What is Logic

So, this post comes out of a discussion I witnessed recently. As I have said in some posts, my idea for this blog has been to get out theories on literary works etc that have percolated in my brain over the years, or sometimes things that have only recently come up and have tied into other ideas that have lain dormant for a while, or when processing and responding to a particular comment has sparked thoughts, after I have pondered them while driving or on breaks from editing etc, I think "hey, I should write this on the blog instead of trying to make sure I remember the idea when mulling it over, then I have record of it AND the writing process usually help formulate ideas better and often kicks new ideas out about it [as Fr Lienhard always says, 'we write to think']."

So, the situation was that two people were talking about a geometry question in a textbook that was not an official proof: given that a shown quadrilateral figure is a square, what can you say about the quadrilateral formed by two radii of a [visually verified] inscribed circle and two segments of of the two sides of the square intersected by the two radii. In a moment I will get to my answer of that (which was not the textbook's answer, as I found out later) and the value I see in working it out, but for here I want set the stage of the current post and give the central point, which relates to that second part (the value). The situation that is really at the core is not the geometry problem, but rather, what was said about the issue and project of giving an answer.The person doing the problem was lamenting misplacing a notebook in which they had written down all the theorems covered so far in the textbook because they are scattered throughout the textbook and not easily located and basically saying that they needed it to answer the question. I happen to agree with them at least on the general project of answering the question, against the other person, who was saying that you can simply look at it an know the answer (which had already been verified in the back of the book as being that the smaller quadrilateral is a square) by "logic."

My main contention is that "logic" is stated way too often as some type of magical word meaning "intuition" and that what is usually going on is an assumption that one's own unreflective perception is, of course, right, and that usually where this leads is a situation in which the one who "wins" the argument is simply the one with the greater psychological dynamism or advantaged position by which to coerce another into accepting their own take on things: a stronger/advantaged person says "that's just the way it is; that's just logical" with a statement between the lines (whether fully conscious or not makes no difference) of "you're just stupid if you can't see that," and the weaker person submits, not out of any demonstrated logic but out of a weakened position. Basically, I think that most of the time, "winning an argument" has nothing whatsoever to do with actual logic and that, in usual discussion involving people who are merely opinionated rather than informed or perceptive, one can "win" the argument without having gotten any nearer any truth (and more likely, moved further away from it). And I think this is a completely fallacious view of logic that relies on an uninformed definition of the word.

I'm not saying that the particular person in this discussion is necessarily that type of person. It's understandable that the fact that grasping (on the subjective side) the self-evident principles of logic does rely on a certain type of intuition, in addition to the fact that work in logic can impact intuition (by, hopefully, properly forming it), can lead to a confusion of intuition with the logic to which such intuition is  hopefully a pathway, although I think that it needs to be checked against the historical collective intuition that bears witness to the self-evidence of principles used AND that it is necessary to demonstrate a grasp of the application of those principles to givens. I'm not saying I think that the person was being a belligerent asshole, but I do think that making this mistake stands in distinct clear and present danger of leading to that sort of brow-beating in the name of "logic," especially if one becomes as, shall we say, earnest about it as the one person in this conversation was becoming ... hadn't reached yet, but was sort of edging toward.

So, my contention is that logic is not some basically magical intuition. I do believe that communal intuition (usually with "communal" stretching timewise, across generations) plays a role in arriving at principles commonly agreed to be self-evident but not tautological (true by definition, the predicate being already present in the subject, see below) that are the principles used in logic, and that the formation of the intuition of the student is a goal in learning to do logic and geometry, for intuition is a mental sense power, and like the mental/emotive sense power we  call conscience, it can be well-formed and a good guide or ill-formed and a bad guide. But in neither of those cases is the intuition the logic itself, they are not identical (communal, traditional intuition of the past flows as a source into the practice of logic and hopefully the individual intuition is formed well as a future guide to finding logical truth in the future as a result of the practice of logic, but neither of those is identity). Intuition is necessary (well-formed intuition, that is) to be able to grasp the self-evidence of the principles AND the manner in which to apply them to the terms of the givens in order to arrive at the conclusions, but the intuition is not itself the logic.

