Death of a Syllogism
The Importance of Syllogism
At Berith Press we want to encourage the reading of godly, pious material — especially from the Reformers and Puritans. Yet anyone who has read John Owen’s Mortification of Sin or Thomas Goodwin’s The Heart of Christ knows that the Puritan approach to theology takes some getting used to. One thing you will see is the use of logical categories such as syllogisms, as well as a heavy use of Latin, Greek, and Hebrew. We tend to put the Puritans and Reformers on a pedestal, ascribing their written mastery to some sort of otherworldly quality. No doubt these were devout men; yet they were so essentially different from us that recreating the quality of their theology is impossible. Rather, we need to rediscover the building blocks of Puritanism. This involves not only retrieving the Reformers’ conclusions, but significantly, their methodology also. While such a quest could branch out into several different avenues — the decline of Latin, the loss of Aristotelian causation, the general ignorance of Scholastic logic in the West — the purpose of this blog post is to focus on one simple aspect: the syllogism.
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The Syllogism in Antiquity
Logic has been a fundamental part of classical education since antiquity. While one might lament the decline of logic, the subject continues to be taught in schools and universities across the world, and logical fallacies are routinely called out in public argumentation.
I think something more subtle is going on: the death of the syllogism.
In his Prior Analytics, Aristotle defined a syllogism thus:
“A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that they produce the consequence, and by this, that no further term is required from without in order to make the consequence necessary.”
He then showed the form of a syllogism, containing premises leading to a conclusion:
“Every premise states that something either is or must be or may be the attribute of something else; of premisses of these three kinds some are affirmative, others negative, in respect of each of the three modes of attribution; again some affirmative and negative premisses are universal, others particular, others indefinite. It is necessary then that in universal attribution the terms of the negative premiss should be convertible, e.g. if no pleasure is good, then no good will be pleasure; the terms of the affirmative must be convertible, not however, universally, but in part, e.g. if every pleasure,is good, some good must be pleasure; the particular affirmative must convert in part (for if some pleasure is good, then some good will be pleasure); but the particular negative need not convert, for if some animal is not man, it does not follow that some man is not animal.”
And further:
“Whenever three terms are so related to one another that the last is contained in the middle as in a whole, and the middle is either contained in, or excluded from, the first as in or from a whole, the extremes must be related by a perfect syllogism. I call that term middle which is itself contained in another and contains another in itself: in position also this comes in the middle. By extremes I mean both that term which is itself contained in another and that in which another is contained. If A is predicated of all B, and B of all C, A must be predicated of all C: we have already explained what we mean by 'predicated of all'. Similarly also, if A is predicated of no B, and B of all C, it is necessary that no C will be A.”
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The Syllogism in the Reformation
The importance of syllogism was upheld by the Reformation logicians, who upheld the value of logic. Franco Burgersdijk wrote:
“So that to syllogize is to collect, that is, conclude, or from some certain propositions to draw up the sum of an argument or proof.”
Theophilus Gale stated:
“Syllogism, which clears the διάνοιαν or discursive intellect from those errors, and hesitations, which remain thereon.”
Pierre Du Moulin explained as follows:
“A syllogism is a reason or argument in which from two enunciations or propositions coupled together by certain laws, we draw and deduce a necessary conclusion.”
And further:
“Every syllogism is compounded of three parts or terms, namely: the subject of the conclusion, the attribute of the conclusion, and the mean or middle term, which knits these two parts of the conclusion together.”
Peter Ramus gave this definition of a syllogism:
“A syllogism is a disposition in which the question being arranged with the argument is necessarily inferred in the conclusion.”
The syllogism essentially formed the framework of Puritan argumentation, and was used extensively in proofs. One of the delights you will have when reading 17th century theology is in the author’s use of syllogisms, and how points are carefully demonstrated from such.
