Peter Kreeft has written an article for Touchstone called “Clashing Symbols: The Loss of Aristotelian Logic & the Social, Moral, & Sexual Consequences.” The thinking goes as follows: Symbolic logic has eclipsed Aristotelian logic in nearly all philosophy textbooks. This is bad news, because symbolic logic undermines metaphysical and epistemological realism, creating a nominalist culture. A nominalist culture can’t grasp true sexual ethics; in particular, it loses the ability to speak of the nature of sex and marriage.
Now, I’m not a philosopher or a logician, but I do use symbolic logic almost daily to write little bits of computer code. I also find the story of symbolic logic in the twentieth century entrancing: It’s an intellectual adventure on a level with rocket science or genetics, and you can read about it in Logicomix. So at the outset I’d like to say that Kreeft drastically understates the aesthetic value of mathematics (“the more important the subject matter, the less useful mathematics seems to be”) and logic (“a computer can do symbolic logic”). Symbolic logic and mathematics speak of important things at least in the same manner as the great fugues, or anything else formally elegant. But the main weakness of the essay is that the mechanism by which symbolic logic undermines metaphysical realism and thereby destroys our culture is not made clear.
For one thing, it’s not clear to me what exactly Kreeft means by “symbolic logic.” Sometimes, Kreeft seems to be indicting the whole of analytic philosophy: “By the 1970s, most of the English-speaking establishment had cast in its lot with ‘analytic philosophy’ and the symbolic logic that was its methodological component.” At other times, it sounds like Kreeft is just talking about truth-functional propositional logic. “Symbolic logic is also called ‘propositional logic’ because it begins with propositions, not with terms.” “Symbolic logic has no way of knowing, and prevents us from saying, what anything is!” Now, this is clearly true for the very simple version of symbolic logic often taught to college freshmen, but it’s not at all clear to me that it’s true of symbolic logic as a whole. In particular, it seems that the basics of Aristotelian logic are simple to symbolize in a predicate calculus, as I’ll try to demonstrate below. If Aristotelian syllogisms are indeed expressible by means of modern symbolic methods, we may just have a pedagogical problem, which is to say that our current logic textbooks don’t do a good job of teaching everyday reasoning.
Let’s turn to something that Kreeft neglects to provide, namely, an example:
1. Aristotelian syllogism:
Premise 1: “All humans are mortal.”
Premise 2: “Adam is a human.”
Conclusion: “Adam is mortal.”
Formal premises: “All S is P.” “A is S.”
Formal conclusion: “A is P.”
2. Propositional calculus:
Premise 1: If “Adam is a human”, then “Adam is a mortal.”
Premise 2: “Adam is a human.”
Conclusion: “Adam is mortal.”
Formal premises: P->Q, P
Formal conclusion – modus ponens: Q
3. Predicate calculus:
Premise 1: “If anything is a human, then it is mortal.”
Premise 2: “Adam is a human.”
Conclusion: “Adam is mortal.”
Formal premises: For all x, H(x)->M(x). H(A).
Intermediate step – universal instantiation: H(A)->M(A)
Formal conclusion – modus ponens: M(A)
Notice that the propositional version (2) has all the weaknesses Kreeft mentions: We can’t get at the content of the propositions. We can’t say much about how or why they’re true; we just have symbols that we evaluate as true or false. But predicate calculus (3) seems to solve that problem: We have a way of representing some terms (“A,” or “Adam”) and things we say about those terms (“H(x),” or “x is a human”). However, perhaps you can see that the predicate calculus does draw the attention away from content and toward logical form, so the tool really might be too powerful for everyday reasoning. It does look to me as if the premises of the Aristotelian version (1) and those of the predicate calculus version (3) express much the same thing, in nearly the same level of detail. I would love to know if I’m missing something here.
