(P→Q)∧¬Q ⇒ ¬P
“‘P implies Q’ and not Q” implies not P
Modus Tollens in Propositional Logic
In the pursuit of knowledge,
Every day something is added.
In the practice of the Tao,
Every day something is dropped.
The Tao Te Ching, 48
Ἐγώ εἰμι ἡ ἄμπελος ἡ ἀληθινή, καὶ ὁ πατήρ μου ὁ γεωργός ἐστιν· πᾶν κλῆμα ἐν ἐμοὶ μὴ φέρον καρπὸν αἴρει αὐτό, καὶ πᾶν τὸ καρπὸν φέρον καθαίρει αὐτὸ ἵνα καρπὸν πλείονα φέρῃ.
I am the true Vine, and my Father is the Vinedresser. Every branch in me that does not bear fruit, He takes away, and every branch that bears fruit He prunes, that it may bear more fruit.
A child, to the Blessed Augustine
In the steps of logic, interestingly claimed by both the disciplines of mathematics and philosophically (or perhaps, disowned by both disciplines), the proof of any great theorem has something paradoxical. Step by step, you go from one statement to another that is more general and asserts less, until at the end you reach a significant and quite specific conclusion at the end. At each step of the way, there is something you lose and something you give up. But when all the blocks are in places, you have a conclusion that is far more substantial than any of the losses ensued.
Modus tollens, for which this piece is named, is one of two prominent “inference rules” in logic. Modus ponens, the way of adding, powers such syllogisms as, “If all men are mortal and Socrates is a man, then Socrates is mortal.” Modus tollens, by contrast, is the way of taking away, and it powers such syllogisms as, “If all men are mortal and the Archangel Michael is not mortal, then the Archangel Michael is not a man.” Now symbolic logic does not deal too much in concrete syllogisms; it is often concerned with more abstract pursuits, but these provide at least slightly concrete of an illustration of two of the major workhorses in symbolic logic. And they are not mutually exclusive to use; I may take modus tollens as my point of departure for this work, but please understand that it would be absurd to say that a logician who agrees with me would stop using modus ponens in proofs and argument.
When I was young I enjoyed night and darkness, and the beauty that things have once your eyes are accustomed to the night. When driving at night, I loathed headlights: I used them in full accordance with the law, and I was glad that other drivers would see me, but I was painfully aware of something I am much less aware of now: headlights effectively limit my vision to where they are pointing; if I want to look to the side of the road, I see far less than my eyes can see when they are accustomed to darkness. I wrote in my cynical dictionary,
Flashlight, n. An instrument of imperception which obscures vision by producing a concentrated glare at one point which is sufficiently intense to prevent the user from seeing anything else. Environmentalists have brought the cleverness of this device one step further by producing the solar powered flashlight.
It was much later that I would learn that as far as core insight goes, I had reinvented a basic building block of ninjutsu. Ninjutsu recognizes that we see optimally in the dark when we have not seen strong light, such as that produced by cars and flashlights, for at least 20-30 minutes (some would prefer longer). The optimal condition from a ninja’s perspective is to retain such night-optimized vision, while any opponents would see bright lights enough to lose that vision. And there are many layers of insight in that basic perspective: a flashlight is not simply, as a naive user would expect, something that lets us see where we could not see. It works in a way that shuts down our natural night vision, the vision that not only ninjas but a million years of our human race had as the only, and best, way to see in the night. If I may put it in these terms, the ninja preference for “natural night vision” should not be seen as a distinguishing feature that sets ninjas apart from other people today, but a retained continuity with the only game in town for well over 99% of the times humans have walked the earth. I don’t want to downplay or diminish the achievement represented by the whole suite of ninja stealth skills, but trying to retain one’s natural night vision is not so much a matter of “Wow, what insight and skill!” as “They have a clue!”
A supreme instance of a universal law
In the Arthurian Torso, C.S. Lewis makes a point about vicarious salvation: “He saved others, himself he cannot save,” the wicked barb of sarcasm unleashed as Christ hung on the Cross with nails through his wrists and labored breaths piercing his lung, is a definition of the Kingdom. All salvation, everywhere and in every place, is vicarious. Every man may paddle his neighbor’s canoe but not his own. And as regards Anselm, who argued that the race of men owed a debt that could only be paid by a man and simultaneously could only be paid by God, so only God made man in Christ could pay the debt, did not describe a fundamental exception that is irrelevant to the workings of the universe, but the supreme instance of a universal law. “He saved others, himself he cannot save” is written lightly in small letters in our lives and deeply engraved on the most monumental scale in Christ, but we participate in what Christ has offered.
