#Logic and Meaningfulness: Do Truth Tables Imply a Limited View of Meaning?

I received an email the other day from someone who had come across my article "Logic and Reality Why Traditional  Logic Does Not Use Truth Tables" (an article that appears on this blog as "Why Traditional Logic Doesn't Employ Truth Tables"). He said that he understood me as suggesting that modern logic "isn't meaningful," and, if this was true, he didn't quite see how it could have value in scientific application or computer science as I seemed to suggest that it did. I thought I would share my answer to him, since posts on logic tend to be among my most read posts on this blog.

I think (and I have not thought this all the way through, so it is still a little experimental), broadly speaking, that the logical thinking that produces the truth tables (specifically Wittgenstein's early positivism) is a kind of thinking that inherently disallows meaning per se--or at least meaning as we think of it. 

When Wittgenstein, who invented the truth tables, says at the beginning of the Tractatus, "The world is everything that is the case," he seems to be positing a sort of sterile, Humean world in which there are things and relationships between things about which we make assertions that have "truth value." The truth tables, it seems to me, by virtue of the way they work, embody this view of reality. It would seem that meaning in such a world is problematized--or at least meaning as it manifests itself in such a world (rather than simply being read onto the world by the human mind) has little of the character we ascribe to it in normal mortal speech and thought.

In regard to modern symbolic logic's application to scientific application and computer science, I think the issue is how the tools of these disciplines limit their meaningfulness. Modern symbolic logic limits itself to the exclusively formal, and because of this limitation, it cannot encompass all we mean in our everyday speech (something Wittgenstein, if I understand him correctly, later realizes). Modern symbolic logic limits itself to the extensional or quantitative aspects of words and statements and does not take account of its comprehensional or qualitative character. 

Another way to say this is that the extensional use of language restricts us to seeing things only from the outside, while the comprehensional use of language allows us to see into the nature of things--and which kind of thing you are. Science, employing methodological naturalism, can only see things from the outside. Likewise computers, which are limited by their mechanical nature--the only difference between the two being that the scientist, being a human being with a soul, can step out of his scientific role and see into things (through philosophy, poetry, etc.), while computers, being mechanical, cannot. 

You have to have a very limited view of language to think that any language that can treated adequately in truth tables. Traditional logic does not limit itself in this way. It is comprehensional in a way that modern logic is not. Traditional logicians recognize that there are aspects of reality implicated in logic that are not purely formal, which is why it incorporates certain aspects of philosophical metaphysics in its study (mostly incidentally in formal logic, but fairly extensively in the branch of logic called material logic). 

So it isn't the kind of logic natural and computer science uses that would limit the meaning of what it expresses--it is rather the methodological limitation it imposes on itself that limits the meaning it can have, and the kind of logic it uses is used precisely because it suits their purposes.

In regard to conditional statements specifically, I'm not saying that the view of modern logic in which a conditional statement of the form "If P, then Q" is true when the antecedent is false is meaningless. I'm saying that viewing it that way is a denial of what we actually mean when we use such a statement. In other words, it may mean something, but it doesn't mean what we mean it to say in normal speech (or any other kind outside of the formalities of modern logic).

I don't think this is a matter of context; I think it is a matter of metaphysical assumptions. If you are a philosophical nominalist, then you will accept the truth conditionality of conditional statements and reject the everyday meaning of them. Whereas if you are a critical realist, you will accept the everyday meaning of conditional statements and reject the truth table view.

I think it's that simple. But I'm always open to another view that makes more sense.

The Critical Thinking Skills Crisis: A response to criticisms of "The Critical Thinking Skills Hoax," Part II

This is the second of two posts addressing some specific points made recently in a critique of my recent post "The Critical Thinking Skills Hoax," on the Sept. 20 broadcast of "Critical Thinking for Everyone," a show hosted by two critical thinking skills scholars, Patty Payette and Brian Barnes. The first post can be found here.

The first five minutes of the show seemed to be intended to address the question, "Who is this guy?" A description of me, apparently gained through a quick Google search, provided fodder for several minutes of speculation and criticism.

One of the key areas of concern seemed to be my qualifications for writing a logic textbook. I have written several texts for high school students (although they are used at the college level as well in several places) that are fairly widely used in classical liberal arts schools across the country and are now being translated into Russian and Dutch. But Dr. Barnes judges them deficient--despite the fact that he has never laid eyes on them.

"I would say," said Dr. Barnes, "that a B.A. [in philosophy and economics from the University of California, Santa Barbara] would not qualify him to write these books."

I'm not sure where one goes to determine the qualifications for writing high school logic texts. And I realize that in Dr. Barnes' world of higher education certification counts for, well, almost everything. Surely there is something to be said for gaining a Ph.D in a subject, particularly if you want to teach it on the post-secondary level (which I don't, which is why I never bothered to get one).

One of the reasons I find Barnes' criticism problematic is because I took the same logic courses as the graduate students in the program. In fact, I was one of the only undergraduates in the upper level advanced logic programs (taught by Francis Dauer, a student of Willard Van Orman Quine at Harvard, whose text we used) and I believe I took all the logic courses that an M.A. or a Ph.D would have taken. If I took the same logic courses as the graduate students in the program, then how exactly would a graduate degree have better equipped me in that particular subject? Would I be more qualified if I got a Ph.D and took additional non-logic courses?

Furthermore, is a Ph.D either a necessary or sufficient condition for being able to write a competent logic text?

Let's think about two scenarios. First, someone with a Ph.D writes a deficient text (it has been done); second, someone without a Ph.D writes a competent text. Under what circumstances would you ever prefer the former over the latter?

I am assuming Barnes would admit that both scenarios are possible. But to admit the possibility of the first scenario is to admit that a Ph.D is not a sufficient condition to do such work. And to admit the possibility of the second is to admit that it is not a necessary condition for doing it. So I am unclear as to how he comes to his judgement.

If my text is a good text, then I am ipso facto qualified to write it. In other words, my writing a good logic text is a sufficient condition for judging me qualified to write one. So the only way to make the judgment he made is to know whether my text is a good text. But he doesn't know this, since he has never seen it.

Therefore his judgment is completely unfounded.

Dr. Barnes might want to read William James famous essay, "The Ph.D Octopus," in which the great psychologist and philosopher discussed the absurdity of the academic obsession with what he disdainfully calls "the three magical letters"--a problem far worse now than when he wrote the essay in 1903.

The number of Ph.Ds per square inch in our society today is reaching alarming proportions. If we had detectors for such things, they long ago would have sounded their alarms. You can't leave your front door before tripping over unemployed Ph.Ds looking for a handout.

