History of Logical Consequence

Expositions

• Coffa, J. Alberto, 1993, The Semantic Tradition from Kant to Carnap, Linda Wessels (ed.), Cambridge: Cambridge University Press.
  An historical account of the Kantian origins of the rise of analytic philosophy and its development from Bolzano to Carnap. (Scholar)
• Kneale, W. and Kneale, M., 1962, The Development of Logic, Oxford: Oxford University Press; reprinted, 1984.
  The classic text on the history of logic until the middle 20th Century. (Scholar)

Source Material

• Ewald, William, 1996, From Kant to Hilbert: a source book in the foundations of mathematics (Volumes I and II), Oxford: Oxford University Press.
  Reprints and translations of important Texts, including Bolzano on logical consequence. (Scholar)
• van Heijenoort, Jean, 1967, From Frege to Gödel: a sourcebook in mathematical logic 1879–1931, Cambridge, MA: Harvard University Press.
  Reprints and translations of central texts in the development of logic. (Scholar)
• Husserl, Edmund, 1900 [2001], Logical Investigations (Volumes 1 and 2), J. N. Findlay (trans.), Dermot Moran (intro.), London: Routledge. (Scholar)
• Mill, John Stuart, 1872 [1973], A System of Logic (8th edition), in J. M. Robson (ed.), Collected works of John Stuart Mill (Volumes 7 & 8), Toronto: University of Toronto Press. (Scholar)

20th Century Developments

• Anderson, A.R., and Belnap, N.D., 1975, Entailment: The Logic of Relevance and Necessity (Volume I), Princeton: Princeton University Press. (Scholar)
• Anderson, A.R., Belnap, N.D. Jr., and Dunn, J.M., 1992, Entailment (Volume II), Princeton: Princeton University Press.
  This book and the previous one summarise the work in relevant logic in the Anderson–Belnap tradition. Some chapters in these books have other authors, such as Robert K. Meyer and Alasdair Urquhart. (Scholar)
• Dummett, Michael, 1991 The Logical Basis of Metaphysics, Cambridge, MA: Harvard University Press.
  Groundbreaking use of natural deduction proof to provide an anti-realist account of logical consequence as the central plank of a theory of meaning. (Scholar)
• Gentzen, Gerhard, 1969, The Collected Papers of Gerhard Gentzen, M. E. Szabo (ed.), Amsterdam: North Holland. (Scholar)
• Mancosu, Paolo, 1998, From Brouwer to Hilbert, Oxford: Oxford University Press.
  Reprints and translations of source material concerning the constructivist debates in the foundations of mathematics in the 1920s. (Scholar)
• Negri, Sara and von Plato, Jan, 2001, Structural Proof Theory, Cambridge: Cambridge University Press.
  A very accessible exposition of so-called Structural Proof Theory (which involves a rejection of some of the standard structural rules at the heart of proof theory for classical logic). (Scholar)
• Shoesmith D. J. and Smiley, T. J., 1978, Multiple-Conclusion Logic, Cambridge: Cambridge University Press.
  The first full-scale exposition and defence of the notion that logical consequence relates multiple premises and multiple conclusions. (Scholar)
• Restall, Greg, 2000, An Introduction to Substructural Logics, Lond: Routledge. (Précis available online)
  An introduction to the field of substructural logics. (Scholar)
• Tarski, Alfred, 1935, “The Concept of Truth in Formalized Languages,” J.H. Woodger (trans.), in Tarski 1983, pp. 152–278. (Scholar)
• –––, 1936, “On The Concept of Logical Consequence,” J.H. Woodger (trans.), in Tarski 1983, pp. 409–420. (Scholar)
• –––, 1983, Logic, Semantics, Metamathematics: papers from 1923 to 1938, second edition, J. H. Woodger (trans.), J. Corcoran (ed.), Indianapolis, IN: Hackett. (Scholar)

Philosophy of Logical Consequence

There are many (many) other works on this topic, but the bibliographies of the following will serve as a suitable resource for exploring the field.