I have referenced Western symbolic logic, the Tao Te Ching, and ninjutsu in connection with “Every branch that bears fruit, [the Vinedresser] prunes that it may bear more fruit.” But the intent is not syncretistic. It is to point to the supreme instance of a universal law. A ninja instructor teaching stealth, I would imagine, might tell someone eager to use a flashlight, “Let me show you what things look like if you put that flashlight away for 20 or 30 minutes.” Robb Wolf, in advocating a neo-Paleo human diet that consists of the same sort of things people ate for a million years before the extremely recent agricultural revolution, says, “Put down that donut. For that matter, put down that organic whole wheat bread, even if it’s not modern wheat but spelt. Would you please try eating just the fuel the human body is made to run on?” But this is not with an intent of syncretism to write some hymn that begins praising Christ and melts into praise of Krishna. The universal law is a law that plays out in many places and is recognized in many ways outside of the Church. For that matter, quite a lot of the Church’s wealth is to be found outside of its proper boundaries; at one place Chesterton defends the Church against things it is charged with simply by calling on The Witness of the Heretics. The boundaries of the Church may rightly be retained, but the Church found Christians before Christ among the pagans as well as among Israel. And pruning is at one stroke a treasure of God in the Church and something forever to be found across the realms of men, who are in any case made in the image of God.
The age of the damned backswing and modus tollens
The Damned Backswing is a real phenomenon, but it need not be the last word; every thing that is taken away can be a cutting of the Vinedresser.
Since ninjutsu decided that it is better for a ninja to have real night vision, artificial light, even of fire, was treated as something that would quench natural night vision. But in our time the pure organic light of incandescent bulbs has been progressively phased out in favor of the plastic light of fluorescent bulbs, whose buzzing is a nuisance even to the blind. There are further steps away from the organic white of incandescent bulbs; LED lights offer a lunar white which is not helpful if you wish to pick out an outfit where the colors fit with each other instead of clashing; lunar white looks white but it provides a greyscale vision with colors barely discernible. (And is there a hint of the future in that lunar white light bulbs have no mercury and take a fraction of a CFL’s power draw?) Once conservatives balked at the brightness of new (incandescent) light bulbs, offering vision comparable to sunlight at any time and any place. But the stern hand of a government that believes it knows better than us may be wielded by one who knows better than government. This One who knows better than government might use the pest of the fluorescent light to draw people to use the day as day and the night as the night. And that may be gain and not loss. We may lose the organic light of incandescent light sources to gain the Organic light of the Sun.
The many ages of modus ponens
Reading, on a doctor’s advice, The Paleo Solution rumbled with a few implications. Probably the biggest change in perspective was that I viewed the New Testament as incredibly ancient, and the Old Testament as even more ancient. The Paleo Solution suggests that the most profound change in the time humans have been around has been the agricultural revolution, which took place after 99.5% of the time people have been around. While Genesis may place nomads alongside builders of cities, Exodus fairly clearly assumes the agricultural revolution has taken place. And even on purely secular grounds the New Testament exists in a closer-to-modern era. Historians may note that people in the U.S. made a very conscious technological decision to have roads connecting places. In the time of the New Testament, there were Roman roads which vastly outstrip any transportation technology in the Old Testament, and the spread of the New Testament, which includes letters to diverse cities, was partly affected by the Roman roads.
And all of that is to look without enlightenment at the Old and New Testaments as well-preserved signposts to where we are technologically today. But let us continue without enlightenment for a moment.
Plastic for breakfast, lunch, snack, or dinner
There has been more material progress in the United States in the 20th Century than in the entire world in all previous centuries combined.
Book News Annotation:
This work by economist Julian L. Simon (d. 1998) was left unfinished at his death but was completed and prepared for publication by his colleague, Stephen Moore. The title states the bias, which is further explicated in the introduction: “…there has been more improvement in the human condition in the past 100 years than in all of the previous centuries combined since man first appeared on the earth.” In support, 100 trends pertaining to the health and welfare of, mainly, US inhabitants are presented in graphs, with interpretive text that maintains the “getting better” thrust (and the conservative orientation of the author and the publisher). Interestingly, Simon’s wife injects an alternate view in a brief foreword in which she discusses her reservations about describing the 20th century in the positive terms used in the book, and she tells of her conversations with her husband on the subject. Annotation c. Book News, Inc., Portland, OR (booknews.com)
There has been more material progress in the United States in the 20th century than in the entire world in all previous centuries combined. Almost every measure of health, wealth, safety, nutrition, affordability and availability of consumer goods and services, environmental quality, and social conditions indicates rapid improvement. With over 100 four-color figures and tables, this book shatters the myths about progress that are often perpetuated by doomsayers in the media and academia.