This is undoubtedly the result, not only of Ph.D's being too easy to get, but a proliferation of subjects in which you can get them. If we are intellectually honest, we will admit that a Ph.D is not necessarily a guarantee that the person who has it is a well-educated person. I meet them all the time: people who have letters next to their names who neither know much nor have acquired the skills to productively acquire knowledge. In fact, I'll go so far as to say that there are otherwise reputable institutions of learning out there that are little better than degree mills.

There are people with Ph.Ds in a particular subject who are qualified to write books on that subject and people with that degree who aren't. And there are people who have Ph.Ds in certain subjects who write books entirely outside their field. In fact James, who is considered by many to be the greatest American philosopher of the 20th century had an an advanced degree in medicine but he didn't even have a bachelors degree in philosophy.

The Critical Thinking Skills Crisis: A response to criticisms of "The Critical Thinking Skills Hoax," Part I

An essay I wrote several years ago and which Memoria Press recently republished was the subject of a radio discussion program at forwardradio.org yesterday. The essay was "The Critical Thinking Skills Hoax," and the radio program is "Critical Thinking For Everyone" (click "all shows" and scroll to the bottom, show #39), hosted by Patty Payette and Brian Barnes, two critical thinking scholars at the University of Louisville.

The link to the show that discusses my article does not appear to be up yet, but you might check in later if you are interested.

Although the title of my article was intentionally hyperbolic, in the thesis of my article there was no hyperbole at all. It was that the vast majority of educators who talk about "critical thinking skills" are incapable of defining the term, and that it serves, practically speaking, as a promotional slogan and an excuse for the failure to do things essential in education, such as teaching academic content to students.

In the article I said, "Not one in a hundred even knows what he means by this term," a common figurative expression like "I'm so hungry I could eat a horse," or "her eyes were as wide as saucers," or "he was as skinny as a toothpick." But apparently critical thinking professionals are more literally-minded that most. Near the beginning of the program, Barnes challenged this statement by pointing to a study that purportedly found that fully "nineteen out of a hundred" educators could define critical thinking skills.

Of course this assumes that those performing studies to determine the percentage of educators who could define critical thinking skills could themselves define critical thinking skills. And I contend that not one in a hundred researchers who do such studies could define critical thinking skills.

I said "vast majority," but, in fact, in my own private, unofficial survey of educators, I have yet to encounter anyone who can give me a coherent definition. And I have talked to far more than a hundred educators on this topic.

In fact, I was waiting to hear a definition of it on the show, but I never heard one. At one point a list of examples of critical thinking skills practices was given. I guess that constitutes a rudimentary connotative definition, and that is certainly informative, but it doesn't constitute the kind of clear, essential, delimited definition (what one would be called a denotative definition) that one would need to have in order to properly design and implement programs that would be useful in schools, which I gather is one of the themes of this show.

But I'm getting ahead of myself. I'll discuss that in a later post.

I will be posting several responses to comments made on the show, none of which, I hope, will not be so impudent as to cause the "Critical Thinking for Everyone" people to retract the gracious offer they have made to me to come on their show to respond, which, according to Patty Payette, the show's host, should be sometime in October or early November. I'll post the date here when we have one.

#Science 's Useful Fallacy

My article in the most recent Classical Teacher magazine:

The expression “the science is settled” has been invoked as a way to end numerous discussions of scientific importance. On issues involving evolution, dietary science, or exercise physiology, it is not uncommon for one side to claim that the research has settled the issue. But, however much evidence there may be for any particular scientific theory, is the science of it ever really “settled”? 

Although many scientists don’t like to hear it, the nature of scientific reasoning itself prevents any scientific theory from ever being settled. The problem of the level of certainty in scientific judgments goes much deeper than any specific issue. It has to do with the very kind of logic science must employ in order to come to its conclusions. To put it bluntly, scientific reasoning is based on a logical fallacy, and because of this fact, science is never settled. 

...The fact that the chief mode of scientific reasoning is a fallacy is not an excuse for dismissing science. Far from it. But it should be a lesson to us that, though certain theories may be said to be well-established, the findings of science are always to some extent tentative.

Read the rest here.

Atheists to gather in Washington to pretend they're rational

One way to convince yourself that you are rational is to simply repeat words like "reason" and "rational" over and over again as a sort of mantra. The other way is to actually be rational by engaging in rational thought processes, such as observing the proper definitions of words, understanding what you are actually saying when you make statements, and observing the simple rules of logical validity.

The first way makes you a poser. The second way means you are the real deal.

As they did in 2012, the nation's atheists are getting together in public to repeat the appropriate catchphrases and to strike the appropriate rational poses so they can all pretend that they are logical. It's called the "Reason Rally," being held on the mall in Washington, DC on June 4. 

In 2012, I openly wondered if something called a "Reason Rally" would involve taking part in logical exercises like formulating valid syllogisms, identifying fallacies, and engaging in contests to see who can reduce syllogisms of the second, third, and fourth figure into first figure syllogisms, like we do in my logic classes. But, alas, all it really amounted to was a bunch of intellectually arrogant people with little to be arrogant about chanting slogans on the lawn.

This year, I was hoping to be available to travel to DC to stand on the lawn and lead them all in a chant of William of Sherwood's medieval mnemonic verse that includes all 19 valid syllogism forms to see if it would do any good.

In reality, these are people most of whom just simply have to scratch their heads when you ask them why secularism is somehow more inherently rational that religious belief. This idea is the unarticulated assumption behind all modern atheist thought. They will employ it in their argumentation, but if you ask them to justify it, they will descend into incoherence (if they haven't already).

For a fun exercise, recite to them various arguments from St. Thomas' Summa Theologica and ask them to identify which argument forms they exemplify.

These are also people who have made science into a religion and worship at the feet of the scientific method, which they seem to think is the only avenue to truth, a belief which itself cannot be proved on scientific grounds. In other words, their central belief is itself entirely irrational.

One of the themes at this year's rally is "LGBTQ Equality." It will be interesting to hear how reason and science support the whole concept of "gender identity," which basically consists of the belief that your gender is determined by your feelings and not your chromosomal makeup, like they teach in, well, science.

Is science based on faith?

Once again a scientist has wandered into the Land of Philosophy, thinking he knows his way around, and has instead become disoriented and confused. And not only that, but the person doing this is a repeat offender.

In a recent post, Jerry Coyne criticized Matt Emerson, whose essay "At it's heart, science is faith-based too," was recently published in the Wall Street Journal. 