So, I should not make a reader (hypothetical or actual) wait any longer for a basic answer to the question in the title of this post: what is logic? I define logic as the process of demonstration of the necessity of conclusions based in givens and the application to those givens of principles communally agreed to be self evident (e.g., the nineteen rules of inference in symbolic logic that you can find in the back cover of Irving Copi's classic textbook), taking place in ordered steps known in both geometry and formal logic as "proofs," generally based most fundamentally in "syllogism."

Syllogism: The "hypothetical syllogism" rule in symbolic logic is: if P implies Q and Q implies R, then P implies R; and the classical example of traditional basic syllogism is: If all men are mortal and Socrates is a man, then Socrates is mortal ... but there are principles involved in this that you have to be able to grasp (especially if you want to go on to apply them to real world statements instead of just P,Q, and R or Socrates and "mortal men doomed to die" [I do love me some JRRT]), you don't get to just say "well of course, that's logical ... there, I just did logic" ... in symbo, if you don't write "H.S." out the side of a specific numbered step in a proof, you don't get credit for having used the hypothetical syllogism rule for demonstrating that step in your proof, and if you don't have anything out the side for that step, then you don't get credit for that step in the proof, and if that step is necessary for proving the conclusions from the givens and you don't get to claim that step, you fail the proof ... somebody put a set of givens in front of you and asked you to arrive at a certain conclusion by doing logic ... the actual discipline called logic ... and you didn't do it ... no matter how many times or how vehemently you said "it's just logical, you can just see it!"

[ASIDE: Simply out of the selfish consideration that I put some thought into it, I will give my understanding and explanation of the elements of the classical syllogism: If you have a universal predication [all men are mortal] and a particular predication [Socrates is a man] and they share a term [man/all men] that is the subject of the universal predication and the predicate in the particular predication, then you are allowed to state the predicate of the universal predication [are mortal] for the subject of the particular predication [Socrates]: All men are mortal (major premise); Socrates is a man (minor premise); therefore all men are mortal (conclusion). What I did just now was a definition ... not an intuition. The ability to do so may involve skills of intuition, but a statement of a definition is not "It just seems logical to me, I can intuit it through logic" ... hopefully one's intuition becomes good enough that one can rely on it when one does not have the time to be fully stating explanations, but a part of getting to that point is putting the time in to formulating definitions and doing proofs "by the book"]

And I usually try not to tout things, and I definitely don't view myself as any type of authority on logic like Dr Richard Trammel, who would not call himself an authority either, but probably something more like an extremely avid fan and poor [only in his opinion] but devoted practitioner, because he was very humble (and immense fun as a prof), but I do think I have some room to talk on the matter here because I did get pretty good grades in both his general logic and symbolic courses in undergrad (which were probably the two most fun courses I took, not as directly impinging on the field in which I chose to study, as I was not doing math or computer languages, but still very foundational for thinking in general, and a ton of fun ... the last night before we got to the twentieth "rule," known as "conditional proof," I spent four hours on two proofs ... and the time just flew by because it was a blast.

The Geometry Problem

But, let us start with this geometry problem and the application of actual logical method to it. Logic moves from givens to conclusions, so we start with the givens (including the method of giving). I'm not going to put a copy of the image here because (1) it would be a pain in the ass, as I don't have one and would have to procure/make it and (2), more importantly, part of doing logic is being able to do it without pictures, being able to do it with only the meanings of the statements, relying on language (interesting fact: "logic" is from the Greek word "logos," which means "word," and a "philologist" is a person who studies languages). Even below, as I have "visually given" ... that is a word, a categorization given verbally (the Latin "verbum" also means means "word," not necessarily spoken word ... emphasis on the spoke would be "orally given"), the categorization being the distinction between visually given and verbally given but that both can arrive at or at least be expressed accurately in the same types of statements as givens and that those verbal expressions are of equal weight in the context of the proof regardless of whether they come from verbal or visual giving.

1. Quadrilateral ABCD is a square (verbally stated)
2. Circle 1 is inscribed in ABCD (visually given)
3. E is the center circle 1 (visually given)
4. EF is a radius of circle 1 that intersects line AB at  point F (visually given)
5. EG is a radius of circle 1 that intersects line DA at point G (visually given)

Question: Given that ABCD is a square, what can you say about AFEG?

