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Profile: Frederick Johnson (Colorado State University, Oberlin College, Cambridge University, Oxford University)
  1. Fred Johnson (2004). Aristotle's Modal Syllogisms. In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic. Elsevier. 1--247.
    McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.
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  2. Fred Johnson & Peter Woodruff (2002). Categorical Consequence for Paraconsistent Logic. In Walter Carnielli (ed.), Paraconsistency:the logical way to the inconsistent. 141-150.
    Consequence rleations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion consequence relations.
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  3. Fred Johnson (1999). Parry Syllogisms. Notre Dame Journal of Formal Logic 40 (3):414-419.
    Parry discusses an extension of Aristotle's syllogistic that uses four nontraditional quantifiers. We show that his conjectured decision procedure for validity for the extended syllogistic is correct even if syllogisms have more than two premises. And we axiomatize this extension of the syllogistic.
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  4. Fred Johnson (1999). Rejection and Truth-Value Gaps. Notre Dame Journal of Formal Logic 40 (4):574-577.
    A theorem due to Shoesmith and Smiley that axiomatizes two-valued multiple-conclusion logics is extended to partial logics.
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  5. Fred Johnson (1997). Extended Gergonne Syllogisms. Journal of Philosophical Logic 26 (5):553-567.
    Syllogisms with or without negative terms are studied by using Gergonne's ideas. Soundness, completeness, and decidability results are given.
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  6. Fred Johnson (1995). Apodeictic Syllogisms: Deductions and Decision Procedures. History and Philosophy of Logic 16 (1):1-18.
    One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.
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  7. Fred Johnson (1994). Review or Open Minds and Everyday Reasoning by Zachary Seech. [REVIEW] Philosophy in Review 14 (3):211-212.
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  8. Fred Johnson (1994). Syllogisms with Fractional Quantifiers. Journal of Philosophical Logic 23 (4):401 - 422.
    Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are given (...)
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  9. Fred Johnson (1994). Zachary Seech, Open Minds and Everyday Reasoning Reviewed By. Philosophy in Review 14 (3):211-212.
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  10. Fred Johnson (1993). Modal Ecthesis. History and Philosophy of Logic 14 (2):171-182.
    Fred's semantics for McCall's syntactic presentation of Aristotle's assertoric and apodeictic syllogistic is altered to free it from Thom's objections that it is unAristotelian. The altered semantics rejects Baroco-XLL and Bocardo-LXL, which Thom says Aristotle should have accepted. Aristotle's proofs that use ecthesis are formalized by using singular sentences. With one exception the (acceptance) axioms for McCall's system L-X-M are derivable. Formal proofs are shown to be sound.
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  11. Fred Johnson (1992). Counting Functions. Notre Dame Journal of Formal Logic 33 (4):567-568.
    Counting functions are shown to be complete by using a simpler argument than that used by Pelletier and Martin.
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  12. Fred Johnson (1991). Suppositional Reasoning. In Frans H. Van Eemeren (ed.), Proceedings of the Second International Conference on Argumentation 1990. 281-287.
  13. Fred Johnson (1991). Three-Membered Domains for Aristotle's Syllogistic. Studia Logica 50 (2):181 - 187.
    The paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universal subsets of the domain to terms such that the model invalidates the polysyllogism.
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  14. Fred Johnson (1989). Models for Modal Syllogisms. Notre Dame Journal of Formal Logic 30 (2):271-284.
    A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.
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  15. Fred Johnson (1989). Analogical Arguings and Explainings. Informal Logic 11 (3).
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  16. Fred Johnson (1984). Arguings and Arguments. Informal Logic 6 (2):26-27.
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  17. Fred Johnson (1984). Trees for a 3-Valued Logic. Analysis 44 (1):43-6.
    Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.
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  18. Fred Johnson (1980). An Introduction to Reasoning. Teaching Philosophy 3 (3):373-375.
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  19. Fred Johnson (1980). Deductively-Inductively. Informal Logic 3 (1):4-5.
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  20. Frederick A. Johnson (1979). Copi's Method of Deduction. Notre Dame Journal of Formal Logic 20 (2):295-300.
    Copi's method of deduction is formalized and shown to be complete.
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  21. Fred Johnson (1977). A Natural Deduction Relevance Logic. The Bulletin of the Section of Logic 6 (4):164-168.
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  22. Fred Johnson (1976). A Three-Valued Interpretation for a Relevance Logic. The Relevance Logic Newsletter 1 (3):123-128.
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  23. Frederick Ernest Johnson (ed.) (1960). Patterns of Ethics in America Today. New York, Distributed by Harper.
    Ethics of Judaism, by M.J. Routtenberg.--Ethics of Roman Catholicism, by J.P. Fitzpatrick.--Ethics of Protestantism, by A.T. Mollegen.--The ethical culture movement, by J. Nathanson.--Rational ethics, by L. Bryson.--Ethical frontiers, by W.G. Muelder.
     
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