How else could symbolic logic undermine metaphysical realism? It’s not clear to me whether Kreeft is arguing that metaphysical realism is inexpressible in symbolic logic or merely easy to avoid. “[The power of abstracting and understanding universals] is the thing that symbolic logic ignores or denies.” Well, does it ignore realism, or does it deny it? This is an important point. There’s a problem with the timeline, too. Symbolic logic was extensively theorized in the early 1900s, but (as Kreeft mentions) nominalism appeared in the 1300s. So it must have been possible to express nominalism by means of Aristotelian logic. There’s a historical question here: Was it difficult for nominalists to make themselves understood? Or can the Aristotelian framework be modified to be anti-realist? We can also ask how modern realists—and they do exist—manage to do their work in the context of symbolic logic. Do they simply avoid symbolization? Or can symbolic logic be used by realists?
And if the symbols themselves aren’t the problem, but rather the presence or absence of metaphysical or epistemological realism, why drag the symbols into this discussion?
December 10th, 2012 | 1:15 pm
I can only comment on the analytic philosophy. As a current PhD student in philosophy, trying so hard to hold onto what has now become known as either “ancient” or “continental” philosophy, I have to agree with Kreeft–if indeed he is indicting the whole of analytic philosophy. This is mere cognitive science, and philosophy as pursuit of wisdom, as love of wisdom is seen as quaint, cute, etc. Analytic thought is outside of any realm of reality. One can only listen to so many thought experiments; it is far too indulgent. I am not anti-science, but philosophy is not a scientific method.
December 10th, 2012 | 1:21 pm
If this prints a reply from Kreeft, please post.
December 10th, 2012 | 1:55 pm
It is not true that computers can do symbolic logic if we take “to do logic” to mean “to use logic to derive theorems.” The computers we presently have are notoriously bad at any problem involving even first-order logic. They tend to go into infinite loops when they try to prove even quite simple theorems.
It is a truism that logic alone can’t give knowledge of the external universe. Deductive logic can only verify whether a theorem follows from a set of axioms. If the axioms are false, one can prove all sorts of false things. In most human endeavors, axioms have to be obtained inductively.
December 10th, 2012 | 2:41 pm
Kreeft may have in mind the practice derived from symbolic logic of defining concepts by sets. This approach, which has a kind of intuitive power to it, is reasonably common. That said, I love symbolic logic, and the idea that it should be condemned wholesale as leading to “social, moral, and sexual” decline seems pretty silly. It’s an intellectual tool, and a finely crafted one. You can misuse it, just like anything, but that doesn’t really speak to the tool as much as to the blindness of those misusing it.
December 10th, 2012 | 3:25 pm
I haven’t read the article in question, but my guess is that the point is that modern symbolic is metaphysically neutral. Using the example, yes you can represent sentences that predicate properties to objects in modern logic, but just what it is for something to have properties, or what properties or objects are, or whether objects have properties essentially according to their kind, etc.–none of that is the business of logic.
That said, some of the more powerful interpretations of modal logic (in particular) are robustly realist and essentialist.
Also, there are some rather cliched and inaccurate depictions of “analytic philosophy” being used here. Alvin Plantinga is an analytic philosopher if anyone is. About all that means is that he tries to write clearly and rigorously and will make use of formal techniques whenever they help advance an argument.
December 10th, 2012 | 3:27 pm
I have to sympathize with Kreeft, as well. The usefulness of symbolic logic in mathematics seems a bit irrelevant as it is unique in having fixed symbols. The elusive mechanism by which symbolic logic becomes destructive is in it’s short-cutting language. By assuming that, like numbers, words like ‘love’ have a universally accepted value (like the number 4), individuals are allowed to plug them into ‘social equations’ for the benefit of their own arguments without having to actually provide an argument. For example, a person can say, “If you think this particular way, you are unloving and bigoted.” They bypass explaining what they mean by love or bigot and simply appeal to the fashionable hierarchy of value. In other words, we just avoided having a conversation about the logic of thinking that particular way. Thus, as Kreeft points out, we create a nominalist culture that uses words as empty shells with a perceived universal value. Why drag the symbols into the conversation? Because that is precisely where the problem is.
December 10th, 2012 | 3:28 pm
*its
December 10th, 2012 | 3:46 pm
Emina, how is analytic thought “outside reality”? Isn’t this charge the very thing Brafford is dispelling? I’d say he did a pretty good job of defending the contrary here. So please explain what you mean.
