What is logic? How logical are we, or the ways we talk or think? Do you know any logical, rational people personally? I don’t know any myself, and I have German scientists in my family, which is a difficult hereditary condition. None of them are infamous in history, just infamous in my family. I originally wanted to be a psychologist like my grandfather, who was a particularly interesting and difficult person, but I got into the history of endless arguments about everything known as philosophy, talking about talking and thinking about thinking, the department which studies the history of thought and often offers Logic as a subject of study.
How can religion, science, politics or any large group of people be logical the way powerful cultures and institutions continuously say they are if most of us individuals struggle to talk to each other, our family, friends and strangers? Throughout history, famous sages have said that many talk and think but few do either well. If so, how would they know, and why would we keep listening to them? Human thought is possibly the most meaningful thing we can think about if meaning is something we think, but then again, that’s just what human thinking would tell us, wouldn’t it? Is there any certain knowledge or worthwhile wisdom? Sometimes it doesn’t seem so. Other times it does. Most like to argue, with themselves and others, and so we talk things out and don’t, agreeing and disagreeing with each other.
Logic has a long, complicated history we will talk through at length, but basically, logic is talking things out, saying what can be said, as they say. The Russian psychologist Vygotsky said that small children learn to think as they learn to talk, narrating their world and mind out loud, such that when they pick up a toy and say, “The horse goes in the barn,” they aren’t talking to you, or the horse, or the barn, or themselves, but talking out the situation as it is, learning to articulate their world with words, and then, as we get older, we learn to talk silently to ourselves when we think on our own, but we continue to talk and think things out loud with others. In many ways words structure our minds and world, but does this make either the human mind or world logical, and how?
Humans talk to each other, and themselves, and do something called think and reason with talking and words, interweaving them with perceptions, emotions, and imagination. Many have claimed this separates us entirely from other animals, as Aristotle thought, who called us the rational animal and claimed, along with his teacher Plato, that other animals lack higher souls and centers of consciousness we use to think. Many have also claimed, like Plato and Aristotle, that not all human cultures are logical and rational, their words and thoughts centered on objects, feelings, emotions, memories, ancestors, images, anything other than on true talking and thinking, logic and reason.
While some, not Plato or Aristotle but others who read them, claim the Greeks were the first to speak logically and think rationally, Anthropologists who study and live with tribal people, like Malinowski did in the early 1900s, tell us that children and adults of all tribes and cultures learn to chain statements together with connectives such as and and or to ask questions and come to conclusions about things, such as whether or not there are still jaguars on the other side of the river if there are birds in the treetops. If the human brain is well-over 100,000 years old, as well as the parts that talk, it is strange that human thought waited for the ancient Greeks to use the word logos, long after the city-state and literacy in Sumer and Egypt.
Are all humans logical? Who or what gets to be logical? Animals? Children? Women? Ethnic minorities? Scientific institutions? Corporate persons? Mathematical equations? I follow Wittgenstein in saying and thinking that we can only say how logical others are insofar as they live like we do, which includes talk and think like we do. We can judge anyone we like whether or not they live like we do, from our culture or other cultures, and we do judge, but we are logical only in the ways we speak and do things, and can only tell if animals and others use words to think like we do in our words and terms.
Animals do communicate with sounds, signaling others, and they are all related to us by degree, but we use words in complex ways such that Wittgenstein thought a dog can expect someone to come soon, but not Thursday. If you and I judge that a dog has no use for Thursdays, and so has no use for a bark or whimper that means Thursday in any way like we use our word, we can and do judge that the dog does not live or understand Thursdays, just as no humans understood what the word Thursday meant before it was used as part of a culture that still strangely praises Thor, for whom Thursday is named.
We do live, us political animals, in different cultures, but there are no cultures according to Anthropology that do not use speaking and thinking to solve problems, which suggests that humanity shares a common form of speaking and thinking, in spite of all the endless agreements and disagreements, that some call Logic. While many teach logic as a formal modern system, there is still a wide ranging debate, a talking back and forth we are all getting involved in as I speak, between those who thing logic is a coherent, formal system and those who think it is a tangle of informal practices, what Wittgenstein called forms of life.