Preliminary: We are not asking what you can intuit visually as concerns quantification. Visual input is allowed (what I have called "visually given") as verification, within accepted approximations, of a standard state of affairs using commonly accepted definitions, such as that a certain labeled point is the center of a circle or that one line intersects another:  You can visually verify that line EF intersects line AB, but not that it bisects it (which would be a further quantification because bisection gets into comparing quantities, 1/2 versus 1).

Beginning question: What would you WANT to say, meaning what is the kind of thing you could say about it that is worth saying but possible to say? It is not worth saying (and there therefore does not count as "saying" anything) "it is quadrilateral" because that is tautological, meaning simply restating something that is true by definition: it is given in geometry that capital letters are points and that two point make a line and that three points make a triangle and that four points make a quadrilateral, and so, saying "AFEG" is a quadrilateral is nothing new because it is quadrilateral by definition because all figures involving 4 and only 4 distinct points (none of the points are on a line between any other two of the points) are quadrilaterals (this is what is called a "tautology," something true by definition, a term used pejoratively when pointing out that somebody is claiming to be saying something new when really they are just restating a definition ... the pejorative sense in logic is connected with the pejorative sense in writing style for saying something twice but in different words, either to eat up space in an undergrad paper or to appear to say more than one really has). However, there is more than one type of quadrilateral: rectangle, square, and whatever the name is for the parallelogram that doesn't have right angles. And THERE is something that is worth saying because it's not discernible by definition alone and because there are multiple possibilities, so determining which one it is is something positive that can be done. It also can be done: you would be trying to say simply that it is one particular kind of quadrilateral, not that that quadrilateral is in some proportion to some other figure other than the one within which it is contained (the relationship to THAT figure, ABCD, would be another thing you might be able to say and that would be worth saying, that the area of AFEG is 1/4 the area of ABCD, but I would say to stick to first things first: get out the things that you can say about AFEG in itself before moving on to what you can say about it in relations)

[ASIDE: Real world application in argumentation: My editing mentor, Fr Joseph Lienhard, when he taught undergrad courses and was giving the standard lecture on writing the paper for the class, used to say "a good thesis is something that needs to be argued [not tautological] and can be argued [not illogical or impossible]."]

The missing theorems (that I am formulating, after years of not having done geometry):

1. When the radius of an inscribe circle intersects one of the sides of the square in which it is inscribed, it does so at the midpoint of that side.
2. The radius of an inscribed circle is equal to half of one side of the circle in which it is inscribed
3. If one angle in a equilateral quadrilateral is 90 degrees, then all four angles are 90 degrees.

Conclucusion: since a square is defined as a quadrilateral that is both equilateral and equiangular, AFEG is a square because the givens can be used to establish that AFEG is equilateral and equiangular (I could write out all the steps, but it gets a bit tedious in both the writing and the reading ... what I just said is the basic actual meat of the reason for the present point being made).

Checking the answer: I asked the student later if they ever found the notebook with the theorems and what one was used for that and they said that it had to do with the sides of the square being tangents to the circle and the theorem being that a tangent of a circle (a straight line touching at one and only one point) is always perpendicular (90 degrees) to the radius of the circle that intersects it (personally, I think that this would require also stating that, if one angle of a quadrilateral is 90 degrees, then all are, but maybe the rules or their tightness are other in geometry than I remember ... I also think that all of my own original "theorems" hold true, although they may need to be translated into the commonly used terminology, and in the process maybe formulated a little more concisely or clearly etc)

The Misuse of "Logic"

Logic is not intuition: intuition is a goal and commonly agreed pathway (not just shared - yes, it is objective and shared, but it does not come to bear on this discussion or any other in any way until it is further openly commonly agreed ... knowledge of such common agreement being what some of us refer to "education") to self-evident principles, but "logic" is not even the self-evident principles themselves: the communal intuition evidenced in publicly recorded dialogue is a source of commonly agreed upon formulations of principles that are commonly agreed to be self-evident. But "logic" is not even the self-evident itself. The closest it comes is in working with, crafting and analyzing, the common definitions by which the self-evident is formulated. But when we ask a student to do logic, we are not asking a student "assert to me that something is self evident." Rather, "logic" is the demonstration in ordered steps of the application of those principles of whose self-evidence we have learned from education about the common agreement (until we reach a later stage of development and go off on our own speculation about the self evidence or what it means for something to be self-evident etc).