December 10th, 2012 | 3:54 pm
I can only wonder about Kreeft’s take on “analytic thomists”…
December 10th, 2012 | 4:41 pm
As for the historical question, to propose the existence of an Aristotelian framework is to propose the possibility of tearing it down, and nominalism rather incisively pre-figures much recent “deconstruction.” At the same time, since the quarrel is over ultimate meanings – not one ultimate meaning vs another but over the nature or possibility of ultimate meanings, or what we might possibly or ultimately mean when referring to them. So, of course, it would be difficult for nominalists to make themselves understood, as are any thinkers who put thinking itself or understanding itself radically in question.
December 10th, 2012 | 5:15 pm
Mr. Brafford, your instincts are entirely sound. See the writings of Peter Geach (especially his collection of short papers Logic Matters); this Kreeft fellow is still plunged in what Geach called “Cimmerian Darkness” (p. 59, in an essay called A History of the Corruptions of Logic). Geach says “Aristotle, like Adam, began right, but soon wandered onto a wrong path.” And finally: “the restitution of genuine logic is due to two men above all: Bertrand Russell and Gottlob Frege”. I.e. exactly the whole modern development of logic that would-be traditionalists disparage. I haven’t got time to give Geach’s arguments on behalf of this, but all his (‘analytic Thomist’) work depends on it. And his wife Elizabeth Anscombe was in full agreement about this. But what can you expect from the King’s College?
December 10th, 2012 | 5:23 pm
You are absolutely right. Kreeft is a laughable buffoon and those who want to promote Catholic intellectual culture should run from him fast. Anyone who knows anything about real analytic philosophy knows that A) symbolic logic can be used to say anything that Aristotelian logic can–and much more! — and B) metaphysical realism of the most robust sort is flourishing as never before. We just call it metaphysics, not logic.
December 10th, 2012 | 5:49 pm
The inability of analytic philosophy, particularly symbolic logic, to treat metaphysical questions with anything more than cordial superficiality—and usually much worse—is that the symbols of metaphysics are words, not algebraic terms, and are marked with all the flaws of language. Symbolic logic, in sum, is a prisoner to the denotations of words, which are their symbolic meanings rightly considered.
Yet all words have rich connotational meanings, and those can never be adequately dealt with by deduction. As with Postmodernism and, before it, Nominalism, the fatal weakness in such “isms” is their fairly uncritical stance towards words. People like Freud and Lacan have a great deal to answer for here. They placed “psycholinguistics” at the center of things after all, and we have never quite recovered from their fetishization of words.
The postmodernist is the heir of Freud, and he sees word/symbol worship as no weakness at all. “What else have we but words?” he asks ingenuously. “What else is there with which to reason?” The answer of course is “not much,” which is exactly why logocentric systems, as they might be called, should summon up our deepest suspicions.
Anyone who has attempted to convey with clarity even the simplest idea that is not purely logical, that is not, say, a proposition of mathematics, is quite aware—or should be—that in addition to the meaning one intends at the beginning of a sentence, there are, alas, always myriad other meanings that sprout like weeds between the slats of the clean white picket fence of meaning we struggle to set down by the end. Sadly, attempts to prune away such unwanted connotations lead inevitably to second-order weeding and so forth. Poets, and to a certain extent novelists, are not spared the struggle with the lubriciousness of the meaning in words, even as they simultaneously strive to exploit it. Metaphysical language is particularly terrifying in that regard. That is why it is so important and to be recommended.
Instead of candidly admitting the problem, soldiering on anyway, and attempting to treat of metaphysical questions in spite of the unavoidable failings of literature, knowing, I say, that the probability of failure is within epsilon of 100%, the nominalist or postmodernist or analytically dedicated logician approaches metaphysics with unwarranted confidence, alà Procrustes, lopping off meanings with abandon, not by craft, but rather by fiat (which he calls “premises,” but which are better understood as systematic question begging). The results are invariably flat and for the most part uninteresting to any but the mathematically minded, who are nonetheless impressed. Unfortunately what they are impressed with is the assortment of rubble to which they have reduced metaphysics. To be frank, that very likely was their primary aim all along.