Nourishing Traditions takes the agricultural revolution as a healthy starting point, but it offers something, even to someone following the Paleo diet, that The Paleo Solution does not. It discusses progress that has been made, and what comes clear is that this is progress from a corporation’s perspective, not progress from a human health perspective. Factory farmed milk, for instance, is not the natural health food it is presented to be. Never mind the question of whether milk represents a part of the Paleo diet. Factory farmed milk has such substances as pus mixed in with the milk from the unnatural condition the cows are under, and 2% milk has its skim portion mixed in from powdered skim milk, and on this point Nourishing Traditions effectively says, “Cholesterol is your friend. Oxidizedcholesterol, such as that produced in powdered skim milk, is your enemy.” I remember one time taking the claim that organic food tastes better as one more marketing ploy to justify Whole Paycheck’s heavy costs. Then, after a time of eating only organic strawberries when I ate strawberries—out of a dutiful sense that it was better for me—I ate a conventionally farmed strawberry and wondered, “What is this that I have bitten into?” My concern here is only incidentally about pleasure, which really does not help us as much as we think. It is something deeper. If you want a rough, unscientific but accurate gauge of how nourishing fruit is, taste how sweet it is. It’s that simple. The taste is not simply a pleasure delivery system; it is also a signal about how nourishing things are for you. And I remember commenting to one parent who was concerned about his children’s sweet tooth, “That sweet tooth is a God-given aid. It should be rewarded, not with candy, but with sweet fruit.” And candy is as bad as nutritionists say it is, but you’d be amazed how sweet the best organic fruit tastes.
I remember picking up a bottle of Aldi’s “Fit and Active” French dressing to read the ingredient list, and stopping at the first ingredient because the first ingredient was corn syrup. This may be progress from a corporation’s perspective, to sell a product consisting large of corn syrup as a health food; it is not progress from a health-oriented savvy consumer perspective.
What has happened with all foods where I live, unless you specifically know what you are doing and are looking for exceptions and are willing to pay noticeably more, is that food is manipulated by chemical wizardry much like a plastic replica. It may be obvious to the discerning that “cherry flavored XYZ” does not exactly has the taste of cherries. The reason why this is the case is that if anything is produced on a mass scale, the engineering process for food finds out what the chemicals are that combine to give a cherry its flavor, and then the cheapest way is found to add these chemicals so that there is a cherry-like taste, but one that heralds none of the health benefits of eating cherries.
And this is, if anything, the subtle objection to It’s Getting Better All the Time. It is the objection that moving from something flavored with cherries to something engineered to taste like it was flavored with cherries is a negative amount of progress. The more obvious objection is not to point to plastic-like engineered foods—or plastic-like engineered pop culture—but to say that we are in an unmistakable global financial crisis, and none of the upward trends discussed in the book are enough to take away the quite bleak economic picture in the U.S., which less than twenty years into the third millenium, is quite drastically failing to retain the prosperity and security of the twentieth century heralded in It’s Getting Better All the Time. If the twentieth century brought more change than anything before, it may be the change that precedes the damned backswing. I know that there are people who like to put a positive face on things, especially with the current president Barack Obama, but I have yet to see a journalist say that the present employment picture and number of people out of work is better than in the 50’s and 80’s. As far as journalists go, I have seen the shift from a war in Afghanistan under Bush that was something we should never have gotten into, to one Nobel Peace Prize later, a war in Afghanistan under Obama with vile enemies who cut off the nose and ears of a woman portrayed on the cover of Time Magazine, because she ran away from an abusive husband. Now I have little doubt that the Taliban did all that and worse, but it was doing all that and worse when the war in Afghanistan was Bush’s war. And with the shift from Bush to Obama, significant progress has been made in reduced jobless statistics, with perhaps the exception of your family and those people you know who are trying to find a job. Not that this is all Obama’s responsibility, regardless of the charge some people make that he wants to make America into a third world nation. The U.S. economy would presumably also be in hard times if McCain had won the election, and it was really quite nasty before Obama took office. ButIt’s Getting Better All the Time champions “change,” and President Obama champions “change,” and both seem to invite multiple aspects of the damned backswing.
In my early work The Grinch Who Stole Christmas, I wrote a story, not of a Grinch trying to kill Christmas by stealing presents, but of a Grinch trying to kill Christmas by overwhelming it with more presents than people would imagine. It tells a story of taking away by giving, and the real story of the twentieth century may not be the logician’s proof that gives away more and more until something substantial is proven, but the opposite story of receiving more and more until true poverty comes, both on a spiritual and on a material level.