• Avron, Arnon, 1994, “What is a Logical System?” in What is a Logical System?, D.M. Gabbay (ed.), Oxford: Clarendon Press (Studies in Logic and Computation: Volume 4), pp. 217–238. (Scholar)
• Beall, Jc, 2011, “Multiple-conclusion LP and default classicality,” Review of Symbolic Logic, 4(2): 326–336. (Scholar)
• Beall, Jc and Restall, Greg, 2000, “Logical Pluralism,” Australasian Journal of Philosophy, 78: 457–493. (Scholar)
• Belnap, Nuel D., 1962, “Tonk, Plonk and Plink,” Analysis, 22 (6): 130–134. (Scholar)
• Bonnay, Denis and Westerståhl, Dag, 2012, “Consequence Mining: Constants Versus Consequence Relations,” Journal of Philosophical Logic, 41(4): 671–709. (Scholar)
• –––, 2016, “ Compositionality Solves Carnap’s Problem,” Erkenntnis, 81 (4): 721–739. (Scholar)
• Brandom, Robert, 1994, Making It Explicit, Cambridge, MA: Harvard University Press. [See especially Chapters 5 and 6 on the account of logical consequence according to which truth is not a fundamental explanatory notion.] (Scholar)
• Caret, Colin R. and Hjortland, Ole T. (eds.), 2015, Foundations of Logical Consequence, Oxford: Oxford University Press. (Scholar)
• Carnap, Rudolf, 1943, Formalization of Logic, Cambridge, MA: Harvard University Press. (Scholar)
• Cobreros, Pablo; Égré, Paul; Ripley, David and van Rooij, Robert, 2012, “Tolerance and mixed consequence in the s’valuational setting,” Studia Logica, 100(4): 855–877. (Scholar)
• Etchemendy, John, 1990, The Concept of Logical Consequence, Cambridge, MA: Harvard University Press. (Scholar)
• –––, 2008, “Reflections on Consequence”, in D. Patterson (ed.), 2008. (Scholar)
• Garson, James W., 2013, What Logics Mean: From Proof Theory to Model-Theoretic Semantics, Cambridge: Cambridge University Press. (Scholar)
• Gomez-Torrente, Mario, 1996, “Tarski on Logical Consequence,” Notre Dame Journal of Formal Logic, 37: 125–151. (Scholar)
• Griffiths, Owen, and Paseau, A.C., 2022, One True Logic: A Monist Manifesto, Oxford: Oxford University Press. (Scholar)
• Hanson, William H., 1997, “The Concept of Logical Consequence,” The Philosophical Review, 106 (3): 365–409. (Scholar)
• Kennedy, Juliette and Väänänen, Jouko, 2017, “Squeezing arguments and strong logics,”, in Hannes Leitgeb, Ilkka Niiniluoto, Elliot Sober and P. Seppälä (eds.), Logic, Methodology, and the Philosophy of Science: Proceedings of the Fifteenth International Congress (CLMPS 2015), London: College Publications. (Scholar)
• Kreisel, Georg, 1967, “Informal Rigour and Completeness Proofs,” in I. Lakatos (ed.), Problems in the Philosophy of Mathematics, (Studies in Logic and the Foundations of Mathematics: Volume 47), Amsterdam: North Holland, pp. 138–186. (Scholar)
• McGee, Vann, 1992, “Two Problems with Tarski’s Theory of Consequence,” Proceedings of the Aristotelian Society, 92: 273–292. (Scholar)
• Murzi, Julien and Carrara, Massimiliano, 2014, “More Reflections on Consequence,” Logique et Analyse, 57 (227): 223–258. (Scholar)
• Murzi, Julien and Hjortland, Ole T., 2009, “Inferentialism and the Categoricity Problem: Reply to Raatikainen,” Analysis, 69 (3): 480–488. (Scholar)
• Patterson, Douglas, (ed.), 2008, New Essays on Tarski and Philosophy, Oxford: Oxford University Press. (Scholar)
• Peregrin, Jaroslav, 2014, Inferentialism: Why Rules Matter, UK: Palgrave Macmillan. (Scholar)
• Prawitz, Dag, 1974, “On the Idea of a General Proof Theory,” Synthese, 27 (1–2): 63–77. (Scholar)
• –––, 1985, “Remarks on some approaches to the concept of logical consequence,” Synthese, 62: 153–171. (Scholar)