"Logic" becomes for some people this magical word of power for claiming what you want to claim out of motivational factors other than actual reason, like maybe your parent's preoccupations with certain issues etc (sorry good Christians, but psychology is real; in fact, I would argue that Christianity has traditionally recognized that it must account for it because not to account for it gives in to gnosticism, and no matter how poorly various branches of Christianity have done at times of avoiding that, and some have done damn near to nothing, if not less than nothing, meaning in the other direction, the Faith as a whole, the true Church, has always made at least some effort to avoid gnosticism because it is not congruent with the Incarnation).

And it becomes a weapon, meaning the word, not the thing. Very few arguments are really about truth, and very few times does the winning of an argument get anyone any closer to truth. Usually, at least in the popular arena, the way an argument is won is that the person with the stronger attitude, the greater psychological dynamism in saying "this is logical because I say it is and you're stupid if you don't see it," beats the other down, and sometimes the beating down is even such a sham of truth as to be like the scene in Fisher King where Jack pops in the soundbite of Edwin saying yes in agreement with his tirade about "yuppie inbreading" (if you have seen Terry Guilliam's film The Fisher King ... do).

Where it leads: A Faith That Is Not Alone

So, here is a real life example of where this type of thing leads. I have to begin by filling in the detail that I use "sense" in a technical meaning. Gottlob Frege was kind of the "father" of linguistics and is at least the one famous for the succinct formulation of the difference between "sense" and "reference." "Sense" is simply whether or not you can make sense out of what a sentence is saying, simply whether you can understand its propositional claim. If I say, "there is a blue car parked at the end of the street," you know what I mean: you know what a car is, you know what it means for a car to be blue (you know I am being literal about the color of the body of the car, not metaphorically saying I think the car is sad), what a street and an end of a street are, what it means to be parked ... you can put it all together and know what I am claiming, you can make "sense" out of it ... regardless of whether there actually is a blue car parked at the end of the street. That question of whether or not there actually is, in fact, a blue car parked at the end of the street is a matter of "reference," a matter of "referential value."

So, once upon a time, when I was considering becoming Catholic, I was at a thing called a circle that was run by Opus Dei. OD has "nights of recollection" (two meditations by a priest, one talk by on virtue etc by a layman in between them, confession available during the talk, and a benediction) at their centers in metro areas, but they also have their official members (either numeraries from the center or supernumeraries from the area) go to somebody's house or location and give a talk on virtue/spirituality etc, and those they call a "circle." So I was at one of these with a couple other guys who had already become Catholic by that time, having converted from the same Protestant circles in which I grew up.

Now, those lands in which I came of age are known as "the Reformed tradition" and are denominations like the Orthodox Presbyterian, in which I grew up from the time I was nine to the time I was twenty-four (before that, for the first eight years of my life, we were Southern Baptist ... sooo ... no wonder I'm diagnosed bipolar II). Those folks are, at least some of them, quite maniacal in their pursuit of their "theology," central to which are, of course, the two great pillars of the Reformation: sola Scriptura (Scripture alone as authority) and sola fide (faith alone as the means of justification).

So, one fine Opus Dei circle evening, after the guy gave his talk, when we were just kind of chilling for a few minutes before departing, one of the guys who had converted from OPC to Catholic relates a statement somebody from family or extended social/church situation (whatever group of people we no longer went to church with on Sundays but still had relations with) had made to him in some conversation or another concerning the "saved by faith alone" thing. The statement was "it is by faith alone, but a faith that is not alone." And said convert cat was giggling uproariously going "I mean, that doesn't even make any sense!"