Coyne is best know for his book Why Evolution is True. But he also frequently makes forays outside his field of expertise, some of which have proved embarrassing. His new book is Faith vs. Fact: Why Science and Religion are Incompatible. There have been several great take-downs of this book by people who actually know what they are talking about, one of which is Ed Feser's review of the book in the most recent issue of First Things magazine.

In his criticism of Emerson, Coyne employs the same fallacious reasoning that characterizes his books and that has become a fixture of his blog.

To Emerson's assertion that scientists have "faith in reason," Coyne responds by quoting his piece in Slate magazine:

Scientists don’t have “faith in reason.” As I noted in Slate:

What about faith in reason? Wrong again. Reason—the habit of being critical, logical, and of learning from experience—is not an a priori assumption but a tool that’s been shown to work. It’s what produced antibiotics, computers, and our ability to sequence DNA. We don’t have faith in reason; we use reason because, unlike revelation, it produces results and understanding.

Sorry, but this is just nonsense.

It's not completely clear what Coyne even means by the term "reason," but I'm going to take leap in the dark and assume he means something like logic in particular and rational thought in general. To say that reason in this sense is not a priori and that we only accept it because it "works" is just ignorant.

All reason in this sense is based on two axioms: the Law of Identity and the Law of Non-contradiction. To say that a belief is a priori (meaning, literally, "from the prior") means that you accept it without any prior reasoning or evidence. Maybe Coyne would like to explain what evidence or prior reasoning supports the Law of Identity and the Law of Non-Contradiction. 

In fact, there is no evidence for them. That's why they are axioms. We accept them purely on the basis of intuition: They make sense that's all. That's the problem with any system of thinking: it is based on beliefs which cannot themselves be proven. All we can conclude about a scientist who says he accepts reason because it "works" is that the scientist saying that doesn't know what he is talking about.

Science too is based on reasoning that is based on a priori assumptions. If it is based on deductive reasoning, then you have the two assumptions (and a few others) above. If it is based on inductive reasoning, there is another a priori assumption. As the philosopher David Hume pointed out, all inductive reasoning involves the premise that the future must be similar to the past. If copper repeatedly and uniformly conducts electricity in repeated experiments, then we conclude--on the basis of the assumption that the future will always be like the past--that it will always do this. But although we believe that the future will be like the past, we have no rational basis for believing it. Again, it's intuitive: It just makes sense.

In other words, at bottom, science too, insofar as it makes logical inferences, is a priori, since its fundamental tools of inference are based on a priori assumptions. 

The only question left is whether this is equivalent to faith. Coyne himself seems to think it is, since he responds to Emerson's claim that scientists have "faith in reason" by claiming (erroneously) that science is not a priori, a claim made more ironic when consider the additional assumptions science makes, in addition to its purely rational assumptions, about the reliability of our own senses.

In fact, Coyne is just proving, once again, that he needs full time philosophical care.

Are traditional and modern logic really different? A response to David McPike, Part II

In the comments section of my post "Why Traditional Logic Does Not Employ Truth Tables," David McPike takes issue with a couple things I said. I addressed some of these yesterday. On a related point, I had said:

Therefore, in the modern system, statements such as: "If the moon is made of green cheese, then ducks can swim" are considered true statements, since their antecedents (in this case, "the moon is made of green cheese") is false at the same time that the consequent ("ducks can swim") is false. In fact the antecedent is false and the consequent true, therefore (according to the modern logician) it is a true statement.

To which McPike responds:

This again seems misleading. In the modern system of "logic", statements such as "If P1 then P2" are considered formally, as being possibly true, possibly false. Insofar as propositions figure into actual reasoning about reality, what reason is there to think that modern and traditional logic are any different in viewing logic "as a linguistic and metaphysical art, not [merely!] a technical mathematical calculus"?

My response to the question of what reason I have for thinking that modern and traditional logic are different in their view of what kind of art they are engaging in is threefold: First, anyone versed in the particulars of the two systems in fact do view them differently; secondly, they admit they treat them differently; and, third, they give the reasons why they, in fact, do treat them differently.

This characterization is less the case with modern logicians than with the traditionalists. Modern logicians are largely unfamiliar with the tradition of the traditional system and seem to be mostly unaware of the assumptions behind their own system since they are never called upon to have to explain them in an English academic world that still operates in the shadow of logical positivism (the ideological mileiu in which modern logic was birthed).

Traditional logicians, on the other hand, being in the minority, are in a position to have to explain why they are not doing the same thing as so many of their peers. Consequently, they seem to have a better grasp on the difference between the two systems. 

Mr. McPike might want to consult several traditional logicians to see what I mean. The first would be Jacques Maritain, whose book Formal Logic (1946) contains a discussion of some of these issues. Maritain considers the two systems so different that he even balks at calling modern logic "logic" at all. He refers to it as "logistics." There are other discussions too, such as that by Andrew Bachhuber in his Introduction to Logic (1957) and in Daniel J. Sullivan's Fundamentals of Logic (1963). There is also a short discussion of this in Peter Kreeft's recent Socratic Logic. Anyone wanting something more in depth can go to the works of Henry Veach, who made a whole career out of examining the differences between the two systems and articulating and questioning the assumptions behind the modern system (Aristotelian and Mathematical Logic (1950), In Defense of the Syllogism (1952); Intensional Logic (1952); Logic as a Human Instrument (1959); and Two Logics (1969)).

And the differences between the two systems has not gone unacknowledged by the moderns, as evidenced by Bertrand Russell's summary dismissal of it (along with Aristotelianism in general, an indication that he understood that the difference between the two systems was rooted in the respective underlying metaphysical beliefs). Irving Copi too acknowledges it briefly in his text, and a good example of the some the issues can found online in Kelly Ross' "In Defense of Bramantip," which is, ironically, a defense of at least one plank in the traditionalist platform by a modern analytic philosopher.

In regard specifically to conditional statements, I'm not sure it is accurate to say that modern logic treats them "as being possibly true, possibly false." If the modal qualifiers ("possibly") in this characterization simply mean that the statement may be true or false depending on the actual state of affairs in the world, then I have no problem with it. But once that state of affairs is taken into account, there is "possibly") about it: If the antecedent is true and the consequent false, then the statement is definitely false. In all other circumstances, the statement is definitely true.

Traditionalists agree with the first part of this, but categorically deny the second. In other words, practitioners of the two systems have contradictory understandings of three of the four possible truth value combinations involved in determining the truth of a conditional statement. This seems to me to constitute a rather marked difference. Moderns believe you can determine the truth of a conditional statement based solely on the truth value of its component statements and traditionalists do not (with the exception of the one case of the antecedent being true and the conclusion false).

