Logic – Talk & Think

For this lecture, please read the entries by the Linguistics Society of America for grammar, language variation, machine translation, semantics, and “correct” language.

Sensing, Feeling, Talking & Thinking

Logic is about talking, chaining words together to think and argue things out, but what is thinking?  Are thinking and logic the same thing? Is thought based on talking more than other things? Thought includes sensation, such as seeing a dog, emotion, such as feeling happy while seeing a dog, memory, such as remembering what another dog looks like to compare to the dog you see, and words, such as saying, “This dog looks like that other dog,” out loud to someone else or silently to yourself.  Wittgenstein argued that if a dog stopped walking across a room and changed direction for no reason we could see or hear, like a person doing one thing but then changing to another, we would suspect the dog of thinking, of having an “inner” mental experience that affected its “outward” behavior.

Do we or the dog need words to change our mind from one thing to another?  While the debate rages on, and we don’t know everything about our minds or how we use them, we can easily imagine the dog having a visual memory without using words, and can imagine a dog feeling out two choices in terms of sensations, emotions and memory, without grammatical forms.  We can think obsessively about our great aunt Mildred while avoiding oncoming cars, like a dog can avoid a car, without we or the dog saying the words “car” or “look out!” to ourselves to structure or inform our behavior. Unfortunately, words are so interwoven in such complex ways throughout our lives and minds that a child quickly comes to thoughts that involve words in ways we don’t feel or think dogs have much use for, such as planning for Thursday.

Before we get into words, we should stop and think about how much we can think without words.  Early in life, babies develop object permanence in spite of the brute fact that no objects or people are permanent.  Perceptions of familiar things lead to memories and imagination, such that we can wordlessly imagine someone standing outside the door, seeing it in our minds without saying the words door, someone or outside.  Many animals, like dogs, seem to share this with us, and some say we have proof they dream, which involves imagination and memory.

Sensations can be wrong, as Gotama of India tells us, as where there is smoke there is fire, but sometimes horses on dirt roads gave ancient Indians mistaken impressions.  What looks like smoke may not be smoke. This leads to mistaken imagination, as ancient Indians see no fire, but seeing dust from the road made them mis-take or mis-sense there was smoke and then mis-imagine and mis-think there was fire.  Sensation is also limited in range, with touch and taste in immediate contact, and smell, sound and sight each working further away, such that Plato stated in his Timaeus that this shows the descent of our minds downward into the world of form and delusion.  If a tree falls in a forest and no one is in earshot, it doesn’t make a sound to us, but neither does a dog-whistle next to your head.

Sensations are feelings, but there are particular powerful feelings we call emotions that we distinguish from other feelings.  While mammals like humans and dogs seek warmth rather than cold at night, feelings of warm and cold are not as involved in all our thinking as much as feeling good and bad, which we often imagine in dogs.  Unfortunately Descartes, the first modern European philosopher, thought that animals don’t feel, like clocks or robots, and they only seem to be in pain but are unconscious. Edgar Allan Poe argues in his detective stories that a true genius emotes and feels for others, and that city-dwellers in the 1800s are sometimes great chess-masters but rarely great people.  It is not recorded what Poe thought of Descartes.

Poe says many insightful things about making meaning, evoking emotions in the readers of his short stories, some of the first popular conceptual fiction of new genres such as horror, mystery and science fiction.  Poe wanted to pack as much meaning and genius into each story, and he openly and shamelessly shares his techniques for maximizing poetic impact, such as choosing a dead young female lover as the theme of his most famous poem The Raven, and contrasting the absence of the beautiful living woman with the presence of the horrid bird and death.

In his search to push everyone’s buttons as much as he could, Poe had his detective Dupin, model for the later and more famous Sherlock Holmes, say that good card-players read the other players as much as their own cards, and watch for four basic emotions: good, bad, tense, and calm.  Emotions are not entirely “inner” experiences that are private, but rather shared publicly in the world through our actions, expressions, gestures and other behaviors, such as keeping our distance from someone threatening. In the book Are We Born Racist, there are several who present evidence that racism is primarily transmitted and learned through body language, not slurs or Klan rallies, with children becoming afraid of people who frighten their parents, without anyone needing to speak a word about it to each other or themselves.