Embracing modus tollens
There are many layers to things; there is at least one material layer to the U.S.’s economic condition, and at least one spiritual layer, and the best picture is one that recognizes what is going on materially but recognizes that the outer shell has an inner sanctum and in this struggle we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. Politics is important, but even with the best candidates in high political positions the struggle is not about flesh and blood, or about logistics and voting trends. On that score I would quote an Orthodox priest who said, “Whatever happens, I will vote and go to confession.”
And in an age of modus tollens, Satan is nothing more than a hammer in the hand of God. There are layers to events, but not only a material and a physical layer. St. Joseph’s words to his brothers, As for you, you meant evil against me; but God meant it for good, to bring it about that many people should be kept alive, as they are today. has more than one dimension, and one dimension is that what Satan means for evil, God means for good. That is the entire point of God the Spiritual Father and God the Game Changer.
We tend to think of God’s Providence in terms of what he gives, but the same Divine Providence that gives also takes away. St. Job lost all of his possessions and then rid himself of the one outward possession the Devil could still take from him, and said, “Naked I came from my mother’s womb, and naked shall I return; the LORD gave, and the LORD has taken away; blessed be the name of the LORD.” He lost massive wealth, but the story in its end is not of the Devil’s victory, but of God’s victory in St. Job. Perhaps St. Job never on earth knew what we are told from the beginning, that Satan, the Accuser, the Slanderer who stands before God slandering his saints day and night, found no one he considered worthy of temptation and God allowed his property and his health to be taken away, not as punishment for his sins, but as a champion who held fast to worshiping God no matter what happened to him. By the end of the book, the Devil is made ridiculous and is all but pushed out of the picture; his slanders against St. Job were just that, slander. God changes the game in speaking out of the whirlwind, but the St. Job who lost everything is the St. Job who gained a place standing before the throne of God in glory. God wins, and God wins in and through St. Job.
St. Paul writes of “want” or lacking things, Not that I complain of want; for I have learned, in whatever state I am, to be content. I know how to be abased, and I know how to abound; in any and all circumstances I have learned the secret of facing plenty and hunger, abundance and want. I can do all things in him who strengthens me. The Providence of God is not only in what we think we need; it also comes with modus tollens, when God takes away what we think we need. St. Paul elsewhere says, There is great gain in godliness with contentment; for we brought nothing into the world, and we cannot take anything out of the world; but if we have food and clothing, with these we shall be content. That’s a much shorter list of what we consider essentials even for the poor; those who give of their own to care for the poor would generally like to see the poor have housing, for instance, with heating and air conditioning. The general list of things one may have around the poverty line are much longer than “but if we have food and clothing, with these we shall be content.” And some of our luxuries are less edifying than they may seem to us; in some sense the Providence of modus tollens may be God taking away a bottle of wine and saying, “You’ve had enough.”
The prophetic word
In Malaysia, one cartoon portrayed Americans at a lavish banquet with half-eaten plates of food set aside casually, while a television showed an emaciated child holding out a hand to give. And where America stands now is a place which the prophetic voice has much to speak to. (Note that by saying this I am not claiming to be a prophet; merely restating what the prophets would have said based on what is on the public record.) We encourage, foster, and nourish narcissism, with each generation more proud than the last. We use our money for ourselves when we could give much more to the poor. We have a number of abortions that exceeds the number of Jews killed in the Holocaust, not to mention embryonic stem cell research. We have the Internet as a porn delivery service, so that a basic household utility now includes unsolicited pornography. We have accepted sodomy as normal, as an alternate lifestyle that others rarely speak out against. It is considered normal for a Christian to practice (Hindu-derived) yoga, and such things as alchemy (celebrated in a patchwork quilt at the American Medical Association headquarters) and Freemasonry increasingly come out, too. Any one of these things would be grave enough; taken together they represent a fall off a moral cliff. And it is old news at best that we patronize sweatshops and otherwise enjoy comfort at the expense of preventable human misery. And God does not let such things slide forever; he gives opportunities to repent, perhaps, and then judgment so that under an iron hand people may learn what they refused to learn by the law of grace. Perhaps, or perhaps not, “[E]ven if these three men, Noah, Daniel, and Job, were in it, they would deliver but their own lives by their righteousness, says the Lord GOD… Even if Noah, Daniel, and Job were in it, as I live, says the Lord GOD, they would deliver neither son nor daughter; they would deliver but their own lives by their righteousness.” applies to our situation. The righteous may be saved by their faith in any case. “The righteous shall live by faith” is originally a quote from the Old Testament when God’s judgment was about to be unleashed.