There are a couple of things with this. One, I don't think said convert cat was probably very precise in what he meant by "making sense." I suspect he meant something at least closer to that technical sense than simply saying "isn't true," but I also suspect a fair bit of sloppiness. But I am going to give him the benefit of the doubt that he was being precise, and part of that is to make the point of the other danger opposite the "brow-beating danger" ... the person who isn't going to be brow beat because they actually have a clue and know that they have a clue. That person is going to say "you say that it doesn't make sense, and that means that you're saying that it has no internal cohesion as a statement." And if that person is thinking for themselves and halfway intelligent, there is a strong possibility that they will arrive at a conclusion that the statement can make sense, and therefore that the Catholic is simply a jackass for saying that it can't, when in fact (as I am about to argue) there are ways in which it can be said to make linguistic sense, and even ways with analogates in Catholic theology.

But before I do that, I have to note that I was just now talking about the person with a clue and a backbone. There are some people who don't have much of either, and it may not be a matter of virtue ... some people get very beat up by the bullshit world that is the detritus in the wake of a lot of "Christian" practice. And there is a whole spectrum of people in between. What I am about to describe is how an intelligent and self-confident person might respond to the maniacal giggling claim, a way of rejecting the Catholic side (ironically, because one of the big themes Opus Dei hits on is "apostolate" and this would be not only failing at apostolate, but actually doing kind of an anti-apostolate). But somebody on the beaten down end of things might not reject the Catholic side; they might go with it .... for all the wrong reasons. Being cowed by alpha-male-attitude tactics is not a good reason, and more pointedly, it is not healthy for the person who is cowed. But, unfortunately, a lot of Christians take an "ends justifies the means" line (they would never let themselves admit it even to themselves, but ...). That kind of bullshit is not what Christ meant when he said to spread the Gospel.

So, anyway, I'm going to give a possible response by the most intelligent and self-confident person to show that, best case scenario, the Catholic "apostle" boy has majorly screwed up by practicing the "it's just intuitably logical that this statement makes no sense, and if you can't see that, it's just stupidity on your part" disposition.

So, here is how it can make sense. The statement "saved by faith alone but a faith that is not alone [truly good action always accompanies faith]" basically says that "thing A causes thing B, but thing A never occurs by itself, it always occurs with thing C, but it is still thing A that, entirely on its own with no help from thing C, does the causing of thing B." Now, the Reformed Protestant says "see" and the Catholic says "that still makes no sense." NOW the informed Reformed Protestant enters the room and says "did you know that there is a place in Catholic theology where this principle is actually used and can be used by analogy here? In the principle of double-effect in Catholic moral theology?" and the Catholic, who more than likely has not studied for shit but thinks he has studied a lot and has probably actually understood very little of what he actually has read, says "uh ....." and the person on the fence says "this guy is a dipshit" and goes with the Reformed guy ... Catholic boy's apostolate all blown to hell.

So, I need to explain this principle of double-effect and how it can inform this particular debate by analogy. The principle of double-effect addresses the question of whether, when one action causes two effects, one good and one evil, one is allowed to do the action for the sake of the good effect, in spite of the fact that the evil will also surely ensue. The answer is "yes" as long as four criteria are met. The first is simply that the action that causes the two effect must itself be at least morally neutral, if not good. Another is that the good effect be at least equal in magnitude with, if not greater than, the evil effect: you can't do an action for the sake of a small good effect when it also results in a big evil effect. Another is that you can't be intending the evil effect and simply using the good effect as a justification to do what you wanted to do anyway.

It is the fourth criteria that interests me, the one I call the "no daisy-chaining" rule. You cannot be accomplishing the good effect by means of the evil effect. The effects have to be independent of each other save their common efficient cause ... the good effect must be directly dependent solely on the action as its efficient cause.

Whatever its status in Protestant traditions, this is official Western Catholic teaching ... the official camp of the person who was ridiculing the "faith that is not alone" line. So, lets see if this officially approved principle (no daisy chains) can be applied analogously to the whole "faith alone" question. We have to strip out the moral qualifiers ("good" and "evil") because, in the justification debate, all the terms are good (even "good works" in the Protestant mind in this context will be works that are done out of true charity, rather than out of trying to "buy" heaven etc). So, we're left with a statement that you can do thing A for the sake of thing B even though thing C also results as long as four criteria are met, and one of those criteria is that thing A cause thing B without any role of thing C. Now, saying that you're allowed implies that it is possible. If it's not about live options, it's not about moral theology. So, can we fit faith, salvation, and good works into this A,B,C schema? Lets say that we have a statement by God in Scripture that faith will always yield good works (say, the book of James, chapter 2? at least in a reading of it that is very plausible to modern ears), but also other statements that faith saves. Can we make "sense" along the lines of the basic (without it's moral qualities) schema from the principle of double effect? Faith (A) causes salvation (B) and also always (because God said so in the Bible) causes good works (C) ... but A causes B without there being any involvement of C. Voila ... sense.