Reading Meaning

If Poe is right to say we read others, we have been reading much longer than our species has been writing.  We watch others and also listen to others’ words to read them for emotions, to read the meaning of their actions, gestures and words, understanding what they are or are not trying to tell us about what makes them feel good or bad, what they seek and avoid, and what makes them feel tense or calm, what will change or stay the same.  In some ways, tense is bad and calm is good, but in other ways tense can be good, like excitement and adventure, and calm can be bad, like depression or inevitability. The psychological types of Pooh, Tiger, Piglet, and Eeyore are these four corners: Pooh feels good and calm, Tiger feels good and tense, Piglet feels bad and tense, and Eeyore feels bad, calm and quite depressed.  We watch others to see how their emotions and motivations are situated with other things, like objects, others, other emotions, memories, and of course, for our logical considerations, words and forms of speech, much as we read stories about animals to understand their fictional feelings.

Are emotions inner mental states?  Wittgenstein argues that meaning is not private, anymore than the colors you see with your eyes are private, but colors are subjective, in that humans who are not color-blind look at them together in the world a certain way, as do colorblind people of all sorts, as do dogs and cats, who can see some color.  The mantis shrimp is said to see and be much more than all of this. When we feel hot, we show outward signs of feeling hot, like sweating, turning red and breathing faster, even if it is “all in our head,” as our friend could say, such that the individual does feel hot, even if it is personal and not shared.  Similarly, meaning is subjective, but so is everything as shared public culture, which we view as perspectives.

The child psychologist Piaget did a famous experiment with a doll that showed children learn to think others have perspectives in the world as they learn language and social skills that require empathy.  Alison Gopnik says that children are fascinated by Oscar the Grouch from Sesame Street because he likes trash and other icky things, which is weird and funny to two and three year old children If we are reading others for emotions as animals, and if we did as we developed language and logic, then we read people for the same ends as we listen to them talk or read what they write: to understand what they mean, which consists largely of how they feel about what in their situation.  Lewis Carroll puts meaning what we say and saying what we mean in the center of Wonderland at the Mad Tea Party, and the Mad Hatter tells us that the two are not the same one bit.  

Wittgenstein presents us with an interesting thought experiment involving a plumber that shows us we read and interpret ourselves, more or less aware of our own emotions and thoughts.  If we watch a plumber try to fit pipes together with more or less success, we could ask the plumber what she was thinking, and she could report to us that she thought something like, “Aha!  This doesn’t fit in that! Maybe something else? Yes, this thing!” but if we ask her if she actually spoke these words to herself, she need not, nor do we need to distrust her as getting herself wrong in translating her feelings and thoughts into words.  What Vygotsky suggests is that we can use feelings and images like words to think much quicker than we can talk to ourselves, so the plumber could get upset while looking at one pipe, and then an image of what might fit could occur to her along with a feeling of hope, without so many of these words, but possibly involving any of them.

How good are we at verbalizing what we want or feel?  Are we as bad at it as we are at understanding the wants and feelings of others?  Much as Wittgenstein says we don’t watch our own arms, legs or eyes to predict our own actions or thoughts, we use our emotions to do everything that interests us, but we do not need to pay them much direct attention, unless a therapist suggests to us that we seriously need to start to monitor our anger and blood pressure.  The Buddha suggests that slowing down and paying careful attention to emotions, ours and the emotions of others, is close to enlightenment and genius itself, like Poe. We pay some attention to the feelings of others, like children do to Oscar, but not as much as we could according to Confucius, Buddha or Poe. It is likely we can each learn more by using our feelings to think more than we do.

There is some fool on the internet, and fools who follow, who are fond of saying facts don’t care about feelings.  I have never seen or felt a fact care or not, in particular, about anything. I have seen my cats care about many things, and people, but words don’t care on their own about anything, not even if they are arranged in ways many of us would consider facts.  If you are not aware of the feelings and concerns of others, including your opponent and the audience, many of whom are not on your side or your opponent’s side, you should care more about both facts and feelings. Situations of feelings, words, debates and other physical objects are everything we deal with, wisely or foolishly.