In the very first topic of his Institutes of Elenctic Theology (1679-1685), Francis Turretin argued for the theological significance of the syllogism in attaining to truth about the Lord, writing:
“Mixed syllogisms (in which one of the premises belongs to natural, the other to revealed religion) do not cease to be of faith. (1) Every proposition receives its denomination from the subject and not from the predicate. (2) A proposition of revealed religion virtually contains that which is drawn from the light of nature to prove it and thus communicates its own force to it. (3) To prove a conclusion of faith, the middle term must be taken not from nature, but from the Scriptures; but where the connection of the mean with the major extreme is denied by the adversary, it must be assisted by the principles of reason, not in order to prove the truth of the mean, but of the connection. For example, I deny that the bread becomes the body of Christ in the Supper (this mean term having been assumed that it has the accidents of bread). But if the connection of the mean with the major extreme is denied (namely, that is true bread which has the properties of bread), it must then be proved from reason because it is not contained in Scripture formally, but only virtually.”
So important was the syllogism to the Christian that William Ames, in his work Conscience with the power and cases thereof (1639) argued that a true syllogism was essential to the proper workings of conscience itself:
“It belongs to judgment discoursing, because it cannot do its act of accusing, excusing, comforting, unless it be through the means of some third argument, whose force appears only in a syllogism, by that which is deduced and concluded out of it. The force and nature of conscience therefore is contained in such a syllogism: He that lives in sin, shall die; I live in sin; Therefore, I shall die. Or thus: Whosoever believes in Christ, shall not die but live. I believe in Christ. Therefore, I shall not die but live.”
And yet, the syllogism would fall away over time, as the theology and logic of Pre-Modern Man were replaced by the more strictly mathematical approach of modernity.
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The Syllogism’s Decline
There was a distinct downgrade in the quality of theological works following the widespread popularity of John Locke’s teachings. In his 1690 work An Essay Concerning Human Understanding, Locke wrote:
“If we will observe the actings of our own minds, we shall find, that we reason best and clearest, when we only observe the connexion of the proofs, without reducing it to any rule of syllogism: and therefore we may take notice, that there are many men that reason exceeding clear and rightly, who know not how to make a syllogism.”
It was Locke’s theory of the human mind as a tabula rasa that helped shape the Enlightenment anthropology, casting man as a free agent with his mind being a blank slate, and effectively the author of his own destiny, without the need for any constraints on his mind from tradition. And so it is significant that Locke saw the syllogism as constricting, and the mind to be more free to reason without it.
Francis Bacon, meanwhile, wrote in his New Organon (1620) — rejecting syllogistic logic in favor of induction:
“The syllogism is not applied to the principles of the sciences, and is of no avail in intermediate axioms, as being very unequal to the subtilty of nature. It forces assent, therefore, and not things. The syllogism consists of propositions; propositions of words; words are the signs of notions. If, therefore, the notions (which form the basis of the whole) be confused and carelessly abstracted from things, there is no solidity in the superstructure. Our only hope, then, is in genuine induction.”
This showed the limitation of syllogisms in discovering new knowledge. Syllogisms could not lead you to new scientific knowledge, Bacon argued, as they were based upon premises that assumed prior knowledge. But in order to discover new knowledge, the syllogism would have to be suspended, with rational inquiry to take its place. Bacon’s argument makes sense: if you discover a new species of fish, for example, you will not be able to accurately deduce their behavior from syllogisms; rather you would have to make new observations about them, and reason from such.
While we may talk loosely of Bacon’s interest in science, it’s worth noting that theology is a science too, and what we might term “science” today would would have been described in pre-modern times as natural philosophy. What distinguishes theology from natural philosophy is that theology is mostly informed by the revelation of holy Scripture. Natural philosophy cannot contradict true theology, and it ought to use theology too in order to be more accurate; yet natural philosophy is not as tightly bound to revelation as theology is.
We might pause here also to note that, because Enlightenment philosophy set aside theology entirely, it deprived itself of the sort of mixed syllogisms combining revelation and observation (that would have met Francis Turretin’s definition mentioned earlier) that could have kept the natural sciences as a Christian discipline. However, as the Enlightenment set aside theology too, modern science took a different track that would come to oppose the true theology of Christian revelation itself.