• –––, 2005, “Logical Consequence from a Constructivist Point of View,” in S. Shapiro (ed.), The Oxford Handbook of the Philosophy of Mathematics and Logic, Oxford: Oxford University Press, pp. 671–695. (Scholar)
• –––, 2012, “The Epistemic Significance of Valid Inference,” Synthese, 187: 887–898. (Scholar)
• Priest, Graham, 1999, “Validity,” European Review of Philosophy, 4: 183–205 (Special Issue: The Nature of Logic, Achillé C. Varzi (ed.), Stanford: CSLI Publications. (Scholar)
• Prior, Arthur N., 1960, “The Runabout Inference-Ticket,” Analysis, 21 (2): 38–39. (Scholar)
• Putnam, Hilary, 1971, Philosophy of Logic, New York: Harper & Row. (Scholar)
• Quine, W.V.O., 1986 (2nd Ed.), Philosophy of Logic, Cambridge, MA: Harvard University Press. (Scholar)
• Raatikainen, Panu, 2008, “On Rules of Inference and the Meanings of Logical Constants,” Analysis, 68 (300): 282–287. (Scholar)
• Ray, Greg, 1996, “Logical Consequence: A Defense of Tarski,” The Journal of Philosophical Logic, 25 (6): 617–677. (Scholar)
• Read, Stephen, 1994, “Formal and Material Consequence,” The Journal of Philosophical Logic, 23 (3): 247–265. (Scholar)
• Restall, Greg, 2005, “Multiple Conclusions,” in P. Hájek, L. Valdés-Villanueva, and D. Westerståhl (eds.), Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress, London: KCL Publications, pp. 189–205. [Preprint available online in PDF]. (Scholar)
• Ripley, David, 2013, “Paradoxes and failures of cut,” Australasian Journal of Philosophy, 91(1): 139–164. doi: 10.1080/00048402.2011.630010. (Scholar)
• Sagi, Gil, 2014a, “Formality in Logic: From Logical Terms to Semantic Constraints,” Logique et Analyse, 57 (227): 259–276. (Scholar)
• –––, 2014b, “Models and Logical Consequence,” Journal of Philosophical Logic, 43 (5): 943–964. (Scholar)
• Shapiro, Stewart, 1987, “Principles of Reflection and Second Order Logic,” Journal of Philosophical Logic 16 (3): 309–333. (Scholar)
• –––, 1998, “Logical Consequence: Models and Modality,” in M. Schirn (ed.), The Philosophy of Mathematics Today, Oxford: Oxford University Press, pp. 131–156. (Scholar)
• –––, 2005, “Logical Consequence, Proof Theory, and Model Theory,” in S. Shapiro (ed.), The Oxford Handbook of the Philosophy of Mathematics and Logic, Oxford: Oxford University Press, pp. 651–670. (Scholar)
• –––, 2014, Varieties of Logic, Oxford: Oxford University Press. (Scholar)
• Sher, Gila, 1991, The Bounds of Logic, Cambridge, MA: MIT Press. (Scholar)
• –––, 1996, “Did Tarski Commit Tarski’s Fallacy?,” Journal of Symbolic Logic, 61 (2): 653–686. (Scholar)
• Sher, Gila, 2022, Logical Consequence, Cambridge: Cambridge University Press. (Scholar)
• Schroeder-Heister, Peter, 1991, “Uniform Proof-Theoretic Semantics for Logical Constants (Abstract),” Journal of Symbolic Logic, 56: 1142. (Scholar)
• Tarski, Alfred, 1986, “What are Logical Notions,” History and Philosophy of Logic, 7: 143–154. (Scholar)
• Tennant, Neil, 1994, “The Transmission of Truth and the Transitivity of Deduction,” in What is a Logical System? (Studies in Logic and Computation: Volume 4), D.M. Gabbay (ed.), Oxford: Clarendon Press, pp. 161–177. (Scholar)
• Wansing, Heinrich, 2000, “The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical Operations,” Studia Logica, 64 (1): 3–20. (Scholar)
• Westerståhl, Dag, 2012, “From constants to consequence, and back,” Synthese, 187 (3): 957–971. (Scholar)
• Woods, Jack, 2012, “Failures of Categoricity and Compositionality for Intuitionistic Disjunction,” Thought: A Journal of Philosophy, 1 (4): 281–291. (Scholar)
• Zinke, Alexandra, 2018, The Metaphysics of Logical Consequence (Studies in Theoretical Philosophy: Volume 6), Frankfurt am Main: Vittorio Klostermann. (Scholar)