On the matter of whether the disagreement between the two systems indicates a different believe about the kind of art logic is, I may need a bit more clarification from Mr. McPike on the import of his question. If it is a question about whether logic is, for both schools, a language art, I would argue that it could not be considered so by the moderns, since they view logic as a purely quantificational system (that's why they refer to logic as "quantification theory") and language is not purely quantitative. If the issue then becomes whether language is, in fact, purely quantitative, as I suppose a logical positive may very well believe (I haven't thought a lot about that), then the difference would go deeper than just logic.

If the question is whether the proponents of two systems of logic agree that logic is a metaphysical art, I would simply point to the fact that, first, most of those who championed it in the early twentieth century explicitly denied the existence of metaphysics since they were, in large part, logical positivists (see A. J. Ayer's Language, Truth, and Logic for a good example, particularly the first chapter, which is entitled, "The Elimination of Metaphysics"); and, second, that the system itself betrays this belief, as I have explained several times.

I'll leave it at that for now.

Are traditional and modern logic really different? A response to David McPike, Part I

Bertrand Russell

In the comments section of my post "Why Traditional Logic Does Not Employ Truth Tables," David McPike takes issue with a couple things I said.

I said:

Traditional logic does not attempt to reduce logic to a quantitative calculus, largely because it views logic as a linguistic and metaphysical art, not a technical mathematical calculus.

McPike responds:

Surely this is just wrong? 'Traditional logic' also views logic as a formal tool, one which it is necessary to master "before" attempting something like metaphysics. It can be treated (taught and learned) just as abstractly and formally as modern logic.

But to say that traditional logic is formal (or at least has a formal branch—the old traditional logic included material logic, which was not formal) is not the same thing as saying that all rational discourse can be reduced to "a kind of mathematical calculus," which was the point of my post. I think the latter statement is more specific than the mere issue of formality.

For one thing, I think it would be fair to say that the system of traditional logic recognizes that there are what I would call "material leakages" in the system which defy exclusively formal treatment. The conditional statements I pointed to are just one example of this. Oblique syllogisms (syllogisms in which there is a relational term playing an essential role in the inference—"John is the son of Mary) would be another. In both these cases the formal clothing we try to fit our rational expression into doesn't perfectly fit. There is some material relation that inserts itself into the otherwise formal structure of the reasoning and that recognition is built into the formal system of traditional logic.

For another, traditional logicians have traditionally disputed the idea that logic—even in its formal aspect—is purely quantitative in nature, in the way in which the kind of logic fathered by the Principia Mathematica seems to be. Most traditional manuals on logic begin with the distinction between comprehension and extension. Comprehension has to do with the intellectual content of logical terms, whereas extension has to do with their referents in the world. The comprehension of the term 'man', for example, would be a "rational, sentient, living, material substance." The extension of the term 'man' would be "all the men who are, were, or will be."

Comprehension is qualitative in nature because it asks questions involving the kind of things to which terms refer, whereas  extension is quantitative, since it asks how much or how many things a term refers to. I'm willing to be disproven here, but it seems to me that modern systems of logic (at least the propositional and predicate calculus) are all extension and no comprehension. That is reflected in the title modern logicians have affixed to their system: propositional and predicate calculus. I'm no expert in set theory, a fixture of much of the modern logic that traces itself to Russell and Whitehead, but from what I know of it, it seems to be one bit of evidence for my claim here.

And it doesn't seem to me a complete coincidence that those who developed modern logic were almost exclusively mathematicians (Frege, Boole, Russell, Whitehead, et al.).

My point was simply that although the formal branch of traditional logic is the treatment of reasoning in a formal way, there is a recognition that, in doing so, there are material (and qualitative) considerations that affect the course and conduct of the reasoning, a recognition that modern systems do not seem to allow for in their attempt to cram all rational discourse into a purely formal system. The modern system of logic not only does not allow for material considerations in its formal system, it doesn't, as traditional logic does, recognize a material (or "major") branch of logic at all, any material considerations having been relegated to the dust heap of rejected Aristotelian metaphysics (e.g. Russell), or to the field of rhetoric (as seems to be the case with what is now called "informal logic").

I will post my answer to McPike's challenge to my use of conditional statements as examples of the differences between the two systems tomorrow.

How necessary is a knowledge of modern logic to the reading of philosophy (or anything else)?

I am going to bring the discussion in the comments section of what is now an old post: "Why Traditional Logic Does Not Employ Truth Tables" back out to the main blog. The interest in my posts on logic, which tend to get a little technical, continues to astound me. Part of the interest in this last one is clearly the fact that the philosopher Ed Feser linked to it. My Sitemeter stats show that clearly. But even before that, my previous post, "The Difference between Traditional and Modern Logic," which just had its three year anniversary, continues to consistently attract more hits than almost any other post on this blog. 

The term "logic" rivals only "science" (about which anything I say seems to invite comment and criticism) and "zombies" as the most popular topics. If I could only devise a post which dealt with all three--imagine what my Google page rating would be!

So here is my response to one of the comments on the "Why Traditional Logic Does Not Employ Truth Tables" post, which will be the first of several.

Leo,

Thanks for your post. Let me take up your comments (and others here) in several posts. Here is the first of these. You say:

"M]uch of logic is usually unnecessary to see basic validity, as many arguments can be seen to be valid or invalid without any conscious analysis. Bringing the entire heft of Aristotle's Logic down an argument like, "My house is painted red, therefore the west wall of my house is painted red," is clearly overkill. All logic is about the more complex arguments.  However, truth tables are very useful in proving theorems like "P V Q === Q V P" (where "===" is used as the symbol for L-equivalence).

I don't know that "all" logic is about more complex arguments. From someone in the academic world, that may be close to being so, especially in modern academic philosophy. Then again, most instances of the use of logic are outside that context and are not even close to being as complicated as that context would require.

I'm sure there are contexts that require a more quantitative treatment, as your example of L-Equivalence illustrates. But, again, this particular illustration seems to me to be required only because L-Equivalence is a concept of equivalence in the field of mathematics. I may need to understand these more quantitative concepts in mathematical logic when I am dealing with modern specialists who are dealing with qualitative concepts in mathematical logic, but in the vast majority of philosophical writings outside this field of specialty it will have no value at all.

I would go further and say that, although I studied mathematical logic in school (and have taught it at the introductory level), the fact is that there is no single instance in all the philosophical writings I have read (or any other writings for that matter), in school and without, that required a knowledge of mathematical logic. A knowledge of traditional logic, on the other hand, was indispensable.