Yes, there is a hubris here in evidence, that of someone standing over a corpse or, better, of someone canting on about there being no such “things as ghosts,” so can we please get on with the “real questions,” whatever they might be. Leave talk of metaphysics and its mistress, theology, to the less gifted intellectually among us.
December 11th, 2012 | 12:14 am
“By assuming that, like numbers, words like ‘love’ have a universally accepted value (like the number 4), individuals are allowed to plug them into ‘social equations’ for the benefit of their own arguments without having to actually provide an argument. For example, a person can say, “If you think this particular way, you are unloving and bigoted.” They bypass explaining what they mean by love or bigot…”
–But there are no private languages. So why is someone’s failng to define the meanings of terms before using those terms in an argument the fault of symbolic logic? Isn’t the fault rather of someone failing to define his terms with definitions everyone can accept?
December 11th, 2012 | 3:38 am
Walt
As Pascal pointed out, the ideal is to define all our terms and to demonstrate all our propositions. But this is impossible, because each term must be defined in terms of others, which leads to a perpetual regress. Likewise, deduction requires premises and so, again, we have a perpetual regress.
Newman, too, pointed out that, in reasoning, all our conclusions are abstract and all our premises are assumed.
December 11th, 2012 | 6:34 am
I don’t know how to parse the distinctions people here are making between, on the one hand, symbolic logic (TFL or different orders of predicate calculi), and on the other hand, the tradition and spirit of analytic philosophy. I for one appreciate that Alvin Plantinga tries to write “clearly and rigorously”.
But I do feel a sense of what I would like to call a linguistic bullying going on. Murray speaks of people who, by assuming that words like ‘love’ have a “universally accepted value”, allow themselves to “plug them into ‘social equations’ for the benefit of their own arguments without having to actually provide an argument.”
No doubt some people do. But this is contrary to my own practice of analytic thought, insofar as I will go through great pains to understand what others mean by by -their- use of the terms. This may involve running through my own finite set of “values” for the terms. But I do not pretend that this set is in any way “universally accepted”. And if others do not think any of my “values” matches their own intended sense, I invite them to enrich me with their own.
However I do not see myself -culpable- for -failing- to know what another means by their terms, even after taking pains to discuss them. But this is where I feel a kind of bullying takes place — not by analysts who insist that others assign terms with “universally accepted values”, but my the others who deride the analysts for failing to understand the others’ use of the terms. If someone says to me that it is important for me to use a metaphysical language (or metaphysical terms) which I do not understand, I must ask them to explain to me (and allow me to question them about) what they mean by “important”.
Because, after all, -using- a language involves more than reading and listening. It involves -producing- in that language. It seems to me that I am being asked (or “recommended”) to use language that I don’t understand, even to the point of -claiming- things in a language that I do not understand.
The moral question is: just -who’s- epistemic duties are being violated?
December 11th, 2012 | 10:08 am
It is perfectly possible for a word to have no definition.
As Wittgenstein argued in the Philosophical investigations, there is no reason to look, as we have done traditionally—and dogmatically—for one, essential core in which the meaning of a word is located and which is, therefore, common to all uses of that word. We should, instead, travel with the word’s uses through “a complicated network of similarities, overlapping and criss-crossing” [Philosophical Investigations 66] He demonstrates that it is impossible to devise some definition of “game” [“Speil” in German, which can include “play”] that includes everything that we call games, but excludes everything that we do not.
More importantly, we do not need a definition and can use the word perfectly happily without one. We are all familiar (i.e. socially) with enough things that are games and enough things that are not games to be able to categorize new activities as either games or not.
It is because words derive their meaning from their use in a given social context that Wittgenstein remarks that, “If a lion could talk, we could not understand him.” Every translator will understand this.
