of strategy and common errors that occur in proof generation
    10. Constructing conditional and indirect proofs
    11. Techniques for demonstrating argument invalidity, premise consistency, and premise inconsistency at level of sentential logic
    12. Philosophical issues associated with material implication and argument validity
    13. Application of the methods of sentential logic to philosophical texts, including works by a diverse set of thinkers such as Zhuangzi, Aristotle, Charles W. Mills, Ruth Barcan Marcus, L.A. Paul, and Kwame Anthony Appiah.
  4. Employ the techniques of predicate logic, and demonstrate a grasp of the differences between sentential and predicate logic
    1. Distinguishing between and symbolizing individuals and properties
    2. Universal and existential quantifiers
    3. Constructing valid proofs in predicate logic
    4. Symbolization with polyadic predicates
    5. Precise formulation and justification of the quantifier rules
    6. Rule QN or equivalent technique in predicated logic
    7. Techniques for proving arguments invalid, premises consistent and inconsistent in predicate logic
    8. Explanation and formulation of the theorems of logic
    9. Identity theorem and proofs involving identity
    10. Formal translation of of definite descriptions
    11. Limitations of predicate logic in relation to higher order logics
    12. Techniques for demonstrating invalidity in predicate logic
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