But to return to our central topic of the syllogism: John Locke took the criticism of syllogism in a different direction to Bacon. Whereas Bacon considered the limitations of syllogisms in scientific discovery, Locke began to question the importance of syllogism within logic itself. Locke wrote in his Essay Concerning Human Understanding (1687):
“He that will look into many parts of Asia and America, will find men reason there, perhaps, as acutely as himself, who yet never heard of a syllogism, nor can reduce any one argument to those forms. indeed sometimes it may serve to discover a fallacy hid in a rhetorical flourish, or cunningly wrapped up in a smooth period; and stripping an absurdity of the cover of wit, and good language, show it in its naked deformity: but the mind is not taught to reason by these rules, it has a native faculty to perceive the coherence, or incoherence of its ideas, and can range them right, without any such perplexing repetitions. Tell a country gentlewoman, that the wind is south-west, and the weather louring, and like to rain, and she will easily understand that it is not safe for her to go abroad thin clad, in such a day, after a fever: she clearly sees the probable connexion of all these, namely south-west-wind, and clouds, rain, wetting, taking cold, relapse, and danger of death, without tying them together in those artificial and cumbersome fetters of several syllogisms, that clog and hinder the mind, which proceeds from one part to another quicker and clearer without them; and the probability which she easily perceives in things thus in their native state, would be quite lost, if this argument were managed learnedly, and proposed in mode and figure.
For it very often confounds the connexion: and, I think, every one will perceive in mathematical demonstrations, that the knowledge gained thereby, comes shortest and clearest without syllogism.
Secondly, because though syllogism serves to shew the force or fallacy of an argument, made use of in the usual way of discoursing, by supplying the absent proposition, and so setting it before the view in a clear light; yet it no less engages the mind in the perplexity of obscure, equivocal, and fallacious terms, wherewith this artificial way of reasoning always abounds: it being adapted more to the attaining of victory in dispute, than the discovery or confirmation of truth in fair enquiries.”
Locke’s argument is essentially that the syllogism is not natural so much as artificial, and argued that the syllogism was even suffocating to the liberty of the mind. He wrote further:
“But however it be in knowledge, I think, I may truly say, it is of far less, or no use at all in probabilities: for the assent there, being to be determined by the preponderancy, after a due weighing of all the proofs, with all circumstances on both sides, nothing is so unfit to assist the mind in that, as syllogism; which running away with one assumed probability, or one topical argument, pursues that until it has led the mind quite out of sight of the thing under consideration; and forcing it upon some remote difficulty, holds it fast there, intangled perhaps, and as it were, manacled in the chain of syllogisms, without allowing it the liberty, much less affording it the helps requisite to show on which side, all things considered, is the greater probability.”
In 1806, Thomas Reid published his Analysis of Aristotle’s Logic, with Remarks, and claimed:
“Although the art of categorical syllogism is better fitted for scholastic litigation than for real improvement in knowledge, it is a venerable piece of antiquity, and a great effort of human genius. We admire the pyramids of Egypt, and the wall of China, though useless burdens upon the earth; we can bear the most minute description of them, and travel hundreds of leagues to see them: if any person should, with sacrilegious hands, destroy or deface them, his memory would be had in abhorrence. The predicaments and predicables, the rules of syllogism, and the topics, have a like title to our veneration as antiquities; they are uncommon efforts, not of human power, but of human genius; and they make a remarkable period in the progress of human reason.”
Reid saw the study of mathematics as more important to reason than logic:
“I agree with Mr. Locke that there is no study better fitted to exercise and strengthen the reasoning powers, than that of the mathematical sciences - for two reasons: first, Because there is no other branch of science which gives such scope to long and accurate trains of reasoning; and, secondly, Because, in mathematics, there is no room for authority, nor for prejudice of any kind, which may give a false bias to the judgment. [...] As he goes on in mathematics, the road of demonstration becomes smooth and easy; he can walk in it firmly, and take wider steps; and at last he acquires the habit, not only of understanding a demonstration, but of discovering and demonstrating mathematical truths. Thus a man, without rules of logic, may acquire a habit of reasoning justly in mathematics; and I believe he may, by like means, acquire a habit of reasoning justly in mechanics, in jurisprudence, in politics, or in any other science. Good sense, good examples, and assiduous exercise, may bring a man to reason justly and acutely in his own profession, without rules.”