I'm sure that will sound heretical to someone inside the academy, and I admit, as someone who does not operate in that world, to having more than a little impatience with unnecessary academic subtleties. In a world of specialists, any generalist must seem a little primitive.

I hate to sound like such a pragmatist here, but even the vast majority of complex arguments don't require the kind of symbolization that modern logic employs, and my evidence for that is the whole history of philosophical writing, the great majority of which was accomplished, not only without the employment of any kind of modern symbolic calculus, but without the least knowledge of it.

I would also assert that there is a tendency among many modern philosophers to employ symbolism in a way that not only does not clarify anything, but actually obfuscates it. I have no proof of this other than my own experience, but I can think of more than one occasion--in a lecture or some academic article--on which the speaker or author has begun some point by saying "Let P equal ...," a few minutes into which it becomes very evident that, not only did we not need anything to "equal P" in order to understand the point, but that letting something "equal P" actually obfuscated what was not a terribly complex point.

In other words, I think most of the time we just need to let P equal P and go on with our philosophical lives. But I am starting to belly-ache here. I hope you see my point, and you are welcome to try to dispel my ignorance on these points on which I am, far from being an expert, simply an interested observer.

Why Traditional Logic Doesn't Employ Truth Tables

One if the interesting things about this blog is that, while most of what I talk about is politics and culture, the post with the most continuing popularity is an older post I did on the difference between traditional and modern logic. I was going to continue that discussion in later posts but not only got rather busy, but ran into some conceptual problems in the next section of what is basically a pamphlet I wrote a few years ago that I have yet to resolve to my satisfaction.

In the meantime, here is a discussion of the differing views on truth conditionality that address some of the same issues I addressed in the earlier article.

One of the questions I get rather often from students and logic instructors about traditional logic is why it doesn't teach truth tables. Modern logic, the most common kind of logic encountered in high school and college, uses them, so why does traditional logic ignore them?

Many people encounter a smattering of logic in high school math courses, which teach a few of the rudiments of modern logic. Here, more than likely, they will encounter simple truth tables. Truth tables were invented by Ludwig Wittgenstein, perhaps the the 20th century's most influential modern philosopher. He invented them to accompany the calculus into which modern analytic philosophers had transformed logic. They were seen a way to quickly solve for the truth of simple and complex logical propositions in the modern system.

Let's take the statement, "There are seven days in the week and twenty-four hours in a day." In the modern system of logic we would want to immediately reduce this down to its formal elements. Let's say that P = "there are seven days in the week" and that Q = "there are twenty-four hours in a day." If we did this, then we could represent the statement as follows:

P and Q 

How do we find out whether the statement "P and Q" is true? In modern logic, the truth value of this statement is determined by its elements--in this case, the statements signified by "P" and "Q". We know as a matter of simple common sense that the statement "P and Q" is true only when both the statements represented by "P" and "Q" are themselves true--in other words, if it is true to say that there are seven days in the week and if it is true to say that there are twenty-four hours in a day. If either one or both of these statements are false (in other words, if a week is made up of something other than seven days or if a day is made up of something other than 24 hours--or both), then the statement would be false.

Using truth tables, we would set forth all of the truth possibilities of P and Q so we could see clearly when "P and Q" is true and when it is false:

P     Q     P and Q

T     T           T

T     F           F

F     T           F

F     F           F

We don't really need to go to all this trouble to verify that a simple statement like "P and Q" is true. But what if you had a statement like "P and (Q or (If R, then S))"? When statements become this complex, truth tables can be an easier way to calculate their truth value.

So if truth tables make the determination of the truth of statements more easy to calculate, then why doesn't traditional logic teach them?

There are several answers to this question. The first is practical, the second is theoretical.

The Practical Usefulness of Truth Tables is Overstated

The first reason is that, although truth tables have certain technical applications, they are not practically useful in actual argument or discussion, since most statements used in everyday speech and even in academic conversation never get to the level of complexity that would require a truth table to figure them out. They are certainly helpful in certain scientific applications and for computer computer programming (modern logic's most practical application), but outside those fields, they are seldom needed.  

I have not only taught logic, but engaged in private and public debate for over 25 years. While I have made use of William of Sherwood's traditional mnemonic verse of the 19 valid syllogism forms and the procedure for backing into missing premises repeatedly (both of these are covered in my Traditional Logic, Book II), I have never had to resort to a truth table. 

This is partly the result of the fact that most real life argumentation is conducted in or reducible to categorical reasoning on which you cannot use truth tables anyway. This is because categorical reasoning operates on the basis of the relations between individual terms (which are neither true nor false, since only full statements can be true or false) and truth tables work only with hypothetical reasoning, which operation on the basis of relations between statements. In addition, even though modern logical techniques were developed primarily to deal with complex philosophical and scientific problems in an academic context, the vast majority of the reasoning you encounter even there consists simply in chain arguments (strings of simple arguments strung together) that don't require any advanced calculus to solve.

The Faulty Metaphysics Behind Modern Logic

The second reason for the absence of truth tables from traditional logic has to do with the philosophical differences between the traditional and modern systems of logic. To state it baldly, traditional logic doesn't believe in truth tables.

The reason they are used in one system and not the other has to do with a concept called truth functionality.  What is truth functionality?  “A compound proposition,” said Edward Simmons, “is said to be truth-functional when its truth as a whole depends solely upon the truth values of its component parts.”  In other words, the truth or falsity of its parts will tell us the truth or falsity of the whole.

In the statement above, "P and Q", we can tell its truth from its component parts. "P and Q" is called a "conjunctive proposition"--it conjoins P and Q. Traditional logicians believe that conjunctive statements are the only kind of statements whose truth can be "solved" in a truth table--the only kind of statements, in other words, that are truth functional. No other kinds of logical statements ("P or Q", "If P, then Q", etc.) are truth functional in this way.

The reason traditional logicians deny the truth functionality of hypothetical propositions has to do with the underlying assumptions about language and reality.  To illustrate this, let's take another simple statement, this time a conditional statement (This is where the problem with modern logic's assumptions become very clear):

If it rains, then my dog will get wet

In modern logic, we would "solve" for the truth of this statement using a truth table:

P     Q     If P then Q

T     T           T

T     F           F

F     T           T

F     F           T

This kind of statement is considered true in every possible case except when P is true and Q is false (the second line). Let's say my dog is an outside dog and has no protection from the rain. In that case, when it rained my dog would get wet--both P and Q would be true, and therefore it would be true to say (as on the first line of the truth table) that the entire statement, "if it rains my dog gets wet" is true.