Say What You Mean & Mean What You Say

Some argue human thoughts are primarily based in words and logic, while others have argued they are based in emotion and intent.  The Scottish philosopher Hume argued that reason is, and ought to me, the slave of the passions, much like the Babylonian servant of the Dialogue of Pessimism who is happy to rationalize anything his master’s heart wants.  Kant, upset at Hume who “awoke (him) from (his) dogmatic slumbers,” argued that reason should be pure, and desire should accept what logic comes to categorically on its own, much like accepting the unwanted answer to a simple algebraic math problem.  We do not need to take sides, as thought can lead from emotion to verbalization and back again in any number of intertwining ways in life and thought.

Wittgenstein’s late work suggests that any interconnection we make with our minds between sensed things, feelings about things, memories of things, and words about things is thinking, so if we are thinking about our aunt Mildred with her image in mind while dodging cars with our dog, the dog may not be multitasking, but we are thinking about Mildred in memories, feelings and words while sensing cars and feeling like moving around them, all at the same time, such that we can screw one up with the other.  Heidegger said we are closer to our friend we see across the street than we are to the pavement right beneath our feet, as we are mentally wherever we are attending, so when we are deep in thought we can easily be off in the clouds, on autopilot, behaving like the walking dead according to Heraclitus, and so like the first Greek scientist Thales, we might fall into a well while watching the stars.

When the Mad Hatter tells us that saying what we mean and meaning what we say are not the same thing at all, he means, along with many other things interconnected, that we say what we mean when we fully say what we mean, which we don’t with an accidental slip of the tongue or an intentional rephrasing that leaves something suggested but unsaid, and we can mean what we say when we honestly say what we mean, which we don’t when we unintentionally or intentionally lie, saying something we don’t actually believe.  These sorts of social situations show us more about how words, emotions and thought work and don’t work together, sharing and not sharing the perspectives of others for our purposes or their purposes. Resent research into lying and deception (reported in, among other places, the documentary (Dis)honesty) suggest that when we lie for what we believe is the greater truth and good, we are unaware we lie or are aware, but don’t feel what we do is untrue.  How much are we true to ourselves or others?

Saying A, In A Way

Once we get to talking, in logic it is useful to start by saying A, as in, “A: You’re standing on my foot,” such that one letter stands for a complete asserted statement, such that A does not stand for standing, or foot, but the whole sentence.  We can also deny A, saying not-A, “No, I’m not (standing on your foot),” which in formal logic is often symbolized and typed as ~A, holding shift and pushing the key to the left of the number 1 at the top of a keyboard, followed by A.  We can, after A, use B, C and other letters to stand for each statement we are asserting or denying.  Often formal logic proceeds from p, lowercase, which stands for the first proposition, with q, r and other letters following, even though p stands for proposition, and q and r are used because they alphabetically follow from p, which is very arbitrary, as the second proposition made is not a question or anything else that starts with q.  We’re going to use A, B and C to understand Aristotle’s syllogisms, Gotama’s forms of proof, Wittgenstein’s truth tables and all the other forms of logic we will study.

In the beginning of Wittgenstein’s Philosophical Investigations, he has us imagine two workers building together who belong to a simple culture where one says “Slab!” and the other hauls a slab out from the pile for use.  Does the word slab mean the object, or the action involving the object?  It could mean either, with no situations for telling the difference, but out of this simple cultural practice the two meanings could diverge, with the word being used for the entire action, but then used to refer to the object, or with the word referring to the object, which is involved in action, and then the word is used for the action, whether or not it involves the object.

Logic, formal and informal, studies how we chain statements together with connectives and conjunctions.  When I was a child, I watched reruns of Schoolhouse Rock that sang about Conjunction Junction, a train-yard where the connectives AND, BUT and OR can get you really far!  I can still sing the song, if anyone needs it. Formal logic uses AND, and OR, but not BUT, likely because formal logic can’t handle conflicting information that suggests opposite perspectives.  Rather, formal logic evaluates everything in terms of fully true (T) and fully false (F), and disregards how relatively true or how false anything is, so there can’t be situations where something is somewhat true, given the evidence and argumentation, but also somewhat false, and critically consider the degree of truth on any sort of scale, which is quite unlike debate and argument in life.

