Comparing and Contrasting Classical and Modern Logic, Essay Example

Introduction

The realm of logic is inherently complex, with deviations and variations in style and approach which become intensely technical.  It is usual to perceive logic as a relatively simple process, and one engaged in all the time. This is true, in a fundamental sense; people continually act based upon the basic logic of the situations before them. For instance, if I do A, then B will inevitably result.  As B is not desirable, I will not do A. This is the deductive means virtually everyone uses, to some extent or another, in life.

This ordinary, “layman’s” logic is little more than an extension of classical, or Aristotelian, logic.  Moreover, this approach was traditionally the only one observed in academic and scientific circles as well. Until the nineteenth century, virtually all recognized logic was classical, and held to the basics laid down by that philosopher. In classical logic, there is an implied acceptance of truths which render the process more simple; as long as the premise is true, it follows that the conclusion must be true (Haaparanta, 2009,  p. 3). As will be discussed, however, modern logicians have developed methodologies in stark contrast to Aristotelian principles.  While modern logic, far more mathematically based than classical, is consequently far more intricate, the reality remains that modern logic parts company with classical in one, essential arena: classical logic assumes established existences and/or premises, and modern logic is enormously more open to unknown variables.  Unlike Aristotelian logic, the modern approach takes something of a quantum view, and relies upon seeing any number of possibilities denied by classical logic.

Basics in Form and Contrast

As devised by Aristotle, classical logic employs a limited number of set formulas.  These rely, in turn, on syllogisms, or reasoning deducted from several subjects and predicates. Syllogistic logic is not of itself elementary; as it depends upon interchangeable factors of major, minor, and middle terms – and as the combinations of the substances of each of these produces further variations and some fallacies – there is an ample framework at play. Ultimately, however, classical logic exists to make a point or substantiate a conviction.  The key components are, always, subject and predicate. The former sets the stage for the conclusion, as the latter is the logical, and usually inevitable, consequence of the logical sequence set forth by the application of the terms. An ordinary example would be: all men are mammals (minor term), all mammals are warm-blooded (middle term), and all men are warm-blooded (major term).  What is crucial in Aristotelian logic, if flaws or fallacies are to be avoided, is that the middle term be relevant to the others.   While there are, again, multiple variations on this basic formula, the essence of the process can be identified as being reliant upon meaning.  That is to say, classical logic eviscerates its own use if it is not understood that a man is a man, and a mammal is warm-blooded.

As noted, this mode of reasoning guided the thinking world for thousands of years. Only by the nineteenth century were scientists and logicians developing alternatives, and these ensued because of  an innate dissatisfaction with classical logic never fully confronted; that is, it was too grounded in philosophy to suit the true logician, or purist. It began to be perceived that classical logic was inherently limited, in that it was fully dependent on accepted, universal qualities and definitions. As was famously noted by mathematician and philosopher Alfred North Whitehead in 1934, Aristotelian logic may be compared to the primitive math of tribal cultures, whereas modern logic reflects the evolved science of higher mathematics (Bell, 1992,  p. 572).  The alternate route for the new thinkers was in these mathematics.

Modern logic is actually more than one type of logic, yet each relies upon mathematical formulas. What is most pivotal in this approach, which was largely developed by German logician Gottlob Frege, is the seemingly obvious fact that mathematics completely rely upon numbers. This goes to the great distinction between classical and modern logic, for it addresses the crucial element of the subjects themselves. As Frege saw it, and as modern logicians adhere to, a number exists independently of associations.  It is a more purely logical instrument because it cannot be tainted by preconceptions of any kind, no matter how universally held (Macbeth, 2005, p. 122). Numbers in this way of understanding become both less and more than what they are known to be: they are concepts unto themselves, divested of any specific meaning save for the current application. With modern logic, thousands of years of suppositions, which may cloud the purity of the logical process, are removed.

Further Contrasts and Similarities

There is, of course, one unifying aspect to both classical and modern logic. Each is in place to determine a conclusion or foresee a potentiality, based upon knowledge already in place. Differences in philosophies exist, yet these do not go to this foundation of philosophy, or intent. No matter the approach, logic is employed to achieve a rational means of thought and produce n objective and comprehensively attained information.

That noted, modern logic nonetheless still greatly differs from classical in what is actually prompting it. Logic exists to isolate essential elements and place them in a useful formula, yet even this may be approached in ways that reflect diverse intents, or at least expectations. Classical logic demands acceptance of natural facts, and things long assumed to be irrefutably real within the natural world, and this in itself narrows the parameters of possibilities. It does not take into account, for instance, the supposition that the facts in evidence are intrinsically subject to interpretation. The philosophical grounding for Aristotelian logic requires rights, wrongs, and various other value judgments maintained regarding actions and things.

Conversely, modern logic is uninterested in any such foundation to begin with: “Where classical logic requires all propositions to be true or false, nonclassical logics have flourished by questioning this assumption…” (Jacquette, 2002,  p. 5). Modern logic may be seen, in any of its incarnations, as a more hypothetical form of logic. Insistent on as absolute an objectivity as possible, it opens the door for a kind of “quantum” logic, one in which much more is possible because all the components are reduced to symbols of anything and everything. With no associations, no subject can be tainted by any kind of predetermined expectation.

This contrast in approach is clearly evident in the temporal way the disciplines are employed. A great problem with Aristotelian logic for modernists centers on not how, but when, existence of a thing is construed. Aristotle made it clear that any verb he employs refers only to present time. For a logician, this opens up dilemmas. If, for instance, classical logic asserts that “S is always S”, it ignores that which is not yet “S” or may become “S” (Back, 2000,  p. 180).  Here is a perfect illustration of how a mathematical logic removes even a seemingly irrelevant constraint.  It is certainly “logical” to assess a thing by the state it currently occupies but, in terms of logical aims, this is a limitation. It defines the thing in terms which may not be counted upon to last, and subsequently locks in the logical potentials.

Conclusion

Classical, Aristotelian logic served the world for a very long time, and it is still very much an active principle. If it is inevitably based on thousands of years of chiefly Westernized thinking, it nonetheless adheres to an ambition to arrive at conclusions free from emotional and/or worldly influences. It is “human” logic, born from human understandings of how the earth and the laws of nature work. Modern logic differs from it in a single and essential arena: classical logic assumes accepted existences and/or premises, but modern logic is determined to view components as “blank slate” variables expressed in numerical form. Ultimately, the modern approach to logic takes something of a quantum view, and relies upon seeing any number of possibilities denied by the associations inherent with classical logic.

References

Back, A. T. (2000.)  Aristotle’s Theory of Predication. Leiden, The Netherlands: BRILL.

Bell, E. T.  (1992.)  The Development of Mathematics. Mineola, NY: Dover Publications, Inc.

Jacquette, D.  (2002.)  Philosophy of Logic: An Anthology.  Malden, MA: Blackwell Publishers, Inc.

Haapararanta,  L. (2009.)  The Development of Modern Logic. New York, NY: Oxford University Press.

Macbeth, D. (2005.)  Frege’s Logic. Cambridge, MA: Harvard University Press.