But let's say it was raining, but my dog was in the garage, dry and cozy. In that case, it would be true to say that it was raining, but false to say that if it rains, then my dog gets wet (as indicated on the second line of the truth table). It rains, but my dog does not get wet. The statement would therefore be false.

But what about the other two possibilities, in other words, when it is not raining at all (when P is false and Q is either true or false--the last two lines of the truth table)? Why, as indicated in the truth table, do modern logicians say the statement would be true in those cases? 

As someone who has heard the explanations of why this is the case--as well as having tried to explain it to his own students in class--I can testify to the difficulty in trying to understand this. 

But the fact is that modern logic's treatment of the conditional statement (particularly its treatment of conditional statements in which the antecedent is false) is problematic not because it is complicated; it is problematic because it is problematic.

In the traditional system a conditional statement is considered true only if the fact that your dog gets wet really occurs as a result of the rain—in other words, if the statement asserts what is called a valid sequence.  To put it another way, there must be a real logical relation between the rain and your dog getting wet.  The fact of it raining must, in some way, materially imply that your dog will get wet.

In the modern system, however, there need be no real connection all.  All that is required is that, as a matter of fact, the consequent (my dog will get wet) is not false when the antecedent ( it rains) is true.  Unless this is the case, the statement is considered true.  Therefore, in the modern system, statements such as:

If the moon is made of green cheese, then ducks can swim

are considered true statements, since their antecedents ( in this case, "the moon is made of green cheese") is false at the same time that the consequent ("ducks can swim") is false.  In fact the antecedent is false and the consequent true, therefore (according to the modern logician) it is a true statement.

While modern logic considers this statement true, traditional logic sees it, again, for what it is: nonsense.  The moon being made of green cheese clearly has no relation (logical or otherwise) to the fact that ducks are able to swim.

In the traditional system, conditional statements are considered to assert a necessary connection between their elements (the antecedent and the consequent), while in modern logic the only connection has to do with the happenstance coincidence of the truth or falsity of the elements. There must be either a cause and effect or ground-consequent relation between the antecedent and the consequent. The rain and the dog getting wet are to be seen as having a fundamental metaphysical relation (in this case a cause-effect relation) to one another. The assumption behind modern logic is that such necessary connections either do not exist or that they do not need to be accounted for in our system of logic.

The underlying problem here is that modern logic is concerned with the attempt to quantify reality. It wants to turn logic into a kind of calculus. This was the dream of philosopher Gottfried Leibniz, who hoped that one day man could create what he called a "calculus ratiocinator"--a logic machine for the "solution" of logical problems. In many ways Leibniz was Aristotelian in his thinking (traditional logic is Aristotelian), but he would have had to have had very non-Aristotelian assumptions in order to believe that this was even possible.

Traditional logic does not attempt to reduce logic to a quantitative calculus, largely because it views logic as a linguistic and metaphysical art, not a technical mathematical calculus. Traditional logicians recognize a distinction between what is called extension and comprehension--on other words, that any comprehensive view of human reasoning would have to recognize both the quantitative aspects of human language, but also the qualitative. It rejects modern logics reduction of all human reasoning to extensionality.

Traditional logicians reject the idea that language can be quantified in the way that modern philosophers believe it can. Logic, according to the traditionalists, is inherently qualitative and logocentric (centered on the Word), and attempts to quantify logical language can only serve to distort the process of reasoning.

Behind the idea of such a calculus is a view of the world fundamentally at odds with traditional metaphysical beliefs. Ultimately, the only way logic can be made into a calculus is by denying the essential metaphysical nature of the world that logical language attempts to portray.

This, of course, is not a problem for the logical positivists who developed modern logic because they did not believe in traditional metaphysics, although, of the three people who wrote the book that put modern logic on the academic map (Bertrand Russell, Alfred North Whitehead, and Wittgenstein, the latter of whom greatly influenced, but did not actually author the book) both Whitehead and Wittgenstein later repudiated it--for different reasons. 

Their progenitor is David Hume, the 18th century British empiricist philosopher who went so far as to question the rationality of the belief in cause and effect. What modern logic has done is to create a system of logic that honors Hume's positivism by ignoring metaphysical reality: You can "solve" an "If P then Q" statement by ignoring the metaphysical implication in it and taking account solely of the "truth value" of its elements. 

In the modern view, in other words, "If, ... then" statements do not posit either a cause/effect or ground/consequent relation. They operate basically like conjunctive statements, ignoring the very relation that those who use them actually mean to assert (cause/effect or ground/consequent).

It is logic for Humeans.

In other words, the question over truth conditionality--in addition to anything else that might be wrong with it--is the logical consequence of a faulty view of metaphysics.

Zombie Logic: Should we be teaching our children how to think like computers?

The following article will appear in the upcoming Classical Teacher magazine.

In 1969, philosopher Henry Veatch wrote a book called Two Logics: The Conflict Between Classical and Neo-Analytic Philosophy. It scandalized the philosophical establishment of the day. The book challenged the underlying assumptions behind the system of modern logic that had been taught in colleges and universities for over fifty years.

The issues addressed in the book were complex, but the main issue was clear: There was a difference between modern and classical logic, and this difference constituted a clash of worldviews.

Most people who have been to college have encountered modern logic somewhere along the way, usually in a mathematics class. While traditional or classical logic sticks close to human language, modern logic favors formulations such as

• "P ⊃ Q" (which means "If P, then Q")
• "P ∨ Q" ("Either P or Q")
• and "P ∧ Q" ("P and Q")

In practice, the systems look very different. The symbolic, mathematical look of modern logic is a striking contrast to the traditional logic's emphasis of ordinary human language. It was Veatch's point that the difference between the two systems was not just cosmetic—that, in fact, modern logic reflects a particular worldview, one much different than that assumed by traditional logic.

Modern logic was a product of the logical positivism that became popular in the 1920s through the work of Bertrand Russell, Ludwig Wittgenstein, and A. J. Ayer (this was the "neo-analytic philosophy" of Veatch's title).

In one sense, logical positivism was an outworking in philosophy of the religion of science—the idea that the only legitimate avenue to truth was through either mathematics or natural science. In the case of the positivists, this took the form of the belief that the only logically meaningful statements were either statements that were true by definition or statements that could be empirically verified.

Under this belief, a statement like "A bachelor is an unmarried male" is logically meaningful because it is true by definition. And the statement "All crows are black" is logically meaningful because it can be checked out scientifically. But the statement "God exists" is not logically meaningful because it is neither true by definition nor can it be empirically verified. The statement "God exists," in other words, is neither true nor false: It is simply meaningless.