Reid concluded that logic was taught far too early, traditionally speaking; and that this must be replaced with mathematics:
“The prejudice against logic has probably been strengthened by its being taught too early in life. Boys are often taught logic as they are taught their creed, when it is an exercise of memory only, without understanding. One may as well expect to understand grammar before he can speak, as to understand logic before he can reason. It must even be acknowledged, that commonly we are capable of reasoning in mathematics more early than in logic. The objects presented to the mind in this science are of a very abstract nature, and can be distinctly conceived only when we capable of attentive reflection upon the operations of our own understanding, and after we have been accustomed to reason. There may be an elementary logic, level to the capacity of these who have been but little exercised in reasoning; but the most important parts of this science require a ripe understanding, capable of reflecting upon its own operations. Therefore, to make logic the first branch of science that is to be taught, is an old error that ought to be corrected.”
During the period of Enlightenment modernity, Gottfried Leibniz stands out as a defender of the syllogism’s enduring usefulness and value. He wrote a dialogue responding to Locke in his New Essays Concerning Human Understanding (1704), in which his character Theophilus critiqued Philalethes, representing Locke:
“Your reasoning on the little use of syllogisms is full of a number of solid and fine remarks, and it must be admitted that the scholastic form of syllogisms is little employed in the world and that it would be too long and perplexing if one desired to employ it seriously. And yet, would you believe it, I consider the invention of the form of syllogisms one of the most beautiful, and also one of the most important, made by the human mind. It is a species of universal mathematics whose importance is not sufficiently known; and it may be said that an infallible art is therein contained, provided we know and can use it, which is not always allowed.”
Thus we see Leibniz greatly treasured the syllogism, even though he admitted it had died out much already by his day. It seems that the Baconian method — an early influence on the Enlightenment — had swept many along in its fervor, but left the syllogism in the dust.
But Leibniz was a minority voice on the effectiveness of the syllogism. As theology was cast aside in modernity in favor of the pursuit of mathematical and natural science, the Enlightenment concepts trickled down into a church, this approach would have a corrosive effect on how theology was to be constructed.
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The Effect of the Dying Syllogism
The decline of syllogistic logic and the rise of induction coincided with the loss of theology from its central place in Western thought, and its replacement with mathematics and empirical science. Yet even where theology has been taught, the syllogism has been set aside as a somewhat useless tool.
We ought to correct this, and affirm that syllogisms are vital in a discipline or science such as theology; whereas the Baconian method of induction is most useful when we are seeking to observe new data empirically.
What has happened since is that in many circles, the syllogism has been replaced by the enthymeme: a truncated syllogism in which one premise is not stated expressly. This makes recognizing someone’s formal argument and refuting it that much more difficult, as theologians do not organize their arguments in a formal syllogistic manner anymore.
In order to refute an argument, therefore, Theologian B often has to discover Theologian A’s unstated premise, to render his enthymeme a complete syllogism. Theologian A, however, may not recognize Theologian B’s reconstruction of his argument, and consider it a steelman. The undecided reader (Layman C) is left confused: perhaps Theologian A is unrighteously angry because Theologian B has spotted the duplicity of his argument; perhaps Theologian A is righteously angry because Theologian B has misrepresented him.
When we link this to the general decline in formal logic in the West, along with a widespread unfamiliarity with the precise Latin terms of the Scholastics, we can see how public theology has weakened since the 17th century, and with it, the quality of theological argumentation has diminished also. Nature abhors a vacuum, and at times, confident rhetoric can mask logical fallacies. When this occurs on two sides of a controversy, more heat than light is generated.
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Conclusion
I believe that we need a way to return syllogisms to their rightful place in logical discourse. In order to do so, we have published several logic textbooks by Peter Ramus, Pierre Du Moulin, and Franco Burgersdijk. We are recommending these books as part of our curriculum supplement. Theophilus Gale has a lengthy treatment of logic also, in his monumental work The Court of the Gentiles, and Lucas Trelcatius Jr.’s Brief Institution of the Common Places of Sacred Divinity is a masterclass in brief, compact logical argumentation.
It is my hope that these works will, by God’s grace, find their way into Christian schools, and help to prepare men for seminary training. As this happens, it is my humble suggestion that Christian teachers might also help older generations who are past their schooling days to recognize logical categories, and even begin to introduce syllogisms as they argue on social media, in books, or even from the pulpit. Indeed, I think that this is the logical thing to do.