That is how it can make sense. And that is where the person on the fence might say "hmmmm, on the one hand I have the Catholic, who makes no argument and simply scoffs, and on the other I have the Reformed person, who patiently sits and explains to me their argument for why it makes sense, wonder who I should go with." Maybe they can work things out further on their own and go with the Catholic position, but that's no credit to the Catholic arguer. That person blew the job royally. And then you always have the other option, which is the person whose end choices can be said to be connected to the Catholic's "good works" ... the person who allows themselves to be beaten into submission by psychological dynamism.

(MY SOLUTION: I should say that I agree with the Catholic side of the sola Fide debate. I think that the "a faith that is not alone" can make sense only if "faith" and "works" are defined in a particular way that I think is erroneous ... I do not think that they are separate things as regards "efficacy for justification," or more to the point, I think that what is meant in Protestant Reformed circles by the term" faith" as what saves is, by definition, in the class of things that they mean by "works," intentional human action [in this case the mental action of assent and, probably more than they like to admit, the act of displaying a certain emotional disposition], so the distinction is, I think, fallacious. I don't have time to draw it out here, but the modern conception of "faith" and "works" beginning with Luther's readings have some very serious confusions about what those terms mean in their specific setting at the time of the writing of the NT, but for a quick example, "works of law" in Romans and Galatians does not refer to charitable works in general ... it refers to the specific ritual codes and actions of the Mosaic law, meaning circumcision and the dietary purity laws [scholarly consensus is that, even when the use is anarthous, meaning have no definite article, when "law" is used in the NT, it most always means the Mosaic Law]).

Forming the Intuition and Newman's Illative Sense

There is a final thing that I would like to add here, and it has to do with the formation of the intuition and the use of a, hopefully, well-formed intuition when full exposition is not exactly convenient. John Henry Cardinal Newman called such an intuition "the illative sense." The example given by the professor from whom I took the course in which I learned about it used the example of a Latin text that has a date on it of 5th century. So you take it to somebody who has spent a 40 yr career studying 4th through 7th century Latin texts, and you ask them, "does that date seem right?" and they read it and say "no, this feels like 7th-century Latin, not 5th." So, you ask them what their evidence is, and they say it just doesn't feel like 5th century, it feels like 7th. Newman's thought on the illative sense is that you should not discard their opinion just because they did not lay out pieces of evidence for you. When they have been reading texts from those centuries for as long as they have, saturating their brain in them, their "feel," their illative sense, is going to carry some weight that should not be ignored.

The thing about Newman's illative sense is that it's not something for which you go "own it, baby!" to a beginning student. The scholar for whom you must be considerate of their illative sense spent decades translating and interpreting texts, which is basically applying extrapolations and adaptations of basic rules they learned as a beginner in hours of paradigms and principle parts, hours of "amo, amas, amat" and answering questions about the passive periphrastic and the technical form of the subjunctive construction used for future-less-vivid. It's not a matter of reading a few texts and then "getting your logic thing on" and getting a "you go girl!" on the test. At the point at which the highschooler I originally started this post with is, they are still at the stage of learning logic analogous to filling in charts of Latin declensions and conjugations. If you tell them to just use their "logic," at best, to use the image of professor Harold Hill (my father was a huge fan of the musical "The Music Man"),  telling them to "think the minuet in G." At worst, and probably often closer to reality, you're basically training them to view psychological brow-beating as intelligent and reasoned, logical, persuasion (the disappointing part is that it was the kid who actually wanted to do the work assigned ... do you know how unusual it is to get a highschooler who cares at all about doing their work in the way it is designed to be done? In putting in the slog work that yields the finely tuned intuition).