It was this view of meaning and language that flowed into the development of modern logic. Its central manifesto was the book Principia Mathematica, written by Bertrand Russell and Alfred North Whitehead, a book that became required reading in philosophy programs until the late twentieth century. And lurking in the authorial background was Wittgenstein, whose book Tractatus Logico-Philosophicus had infiltrated the thinking of the two authors.

The Tractatus, as it came to be known, cast a sterile and frightening vision of a world bereft of meaning and purpose. "The world," said Wittgenstein, "is everything that is the case." In other words, the only meaning in the world is formal logical meaning, which consists exclusively of definitional and scientific truths as they are expressed in logical propositions.

For the logical positivists, truth was merely a property of propositions. Under this philosophical regime, "truth" became "truth value"—the assigning to a statement of either a "T" (True) or an "F" (False). In fact, it was Wittgenstein who invented "truth tables," a mechanism of modern logic whereby the truth or falsity of a statement could be determined solely on the basis of the truth value of its components.

In other words, the truth of a statement like "It is sunny (P) and hot outside (Q)" is true if, on the one hand, P is true, and if, on the other hand, Q is also true. But if either P or Q are not true, or if neither is true, then the whole statement is false. This works with some propositions (such as conjunctive statements like "It is rainy and cold outside"), but it does not work with many others (such as conditional statements like "If the moon is made of green cheese, then ducks can swim").

Quantifying language in this way allowed the positivists to make all meaningful language into a sort of calculus: You could "solve" for the truth in the same way you "solve" an equation in mathematics. In fact, all computer languages are based on modern logic.

The positivists, of course, were mostly atheistic as well, and so there was the additional benefit that religious language was rendered meaningless.

What Russell and Whitehead thought they had discovered was a purely scientific language what encompassed all meaningful statements which could then be used to solve all scientific problems. Such a language had been a dream of modern philosophers since at least Gottfried Leibniz in the eighteenth century.
Although this system of logic went on to displace the old Aristotelian system in colleges and universities, at least one of the original authors, as well as Wittgenstein himself,  later repudiated many of the key assumptions behind the Principia.

Not only that, but the philosophy that produced it (logical positivism) has since gone out of fashion among many professional philosophers.

The philosophical establishment never answered Veatch's challenge 40 years ago, and the system of modern logic he defied is still studied and taught today, but with little understanding of its now-mostly rejected foundation. It continues to live on in a kind of zombie existence: It has lost its soul, but it lives on anyway. It has become the philosophical equivalent of The Walking Dead.

Traditional logic is not a calculus by which we can "solve" for the truth. Modern logic speaks the language of the computer, which was created by men; traditional logic speaks the language of men, who were created by God. While modern logic is how computers think, traditional logic is how human beings think. We are not computational beings and our language is not some kind of mathematical calculus. When we think and speak and write, we do it not as human machines, but as logocentric creatures. And we need a logic that takes this into account.

The Difference between Traditional and Modern Logic and the Difference it Makes

This is the first two pages or so of a 20 page essay I wrote some years ago. I've gone back to it several times, realizing it needed more work. I am going to use the recent article by Peter Kreeft in Touchstone Magazine and the recent response at First Thoughts as an excuse to go ahead and start posting it in pieces here to give me an excuse to finish it. It is still in draft form and parts of it clearly need more work, but what I'll publish here is at least approaching some kind of finished form.

I am often asked why, as a logic teacher, I teach traditional logic rather than the modern system of logic, which is much more common today.  I would like to answer this question by explaining what traditional logic is and how it differs from modern logic.

In analyzing the differences between traditional and modern logic, we will discuss the assumptions behind the two systems, the structure of the systems and their competing purposes.  As we do this, we should be aware that, for the most part, the nature of these differences is not disputed by the chief proponents of either system.  In other words, both traditional and modern logicians agree that these are in fact the differences: their only disagreement has to do with the extent of the differences and the merit of the respective systems.

What is Traditional Logic?
Traditional logic is the system of logic originally formulated by Aristotle, the Greek philosopher, in the fourth century B. C.  It was taken up by the great Christian thinkers of the Middle Ages, who simplified its structure and formalized the methods of teaching it to students.

Traditional logic involves mostly the study of the classical syllogism.  Here is a classic example of a simple syllogism, which we will use shortly as a way to see how the two systems of traditional and modern logic are different:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal

Traditional logic has also been called “term logic,” since it deals primarily (but not exclusively) with the relation of terms in an argument (in this case, the terms man, mortal, and Socrates). Whether the reasoning is valid depends on the proper arrangement of these terms in an argument.

It wasn’t until the 18th and 19th centuries that Aristotle’s system of traditional logic fell on hard times.  Beginning in the Enlightenment, the influence of scientific materialism grew tremendously.  Because of the incredible technological progress made possible by the sciences, the quantitative methods of science came eventually to be seen as an intellectual elixir, applicable to any and all intellectual disciplines.  The whole discipline of philosophy changed, beginning with William of Ockham, and continuing on into the radical rationalism of Descartes and the radical empiricism of Francis Bacon—the two intellectual traditions that still constitute the two basic impulses of the modern mind.

Traditional logic appealed to Medieval thinkers not only because it was based on Aristotelian metaphysical assumptions (not a big surprise since it was Aristotle who developed it in the first place), but also because of its uses in the determination of Christian truth. It was displaced by modern mathematical logic for two reasons: first, because of the rejection by modern philosophers of certain traditional assumptions about meaning and reality—assumptions that affect the entire system of logic; and second, because modern philosophers were looking for a way to make a science out of human reasoning—a way to completely capture the intricacies of human statements in a formal “scientific” system.

The chief actors in the drama that produced modern logic were Gottlob Frege, Bertrand Russell, Alfred North Whitehead, and Ludwig Wittgenstein. Frege, partly through his unsuccessful effort to show that mathematics was reducible to logic, developed a method of quantifying thoughts and inferences in a system of symbols. Russell and Whitehead took the basic conceptual framework of Frege’s symbolic system and used it to develop a full-fledged system of symbolic logic in their book, Principia Mathematica, the purpose of which, like Frege’s work, was to prove that mathematics was an extension of logic, but the most influential aspect of which was its system of logic. Wittgenstein both influenced and was influenced by Russell, and many of his ideas affected the Principia. Wittgenstein is reputed to have invented the truth tables that have become an essential fixture of modern logic.