December 11th, 2012 | 1:01 pm
Mr. Brafford’s artcle raises some good questions. I think he may be right to the extent that Kreeft does overstate his case. Symbolic logic no more prevents one from defining his terms clearly or in reference to the essences of really existing things than Aristotelian logic.
However, I do think Kreeft has a point, and that his point may best be illustrated by an analogy to another “method,” which, like logic (symbolic or otherwise), is often considered “neutral.”
What I have in mind is the “historical-critical method(s)” of interpreting Scripture. The problem in viewing these methods (source criticism, form criticism, redaction criticism, etc.) as “neutral” is that they arose out of an historical context that was antithetically opposed to the admitting the reality of the supernatural. What this means is that the “historical-critical method(s),” while “neutral” in one sense, methodologically incline its user toward naturalistic (=anti-supernaturalistic) explanations of the Biblical data.
By analogy, while there is no reason for supposing that symbolic logic cannot be employed by epistemological and metaphysical realists (and it is), there is an inherent tendency of the medium and method to focus on formal relations to the exclusion of content. These tendencies were given their initial nominalistic impetus by historical figures like Peter Abelard and William of Ockham, but can be seen in Russell and Frega, Goedel, Kripke and other moderns as well.
Like modern science, whch under the influence of Francs Bacon’s exclusion of formal and final causality and Positivism’s legacy of empiriometric methematization of the physical world, symbolic logic inclines its users to focus on formal relations of propositions and syllogisms without much interest or attention to the material content of essential natures by reference to which those terms may be defined. There is nothing wrong with this as far as it goes. But as with mathematical physics, its user can sometimes forget that he is dealing with formulae two or three steps removed from the pre-theoretical world he inhabits, and sometimes he may even cease to care about that fact.
And that, as Adam Murray so nicely suggests, can be a problem.
December 11th, 2012 | 2:51 pm
Walt,
I might point out that the problem is not necessarily a failure to define terms. The problem is exploiting the social value of a word in order to dismiss someone else’s logic. So, in my example, the actual argument has a neutral value and is then associated with words that either have a negative or positive social value. Love = 10, Hate = -10. Joe, I think, summarized this nicely as a ‘fetishization of words’. Because symbolic logic is propositional, it forms a bond between words and syntax, allowing the user to ignore the pesky task of semantics. As, Kreeft’s argument follows, public discourse is then reduced to bullying, and whoever best exploits the propositions is perceived to have the better logic. A good example is the marrying of terms to ‘civil rights’.
In response to LARGO (and concerning linguistic bullying), I am not equivocating the terms ‘value’ and ‘meaning’ or ‘definition’. I am using value in the economic and mathematical sense. The danger is not in misunderstanding the connotation, rather in exploiting the socio-cultural economic value of symbols/words that have a currency beyond their specifically symbolic nature. The battle then becomes whose argument can appeal best to a culturally elevated symbol/word. Basically, this gets around the more interesting task, as you seem to be doing, of actually understanding what we are talking about. A task which is deliciously metaphysical, and I would suggest, much more akin to the ‘Aristotelian’ logic that Kreeft is getting at.
December 12th, 2012 | 1:21 am
It would probably help if Mr. Brafford read some of the literature from the Aristotelian perspective on this, particularly the work of Henry Veatch. I recommend Two Logics, Intentional Logic, and Logic as a Human Instrument.
The most obvious difference is that symbolic logic assumes without warrant that existential import for particular (but not universal) propositions. The result of just these two assumptions is that five of the traditional 19 valid categorical syllogism forms are rendered invalid, and the “square of opposition” becomes the “cross of opposition,” since three of the four kinds of opposition are eliminated.
This assumption is embedded in Venn Diagrams commonly used in logic courses.
Another big difference is that, in symbolic logic, all statements are considered truth conditional when they clearly are not. This was one of the reasons why Wittgenstein, who devised the system of truth tables, later repudiated them.
In fact, two of the principals involved in the Principia Mathematica (whence virtually all modern symbolic logic derives) later repudiated the project–Wittgenstein and Alfred North Whitehead. Russell stayed with it, and was not nearly so sanguin as Brafford about the two systems being consistent.
