Philosophical Accounts of First-Order Logical Truths

  • Constantin C. BrîncuşEmail author


Starting from certain metalogical results (the completeness theorem, the soundness theorem, and Lindenbaum-Scott theorem), I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach to these truths should account for this evidence, i.e., that first-order logical truths are a priori, necessary, and analytic, and it is my contention that the semantic account is a better candidate.


First-order logical truths Completeness theorem Lindenbaum-Scott theorem 



I would like to thank Mircea Dumitru, Mircea Flonta, Matti Eklund, Ilie Pârvu, Gabriel Sandu, and Iulian Toader for their feedback. Special thanks to a reviewer for this journal whose substantial comments helped me improve this paper.


  1. Bacciagaluppi, G. (2009). Is logic empirical? In K. Engesser, D. M. Gabbay, & D. Lehmann (Eds.), Handbook of quantum logic and quantum structures (pp. 49–78). Amsterdam: Elsevier.CrossRefGoogle Scholar
  2. Boghossian, P. (1996). Analyticity reconsidered. Nous, 30(3), 360–391.CrossRefGoogle Scholar
  3. Bonnay, D., & Westerståhl, D. (2016). Compositionality solves Carnap’s problem. Erkenntnis, 81(4), 721–739.CrossRefGoogle Scholar
  4. Brîncuș, C. (2016). What Makes Logical Truths True?, Logos & Episteme. An International Journal of Epistemology, VII, 3: 249–272.Google Scholar
  5. Carnap, R. (1942). Introduction to Semantics, Cambridge, Mass.: Harvard University Press.Google Scholar
  6. Carnap, R. (1943). Formalization of Logic, Cambridge, Mass.: Harvard University Press. Google Scholar
  7. Carnap, R. (1950). Empiricism, Semantics and Ontology. Revue Internationale de Philosophie, 4(2), 20–40.Google Scholar
  8. Carnap, R. (1963). W. V. Quine on Logical Truth, in The Library of Living Philosophers, Vol. XI, The Philosophy of Rudolf Carnap (pp. 915-922), edited by Paul Arthur Schilpp, Open Court Publishing Company.Google Scholar
  9. Einstein, A. (1934). On the method of theoretical physics. Philosophy of Science, 1(2), 163–169.CrossRefGoogle Scholar
  10. Etchemendy, J. (1990). The concept of logical consequence. Cambridge, MA: Harvard University Press.Google Scholar
  11. García-Carpintero, M. (2003). Gómez-Torrente on modality and Tarskian logical consequence,  Theoria. An International Journal for Theory, History and Foundations of Science, 18(2), 159–170.Google Scholar
  12. Gentzen, G. (1969). Investigations into Logical Deduction. In M. E. Szabo (Ed.), The collected Papers of Gerhard Gentzen (pp 68-131), Amsterdam: North-Holland Publishing Company.Google Scholar
  13. Hacking, I. (1979). What is logic? The Journal of Philosophy, 76(6), 285–319.CrossRefGoogle Scholar
  14. Hilbert, D. (1930/2005). Logic and the knowledge of nature. In Ewald, W., editor, From Kant to Hilbert: a source book in the foundations of mathematics. Vol. II (pp. 1157-1165), Oxford University Press.Google Scholar
  15. Hintikka, J. (1999). The Emperor's new intuitions. The Journal of Philosophy, 96(3), 127–147.Google Scholar
  16. Hjortland, O. T. (2017). Anti-exceptionalism about logic. Philosophical Studies, 174(3), 631–658.CrossRefGoogle Scholar
  17. Kant, I. (1781/1998). Critique of Pure Reason, translated and edited by Paul Guyer and Allen W. Wood, Cambridge University Press.Google Scholar
  18. Koslow, A. (1992). A Structuralist conception of logic, Cambridge University Press.Google Scholar
  19. Koslow, A. (2010). Carnap’s problem: what is it like to be a normal interpretation of classical logic? Abstracta 6:1, 117–135.Google Scholar