How much does human thought share an underlying form, and should it? Young children often do not believe in what they can’t see themselves or in images, or what they can’t touch or hear. The Piraha tribe of the Amazon don’t have a creation myth, don’t have words for numbers or math, and don’t believe in anything that someone told someone, who told someone. If it is further from them than someone they trust hearing it from someone that person trusts, it is untrustable, and not treated as true, which is far from unreasonable. If someone is telling you about a jaguar they saw today, that is worth talking about.
Unlike the Piraha, many human cultures that talk and trade with other tribes settle from nomadic hunting and village fishing into trade posts called walled cities, and in these cities they develop systems of writing, talk that isn’t just talk, but written in stone, along with myths, math, recipes and histories. Writing brings texts that survive much longer than we each do. Just as using words to refer to groups of two, three and four things helps do many, many things, words written down help us read and reread things others say, such that cultures, histories, sagas, legends, religions, sciences and arts settle into traditions that remain oral, still spoken through the air but also fixed in parchment, papyrus and clay tablets.
The Piraha tribe use two or three things at a time by using the words more and less, but not one, two or three, so they do not know that two things gathered together with three things leaves five things remaining if nothing else happens to them. What city-dwelling psychologists of the 1900s studied illiterate peasants in rural Georgia, not in the South of America, nor South America, but Southern Russia, and asked them how many are five and seven together, they say that it depends, because they can gather that many potatoes together in a wheelbarrow, but not cats, which would not put five and seven cats together. After taking many math classes and being rewarded for doing as we are told, we learn to treat quantities as words, numbers, and as fixed, timeless ideals, and deal with problems later that arise “in the real world.”
The psychologists also found that Georgians had trouble with logical syllogisms, Aristotelian forms of ideal reasoning that work somewhat like algebraic math and form the basis of most modern formal and informal logic classes. When they’re asked, All people who live in Monrovia are married, and Kemu is not married, so does she live in Monrovia? many say yes, as not everyone in Monrovia is married, so Kemu could live there, contradicting what they are told by the scientists as unreasonable. They don’t understand that math problems don’t work like the real world, where the information you are told by others and authorities can change, or be wrong, or worst, lies!
When asked, In the far north, all bears are white, and Novaya Zemlya is in the far north, so what color are the bears there? the interviewer was scolded by one Georgian, who replied, “You should ask the people who have been there and seen them. We always speak of only what we see.” When asked, All people who own houses pax house taxes, and Boima does not pay a house tax, so does he own a house? some Georgians make up stories to explain how an exception to the rule can arise. This is hardly a thoughtless, irrational action on the part of the Georgian peasants, and quite hilarious in hindsight, as they don’t have any reason to take standardized tests to stand out for any reason regardless of what sense the words of the test make or what relevance they have to their lives, unlike us moderns, as the French sociologist LaTour would say about all of us living in cities who take math and logic classes.
Ancient Indian, Greek and Chinese philosophers who argued about how language and arguments work and what they tell us are known as logicians. For example, there were logicians of ancient Athens other than Aristotle, but his syllogisms were the most famous forms of argument for many Muslims and Christians, the two largest cultures the world has seen, with Buddhism close by. Lewis Carroll, author of Alice in Wonderland, gave us many examples of what can be said with certainty given syllogisms, such as: No lizards have hair, and no bald creature needs a hairbrush, so no lizard needs a hairbrush. But Carroll also cautioned us against following the form and neglecting content and context, such as the passage of time, giving the false example: The meat I eat is the meat I buy, and the meat I buy is raw, so the meat I eat is raw.
Consider a logic puzzle mentioned by Roy Sorensen: In 1889, Senator John William Harreld married his widow’s sister. Senator Harreld married the sister of the woman who was his wife when he died. How did he do it without dying beforehand? Is it all a terrible legal mistake? If Harreld married one sister, she died, and then he married the other sister, and he died, he married his widow’s sister before her sister was a widow, which he later made her when he died. The trick is that he did marry his widow’s sister, but not all at once, like the meat in the market. In hindsight, we can say and state truly what no one would or could at either wedding, that Harreld did marry his widow’s sister. If logic is the study of what can be said with certainty, this is a confusing way of saying something logical, something said, stated, argued and believed, but only afterward, as it wouldn’t have been logical to say at the time he married the woman who would be his widow’s sister. If she had known, she might not have married him.