The Differences Between Traditional and Modern Logic
The first thing to note about the differences between traditional and modern logic is that they are indeed different.  Although most modern logicians see the differences as differences in degree, they still consider these differences significant.  Irving Copi, the author of one widely used college logic text, does not reject the traditional system, but he does see the two systems as being very different:

Although the difference in this respect between modern and classical logic is not one of kind but of degree the difference in degree is tremendous.” [Introduction to Logic, 3rd Ed., 1968, Irving Copi, p. 212]

To the traditional logician, the difference goes even deeper:

“Aristotelian logic and symbolic logic,” says Edward Simmons, “are radically distinct disciplines.” [The Scientific Art of Logic: An Introduction to the Principles of Formal and Material Logic, 1961, Edward D. Simmons, p. 322]

Jacques Maritain, a traditional logician who referred to modern symbolic logic as “logistics,” put it this way:

Logistics differs essentially from Logic … Logistics and logic remain separate disciplines, entirely foreign to one another. (emphasis in the original)

Many traditional logicians, in fact, reject much of modern logic as mistaken.  Maritain, in fact, goes so far as to argue that modern logic is not logic at all.  This favor is returned by some modern logicians.  Traditional logic, says Bertrand Russell, one of the founders of the modern system, “is as definitely antiquated as Ptolemaic astronomy.” [Bertrand Russell, A History of Western Philosophy (New York: Simon and Schuster, 1945), p. 195].  Anyone wanting to know Russell’s view of Aristotelian logic will find it at the end of his chapter on Aristotle in this book:

I conclude that the Aristotelian doctrines with which we have been concerned in this chapter are wholly false, with the exception of the formal theory of the syllogism, which is unimportant.  Any person in the present day who wishes to learn logic will be wasting his time if he reads Aristotle or any of his disciples. [Russell, p. 202]

So there.

In short, some of the most important traditional and modern logicians agree that the systems are different, and some advocates of the respective systems reject, in whole or in part, the opposing system.

As we mentioned above, the two systems differ in three respects:  First, the assumptions behind the two systems are different.  Second, the format or structure of the two systems is different.  Third, the respective purposes of the two systems are different.  In all three cases—in the assumptions, structure, and the purpose—the traditional system reflects traditional views, and the modern system reflects modern views about reality. Each system is based on a different metaphysic.

To be continued ...

UPDATE: Although I am still in the process of finishing the line of thought started in this post, I have posted another related article on the issue of why traditional logic does not employ truth tables that should be of interest to those interested in this article: here. 

Traditional vs. Modern Logic: A short response to William Randolf Brafford's response to Peter Kreeft

I am going to post an article tomorrow that I worked on a few years ago on the differences between the traditional Aristotelian system of logic that I use in my logic texts (and which is still used at many Catholic schools) and the modern system that is emphasized in most college logic courses today. 

In the meantime, here is a response I wrote to William Randolf Brafford, who wrote an article at First Thoughts as a response to Peter Kreeft who has an article in the newest issue of Touchstone Magazine called, "Clashing Symbols: The Loss of Aristotelian Logic; the Social, Moral & Sexual Consequences." I haven't read the Kreeft article because it is available only to subscribers and I haven't gotten my magazine yet. 

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 (from which virtually all modern symbolic logic derives) later repudiated the project--Wittgenstein and Alfred North Whitehead. Russell stayed with it, and was not nearly so sanguine 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 philosophy, "with the exception of the formal theory of the syllogism, which is unimportant."

On the other side, Jacques Maritain said, "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 one ever responded to him. I asked Kreeft about this one time and he said that, to his knowledge, no one ever did.

What passes for reason at the Rally for Reason

Ed Brayton, an atheist who spends the better part of his time patrolling the internet for stupid-things-people-who-disagree-with-him-say then blogging-about-them-as-if-anyone-really-cares (he must provide World Net Daily with the better part of their site hits) commented on the possibility of protests at the Rally for Reason from Christians.

Ed the Logician has already refuted any arguments these irrational Christians might use:

"They’ll undoubtedly be using the same tired arguments we’ve all heard a million times."

I mean, we all know, don't we, that all it takes for an argument to be rendered invalid is that it be used multiple times? I guess this is the kind of thing that will be passing for Reason at the Rally.

Learning logic vs. learning about logic

If you wanted to learn to be a mathematician, you wouldn't want to read about mathematics; you would want to actually do math. If you were wanting to learn how to learn how to write, you wouldn't settle for just reading about writing, you would want instruction that involved actual writing.

The art of logic is like math or writing: you can't learn how to do them without actually doing them.

Most logic books are not logic books; they are books about logic. But doing logic and reading about logic are two very different things.

I noticed a post on a Christian apologetics blog the other day that referred to some logic classes at an online school. And I took a look at the books they were using in their class. One of them was Critical Thinking: A Concise Guide, by Tracy Bowell and Gary Kemp. It looks like a fine book about logic, and one that I will probably pick up for my own enrichment. It defines logic, divides it, and generally explains what logic is. Now that certainly is a part of actually learning logic, but just doing these things will not train you in how to actually use logic yourself.

Another is A Rulebook for Arguments, by Anthony Weston. I actually have this one in my library. Again, it is a useful book for someone who knows logic or generally how to argue. It has a lot of great tips about things you should do when you are actually engaged in argumentation, but it doesn't actually teach logic.

These are books about logic. They are not a logic books.

I would say the same thing about most books that try to teach fallacies. Of course, they do not really teach fallacies. There wouldn't be much use in having students learn how to commit fallacies, would there? All these books do is teach students how to identify certain bad argument forms. But students never really learn why these fallacies are mistakes in reasoning because they have not been taught how correct reasoning works.

Identifying something is the most basic step in understanding what something is, but it doesn't get you very far in the process of actually learning how to use it.

In order to be able to use logic, you have to spend time methodically learning a number of particular concepts and practice them repeatedly. You then have to practice applying these concepts to arguments, and know how to internally manipulate arguments.

The two most valuable drills in logic are

1. Backing in to a missing premise; and
2. Reducing 2nd, 3rd, and 4th figure categorical syllogisms to the 1st figure

If a student is able to do these things competently, then you know he knows all the important aspects of logic. If he can't, then you cannot say he knows how to "do" logic. The student will still be a spectator of the subject, and not an actual practitioner.

This kind of skill constitutes competence in basic logic. I would add that, if you want to determine whether a student is

It's interesting to note, by the way, that most modern logic programs pass these things over.

If a logic program doesn't incorporate these two drills, then it really isn't a good logic program. Again, it may be a great book about logic, but, as I said, that is a very different thing.