  20. Kripke, S. A.. (1980/2001). Naming and Necessity, Harvard University Press (twelfth printing).Google Scholar
  21. Maddy, P. (2012). The philosophy of logic. The Bulletin of Symbolic Logic, 18(4), 481–504.CrossRefGoogle Scholar
  22. Manzano, M., & Alonso, E. (2013). Completeness: From Gödel to Henkin. History and Philosophy of Logic, 35(1), 50–75.CrossRefGoogle Scholar
  23. McEvoy, M. (2013). Does the necessity of mathematical truths imply their apriority? Pacific Philosophical Quarterly, 94: 431- 445.Google Scholar
  24. Payette, G., & Schotch, P. K. (2014). Remarks on the Scott–Lindenbaum theorem. Studia Logica, 102, 1003–1020.CrossRefGoogle Scholar
  25. Prawitz, D. (2005). Logical consequence from a constructivist point of view. In The Oxford Handbook of Philosophy of Mathematics and Logic (pp. 671- 695), edited by Stewart Shapiro, Oxford University Press.Google Scholar
  26. Prawitz, D. (2006). Meaning approached via proofs. Synthese, 148, 507–524.CrossRefGoogle Scholar
  27. Putnam, H. (1975). The logic of quantum mechanics. In: Mathematics, Matter, and Method, (pp. 174 - 197), Cambridge University Press.Google Scholar
  28. Quine, W. O. V. (1950/1966). Methods of Logic (revised edition). New York: Holt, Rinehart and Winston.Google Scholar
  29. Quine, W. O. V. (1951). Two dogmas of empiricism. Philosophical Review, 60(1), 20–43.CrossRefGoogle Scholar
  30. Quine, W. O. V. (1953). Three grades of modal involvement. In in The Ways of Paradox and Other Essays, 1966 (pp. 156–174). New York: Random House.Google Scholar
  31. Quine, W. O. V. (1995). Naturalism; or, living within One’s means. Dialectica, 49(2–4), 251–261.Google Scholar
  32. Rumfitt, I. (2015). The boundary stones of thought. An essay in the philosophy of logic, Oxford University Press.Google Scholar
  33. Russell, B.. (1919). Introduction to Mathematical Philosophy, London: George Allen and Unwin; New York: The Macmillan Company.Google Scholar
  34. Scott, D. (1971). On engendering an illusion of understanding. The Journal of Philosophy, 68(21), 787–807.CrossRefGoogle Scholar
  35. Scott, D. (1974). Completeness and axiomatizability in many-valued logic. In L. Henkin et al. (eds.) Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics, vol 25 (pp. 411 - 436),  American Mathematical Society.Google Scholar
  36. Shapiro, S. 2000. The status of logic. In Boghossian, P. and Peacocke, C. (eds.) New essays on the a priori (pp. 333-366), Oxford University Press.Google Scholar
  37. Shapiro, S. (2018). Possibilities, models, and intuitionistic logic: Ian Rumfitt’s the boundary stones of thought. Inquiry 1−14. DOI:
  38. Sher, G. (2011). Is logic in the mind or in the world? Synthese, 181, 353–365.CrossRefGoogle Scholar
  39. Sloman, A. (1965). 'Necessary', 'A Priori', and 'Analytic'. Analysis, 26(1), 12–16.Google Scholar
  40. Tahko, T. E. (2014). The Metaphysical Interpretation of Logical Truth. In Penelope Rush (ed.) The Metaphysics of Logic: Logical Realism, Logical Anti-Realism and All Things In Between (pp. 233-248), Cambridge University Press. Google Scholar
  41. Tarski, A. (1936/1956). On the concept of logical consequence. In Logic, semantics, Metamathematics (pp. 409–421). Oxford: Clarendon Press.Google Scholar
  42. Tarski, A. (1966/1986). What are logical notions?, edited (with an introduction) by John Corcoran. History and Philosophy of Logic, 7, 143–154.Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.University of Bucharest, Faculty of PhilosophyBucharestRomania

Personalised recommendations