In any case, after we have gone apostate under modus ponens, it looks as if we shall experience the refining fire of modus tollens, of God providing as he chastises. Not that Barack Obama is devoted to doing the Lord’s will; Buckley’s quote, “I would rather be governed by the first two thousand people in the Boston telephone directory than by the two thousand people on the factory at Harvard University,” applies in full force, and if you say that it seems an extremely uncharitable reading, and unreal, to say that Barack Obama wishes to make the U.S. a third world nation, I would say that you do not understand Harvard Ph.D.’s. Wishing the U.S. were a third world nation is nothing strange for a graduate of Harvard. When he announced that health plans could no longer discriminate on the basis of pre-existing conditions, my first thought was, “He is banking on the premise that Americans can’t do basic math.” Speaking as someone who has worked briefly in the insurance industry, one of the basic rules if you are going to run a profitable insurance business is that you exclude bad risks: if you are an auto insurer, you want people who have few accidents, if any, on their record, and not daredevils with a stream of one accident after another. And you charge less for people with a squeaky-clean driving record than you do to someone who you’re willing to take on but has a few accidents. It may be a wonderful thing in the short term for people with pre-existing conditions to now be able to get coverage, but unless insurance is going to cost vastly more, it cuts away the ability of non-government insurers to do business—as has already started to happen. Fewer businesses are offering health insurance plans.
But this is almost a side point, a distraction. Let us assume the worst, that the President holds no love for America and is re-elected at the next election. The same rules apply.
Tools of God
C.S. Lewis said that all do the will of God, Satan and Judas as instruments, Peter and John as sons. And it is a fundamental mistake to think that Barack Obama is too bad to be an instrument of the Lord’s action. No one, not Satan, is too bad to do the will of God. I’m not sure how to put this delicately, but it is not at all clear to me that it is to the U.S.’s edifying benefit to be a first world nation. Some have said that across history powerful nations have played the role of gangsters and weaker nations have played the role of prostitutes. In The Last Battle, enemies push true Narnians to a stable said to be devoted to the demon-god Tash, and we read:
“I feel in my bones,” said Poggin, “that we shall all, one by one, pass through that door before morn. I can think of a hundred deaths I would rather have died.”
“It is indeed a grim door,” said Tirian. “It is more like a mouth.”
“Oh, can’t we do anything to stop it?” said Jill in a shaken voice.
“Nay, fair friend,” said Jewel, nosing her gently. “It may be for us the door to Aslan’s country and we shall sup at his table tonight.”
Jewel spoke only a guess, but none the less spoke words of truth. It is through that door they meet Heaven, and God’s providence will not be thwarted by leaders who are questionable in their pursuit of goodness. God’s providence is not just for when we have good presidents; it is equally true if we have not-so-good presidents. It has been twice or thrice that modern medicine saved my life, first-world medicine that I doubt I could afford if the present economy worsens and worsens and worsens. But this will not be responsible for my death: all of us die, save one or two like Elijah; mortality is total in every generation. My death may be sooner if good medicine is denied me, but it is inevitable by some means, and as one Orthodox priest said, “There’s nothing that goes wrong in Orthodoxy that a funeral cannot solve.” We will be judged by how we live with the hands we have been dealt, not whether we could have been dealt a better hand, or rather a hand that was more to our liking.
Everything that happens is either a blessing from God, or a temptation that has been allowed for our strengthening
Still God reigns sovereign. Still he rules. Persecutions may come, but only if God allows it, and only the degree that he allows. Persecutions have been one of many ways God has strengthened the Church, and the normal condition of Orthodoxy is to live under hardship, with such things as fasting and voluntary self-deprivation existing as surrogate hardships. And if God’s Providence comes by taking away one thing we think we need, this is not a failure of his Providence but as much a success of his Providence as when he answers our prayers. We may lose artificial light and find our true night vision. All of this is a Providence that whispers in the way of adding, modus ponens, and shouts in the way of taking away, modus tollens.
It has been said, “Whatever you focus on, that is your God.” We are not to focus our attention on the demons; the ?Ladder? says that the proper use of arrogance is towards the demons. Focus on God, and the demons themselves will be ministers of trials and temptations that make you stronger in the sight of God. And while I intend to vote, in one of the most monumental elections in U.S. history, it is a mistake to believe that God will only provide if the election goes as I would wish it to; God’s providential love is not so fragile, nor near to being so fragile.