For Aristotle, as for Heraclitus and many other ancient thinkers, the world is logical because the world is intentionally designed, directed, and ordered around with language by the gods, much as the Book of Genesis says, “Let there be light,” and light and darkness separate like the units of an army commanded by a king. If the world is created by language, before or underlying time, then human language can be logical, correct and in line with the structure of the world. But if the world is not structured with human-like words, whether or not there are gods in the ancient or modern world, reality does not have to conform to human logic, talk or thought. We have enough trouble sticking to our own words, let alone discovering a world in line with them, and humanity seems to disagree with itself on everything as much as agree.
Around 2500 BCE in ancient Egypt, two thousand years before there were lectures on logic in Athens, Ptahhotep, who some call the first genuine philosopher in human history, wrote many wise things about saying things and not saying things to others, but listening instead. Ptahhotep says speaking is harder than all other work, but listening is better than everything else and unites us. Hearing well is speaking well. Those who can’t hear others are fools who can’t do anything, see the bad as good, do everything everyone hates, and are blamed for everything.
Ptahhotep tells us to talk to everyone, those who speak foolishly and wisely, as there is no limit to speaking wisely, and wise words can be found in the lowliest of people, even the maids at the grindstone. Silence is better than chatter. Say what you see, not what you hear. If it isn’t important, don’t say anything. Speak when you know you have a solution. Don’t let your stomach do the talking. Listen to others who need to talk and they won’t try to defeat you with words. When you speak don’t lean to one side, or your judging words will turn into the words of others that judge you. You don’t have to talk to enemies, as the stronger will say things to others that get them in trouble, and the weaker will turn on themselves with words.
Ptahhotep and Aristotle, like Gotama of India, Mozi of China, Avicenna of Persia, Aquinas of Italy, Mill, Boole, Carroll, Venn, Russell and many other thinkers we study argue that we live in a rational world insofar as we speak correctly and only speak when we speak the truth. Given how much changes with perspective and time, this does make speaking truly and logically very hard. I have a philosophy meme I enjoy that shows the French postmodern philosopher Lyotard at a lectern, stating, “Dissensus, not consensus, is the real point of communication!” which means disagreement, not agreement is what really happens when we talk. The class out of view respond in lock-step with, “We totally agree!” and Lyotard says, “Damn it!” Are agreeing or disagreeing more, less or equally the point of talking about anything with anyone?
My logic text, for UC Berkeley, was born just around the time that I was, (The Logic Book, 1980, my copy is the edition from 1998), and it begins with a few paragraphs on what formal logic is and why it is good and useful that I don’t find good or useful at all that illustrate very well why this will be a history of logic which considers time, change, and learning from the mistakes of everyone about the mistakes we are going to make in our lives and hopefully, as a species, far into the future if we continue to have the same brains and minds:
Historically, two overlapping concerns have driven research in deductive logic: the desire to formulate canons or principles of good reasoning (in everyday life and in science) and the desire to formalize and systematize existing and emerging work in math and science. Common to these concerns is the view that what distinguishes good reasoning from bad reasoning, what makes deductive reasoning “logical” as opposed to “illogical”, is truth-preservation. The hallmark of good deductive reasoning is that if we start from truths and use good reasoning, we will always arrive at truths and never at falsehoods. Because we are all interested, as students and scholars, in everyday life and in our careers, in gaining truths and avoiding falsehoods, we all have reason to be interested in good reasoning in the above sense.
Before we continue, or consider if we can still have careers, what reason do we all have, in particular, to be interested in good reasoning, and in what “above” sense has the paragraph told us anything about reasoning at all? What principles of good reasoning do you or anyone you know have, how often do you follow them, and are they particularly useful in math and science? How important is it in science, life or anything else to always arrive at truths and never at falsehoods? What is avoiding falsehood, ducking it on the street? Ignoring it in the press? It could be never telling a lie, like George Washington did before and after he perhaps never cut down a cherry tree. Should I have avoided the example? Should we avoid lies, or engage with them? Do we know when we lie, and does trying to avoid lying make us self-aware of lying? Heraclitus in Greece, Confucius of China and Nietzsche of Germany would all tell us to try, fail and learn from failure, not avoid it. Is argument about perfection and preservation?