“I conclude that the Aristotelian doctrines with which we have been concerned in this chapter are wholly false,” he says, in his history of Western philosopy, “with the exception of the formal theory of the syllogism, which is unimportant.”
On the other side, Jacques Maritain says, “Logistics [which is what he calls modern symbolic logic] and logic remain separate disciplines, entirely foreign to one another.”
Brafford says that it must have been possible for nominalists to use Aristotelian logic since nominalism goes back to the 1300s and modern logic does come along until about the turn of the 20th century. That ignores the fact that there was quite a bit of discomfort with a system of logic that philosophers knew was based on Aristotelian metaphysics. The problem was there simply wasn’t any alternative until Frege and Boole began to develop the rudiments of the modern system, a system that was brought to fruition by Bertrand Russell, Whitehead, and Wittgenstein. This was one of the reasons that the then mostly logical positivist (and by implication nominalist) philosophical establishment immediately seized upon it.
To borrow a phrase from Richard Dawkins, the modern system made it possible to be an intellectually satisfied positivist.
William Barrett has perhaps the best popular account of how all this went down in his Illusion of Technique.
Veatch challenged the academic establishment on its almost exclusive emphasis on symbolic logic and as far as I can find in the journals, no ever responded to him. I asked Kreeft about this one time and he said that, to his knowledge, no one ever did.
December 12th, 2012 | 1:24 am
I am going to go ahead and post a draft of an article I am working on on this issue at my own blog today in case anyone is interested.
December 14th, 2012 | 8:54 am
Michael PS,
“But this is impossible, because each term must be defined in terms of others, which leads to a perpetual regress”
–Why is the possibility of an infinite regress a problem only for symbolic logic and not for ordinary language too?
December 14th, 2012 | 10:05 am
Adam Murray,
“I might point out that the problem is not necessarily a failure to define terms. The problem is exploiting the social value of a word in order to dismiss someone else’s logic.”
–Again, why is this a problem facing symbolic logic but not ordinary language? If my opponent calls me a ‘bigot’ to avoid addressing my argument, my opponent is not even using symbolic logic. He is merely exploiting the social value of a word–as you rightly said.
More importantly, calling me a ‘bigot’ is a fallacious Red-herring, an ad hominem, a form of mising the point. So even if I WERE a bigot and what I said was bigoted, this is not a counterexample to the truth of what I said, nor does it undermine the validity of my argument. My opponent could also call me a ‘sexist’ for pointing out that most women do not have as much upper body strength as most men. But just because he finds my observation personally distasteful, and I am indeed ‘sexist’ by his lights, my alleged ‘sexism’ and his distaste doesn’t make what I said any less true, nor does it undermine the validity of the argument in which this assertion is found.
The first and foremost problem here is that my opponent refuses to engage in intelligent dialogue, not that he is using symbolic logic to somehow steer the argument in his direction. We see this happen all the time in our culture, but I don’t see why symbolic logic is the problem. Isn’t the opposite true? My opponent is being very ILlogical.
“”Because symbolic logic is propositional, it forms a bond between words and syntax, allowing the user to ignore the pesky task of semantics.”
–But since when does symbolic logic allow this strategy as an acceptable form of argumentation? A person cannot just start assigning symbols to what he things is the semantic values of words and hope to get an intelligent rebuttal out of it. You should always define your terms when the words you use are central to your argument!
December 14th, 2012 | 10:07 am
Walt
It is a problem for both. See my remarks on Wittgenstein above
December 14th, 2012 | 10:55 am
Michael PS,
Well yes, so if this problem effects both logic and natural language, why is everyone harping on symbolic logic? Aristotelian logic is just as vulnerable because it uses natural language.
December 14th, 2012 | 9:45 pm
[...] Randolph Brafford has published a rejoinder defending symbolic logic which can be found on the First Thoughts Blog. [...]
December 21st, 2012 | 7:40 am
Geach’s article can be found here:
http://www.mediafire.com/?r7tuym1gp06dyji
A PDF download.
Links
Blogs
Find Us
Contact