Comparing and Contrasting Modern and Classical Logic, Essay Example

Classical and modern logic can be viewed in terms of a shared continuity that takes the form of a fidelity to the basic principles of logic, particularly the premise that arguments should be consistent, and that truth is the product of such consistency. Concomitantly, there is nonetheless a shift present in modern logic that attempts to render classical logic more rigorous. In other words, modern logic assumes the basic essence of classical logic and a good majority of its technical commitments, but afterwards attempts to expand the scope covered by logic, in order to cover over any omissions, thus making the general project of logic more thorough. This is particularly realized through the formalisation of modern symbolic logic, which endeavors to treat a wide array of propositions; furthermore, modern logic can be viewed as taking a somewhat critical view towards tenets of classical logic.  In this regard, it is useful to summarize some of the main contentions of classical logic and then understand its continuity to the project of modern logic. Once this initial continuity is established, it can then be grasped how modern logic addresses some of the gaps in classical logic, and thus attempts to radicalize the extent of logic itself.

Classical logic is recognized in the academic literature as being established as a discipline by Aristotle. The foundational stone of Aristotelian logic is three laws or principles. (Andrews, 1996) Firstly, the principle of identity, that maintains that A = A, or in other words, that there is a consistency to an object; secondly, the principle of contradiction, in which an object “cannot be thought as at once having a certain character and not having that character (A cannot be B and not B)”; and the Principle of Excluded Middle, formulated as A is either B or not B. (Andrews, 1996) These foundational principles allow for a consistency in the formation of arguments and discourses, and moreover, permits one to evaluate the truth of a statement. As Maat (2006) succinctly summarizes this aim, “logic is a knowledge that teaches us how to think systematically by using the appropriate rules in logic. The rules help us to produce the right answer in decision making…logic is developed by the excellence of the human mind that generates the thinking of all knowledge…logic as the knowledge that can be developed through argument.” (p. 2) Accordingly, in classical logic, the development of an argument occurs through a primarily utilization of the three Aristotelian principles. This allows for a certain consistency to logical formulation, through the elimination of inconsistent or incoherent statements: such statements, in the classical logic system, are necessarily false. At the same time, classical logic can therefore be viewed as consisting of “built-in assumptions about the exactness or discreteness of objects” (Gabbay & Woods, 2004, p. 271) This means that classical logic relies on a consistency of the objects it is discussing, so as to maintain the rigorousness and ultimately the truth of its claims.

Modern logic continues this process, insofar as it maintains this same commitment to truth and the consistency of argument. Moreover, as West (2000) also notes, “both classical logic and modern logic are systems of deductive logic.” Deductive logic maintains that the premises of a true argument already deduce the conclusion, such that they follow from each other. This is once again indicative of the underlying consistency of the two logics in terms of the precise scope of their commitments to a specific vision of truth and the form of what constitutes a valid argument.  However, as Sion (2004) notes, one of the reasons for the necessity of the development of a modern logic lies in the notion that modern logicians sought to put in doubt or discard the Aristotelian “laws of thought”, insofar as some of these laws may be viewed as “debatable, if not arbitrary.” (p. 82) Accordingly, modern logic tries to make the Aristotelian laws more rigorous, or in other words, ground them through a variety of different means. Moreover, in a certain sense it can be said that modern logic thus maintains a critical relationship to classical logic and principles: modern logic does not merely accept these principles as axiomatic, but tries to more thoroughly understand them through the elimination of as much intuition and language from the field of logic as possible. At the same time, as Atkinson (2009) writes, paraphrasing Bertrand Russell, “the aim is to replace classical logic with a modern logic that…’enlarges our abstract imagination.” (p. 13) This abstract imagination thus expands what is possible to be logically true: what is logically true is not merely what is intuitive.

A means by which this enlargement is realized is through the increasing formalisation of modern logic, which can be understood as a means by which to radicalize this conceptual imagination through allowing different possible forms of propositions to be analyzed according to the same logical framework.  The introduction of formal notations within the modern logic – referred to as symbolic logic – suggests an attempt to eliminate some of the ambiguities existing in purely discursive or common language formulations of arguments. According to Henry West (2000), these modern logic systems “cover a far greater range of possible arguments than those that can be cast into syllogistic form.” Hence, modern logic attempts to recapitulate the basic structure of sentence propositions within its own consistent formal scheme, thus eliminating the ambiguity of language. This underscores the need for logic to be as rigorous as possible, while also expanding the number of propositions that may be analyzed logically.

Accordingly, classical and modern logic can be viewed as similar according to their shared commitment to rationality, the possibility for rigorous formulations of truth and the veracity of consistent arguments. However, the means by which to achieve this aim is what separates the two. Whereas classical logic is based largely on the discursive and intuitive reasoning of Aristotle, one that relies on a certain consistency of objects, modern logic displaces this approach through a more thorough and dynamic image of logic, as formalism and symbolism attempts to capture as many propositions as possible, while also seeking to eliminate some of the more intuitive claims of classical logic.

Works Cited

Andrews, Floy E. (1996). “The Principle of Excluded Middle Then and Now: Aristotle and Principia Mathematica.” Animus: The Canadian Journal of Philosophy and Humanities,  Vol. 1, No. 1.

Atkinson, J.R. (2009). The Mystical in Wittgenstein’s Early Writings. London: Taylor & Francis.

Gabbay, D.M. and Woods, J. (2004). Handbook of the History of Logic: The Rise of Modern Logic: From Leibniz to Frege. Miami, FL: Gulf Professional Publishing.

Maat, S.M.B. (2006). A Comparative Study of Classical Logic and Modern Logic from the Malaysian Perspective. Proceedings of the 2nd IMT-GT Regional  Conference of Mathematics, Statistics and Applications, June 13-15, 2006. Penang, Malaysia: IMT-GT and Universiti Sains Malaysia.

Sion, Avi. (2005). Ruminations: Sundry and Essays on Logic. Geneva, Switzerland: Avi Sion.

West, Henry R. (2000). “Logic”, Microsoft Encarta Online Encyclopedia.