Wittgenstein says we use too few examples all too often, and the only two historical examples the text gives us are two Greeks, Euclid and Aristotle, the axiomatic geometer and syllogistic logician. We are told Euclid may have been the first to develop a reasonably complete axiomatic system, with no metrics or further explanation of what distinguishes an axiomatic system from any sort of system, nor what makes a system reasonably complete, as opposed to completely complete. We are told Aristotle, at the same time nearby, was not the first person to try to reason well or point out errors in arguments, but he was the first in the Western world, not Western Europe, nor the Western Roman Empire, but highly identified with both, “to offer at least the outlines of a comprehensive system for codifying and evaluating a very wide range of arguments and reasoning.” I do not know how much this qualifies as a complete axiomatic system, reasonable or otherwise.
Sarah and Hank are the only finalists for a position with Bowles, Blithers and Blimy, an accounting firm. Whoever is hired will have a baccalaureate degree in accounting. Hank will get his baccalaureate in accounting only if he passes all the courses he is taking this semester. Sarah will get her baccalaureate only if she passes all her courses and gets an A in the each of them. Hank will fail logic and Sarah will get a B in Principles of Accounting 306. So none of the finalists will be hired by Bowles, Blithers and Blimy.
This problem sets up the answer to prove logic can demonstrate things, but note the strange future knowledge that lets us come to an obvious conclusion. We are told that A or B will be C if A does D and B does E, but then we are told that A won’t do D, and B won’t do E immediately afterwards, so anyone with half a mind on what they are saying would not be wondering about the candidacy of either A or B, given we know they will fail, and this is the conclusion. Ask yourself this: What axioms of good reasoning, however defined here or nowhere, did you use, in words, feelings, visuals, or otherwise, to draw the obvious conclusion? Is this particular to math, science, or the work of Aristotle, or would a reasonable person follow this without formal logical training, such that it can hardly qualify as particularly good reasoning in skill?
The second example is even worse, given to show why Aristotle’s syllogisms were not enough for later logicians who use connectives such as or, and, if then and not, without mentioning Chrysippus, Boole, Wittgenstein or anyone else historically involved.
Karen is either in Paris or Nairobi. She is not in Nairobi. So Karen is in Paris.
Simple arguments such as the above are not readily represented within syllogistic logic. Yet the above argument is clearly an example of good reasoning. Whenever the first two sentences are true, the last sentence is also true.
Unfortunately, this is not an example of good reasoning, but rather common sense, which is not necessarily up to anything good here, nor is it generally. Is it true that if the first and second sentences are true, then the third follows? There is no situation where an individual would say the first and second sentences together. If someone said the first, and then someone else reported the second, the third could be true, but not necessarily.
First, in the time between the first and second reports, Karen could go elsewhere, as Gotama of India might point out or a Georgian peasant might insist. Second, anyone of us moderns might think Paris and Nairobi are different places with different people, but any formal logician should know that or is used inclusively unless specified otherwise, so Paris could be a neighborhood of Nairobi. In this case, and given that time can pass, the second report would disconfirm the first, and good reasoning would assume, syllogistically along with Aristotle, that if Karen is not in Nairobi, she cannot possibly be in Paris.
Formal Logic may be about rules and truth-preservation, axioms proper to good speaking or thinking that must be upheld, but a History of Logic like we will study does not assume there are unchanging rules or strategies of speaking and thinking that always lead to truth, anymore than history has to assume that laws, in general, should be followed without question, without speaking or thinking about them. Rather, speaking and thinking are practices, physical activities that are also social and mental, or psycho-social. I let the other view have the first word, and Wittgenstein will have the last in this class. On the way, we will study human reason, arguments, fallacies, and the long history of Indian, Greek, Chinese, Islamic, medieval, early modern, algebraic, and formal logic.
First Assignment: Write at least one typed, double-spaced page about your thoughts on logic. Are there things everyone can agree to or should? Can you give examples? What principles of good reasoning are there, and are these basic to the mind or learned through culture?