DeMorgan, who we will study, argued that the moves of formal logic can be boiled down to two: NOT and OR, but this is slightly incorrect.  The first move of logic is not a conjunction, but assertion of something like A. If I say A, and then say B, and then say C, I have, without explicitly vocalized conjunctions, asserted A, B and C, which gives us an inaudible AND of sorts.  Without asserting A, or several things that put A together with them as an AND, neither DeMorgan’s NOT or OR could get anything done. Then, after we have introduced NOT (~), we can say things such as A, not-B (~B) AND C, asserting something that contains both assertions and denials, like saying, “I will be here Tuesday, I won’t be painted blue, and I like kittens.”

Formal logic deals exclusively in universals, such that A is B means ALL A is B, without any As being Bs, no matter how it Bs.  In life, assertions can be universal, but they are also understood in context as localized and partial, such that when I tell you A is B, you don’t know from what I have said alone whether or not I mean it universally, such that every last A is a B, or if I mean it in a restricted sense, such that next Tuesday, this one time only, some As will be B for a bit.  If I tell you, “Steve is perfect,” I could mean Steve is a perfectly flawless human being, or I could mean Steve is the perfect choice for a hit-man, which we thankfully need only once, but other than that he is the worst person I know.

Humor relies on this all the time, as it is the source of continuous misunderstandings, in daily life and in popular political forums.  One side says, “We need X!”, the other says, “We don’t JUST need X completely!”, the first side says, “That’s not what I meant,” and the other says, “But that’s what you said!” which isn’t entirely incorrect, but isn’t allowing the other side to qualify what they say.  Much of the time, this misunderstanding isn’t intentional, but involves things that we may need somewhat but are also feared in part. The Belgian surrealist painter Magritte famously produced a canvas with a pipe and the words, “This is not a pipe,” but in French. It the image a pipe or not?  Yes, insofar as it is the image of a pipe, not a donkey, but also no, insofar as it is merely an image of a pipe, and not the sort of pipe we could smoke.

When I was a small child I was told by my progressive parents that women can be astronauts.  This made me excited, as I loved astronauts and thought I might be one, so I happily asked several adult women if they were indeed astronauts, much to the delight of my parents, who then had to tell me that sadly most women aren’t astronauts, as most people aren’t.  It is true to say that all women can be astronauts, as being a woman doesn’t disqualify anyone from being an astronaut, but it is also, contradictory-wise, true to say that most women can’t be astronauts, not because they are women, but because astronauts are equally rare among men and women, so the meaning of the two phrases are quite distinct, thought they do function in contradictory ways such that the first doesn’t restrict most women from being astronauts at all, but the second certainly does.  Is this a contradiction or not? Is a stupid argument an actual argument, even if we could reason through it? Is the misunderstanding illogical to have, breaking a rule?

AND and/or OR

Two of the most important connective conjunctions in talk and logic are AND and OR, which we use all the time and seem deceptively simple.  In formal logic, which Wittgenstein invented truth tables to do, AND and OR can only function in one, rigidly mathematical way, much as addition and subtraction do in arithmetic, but in life, as Wittgenstein says, our words are more like elastic parts of a machine that can stretch and bend to fit particular situations and contexts, and without our notice.  One of the most interesting things I learned in logic as an undergraduate which still fascinates me is the difference between inclusive and exclusive OR, the two ways we use OR in life without noticing it when it comfortably fits.

Let’s say I take you to a buffet for lunch, and I say, “You can have eggs, or salad, or pizza,” you go get some eggs, salad and pizza, and I say, “Whoa!  I said eggs OR salad, OR pizza, not eggs, salad AND pizza, you ingrate!” You would justly be confused, as in our culture, a buffet is somewhere you can have more than one sort of food, so you would understand my OR inclusively, such that A OR B OR C could mean A, or C, or B and C, which all make the statement true.  Now I take you to a car dealership, and I say, “You can have a Toyota, or a Ford, or a Subaru,” and you pick a Toyota and a Subaru, I would rightly say, “Whoa! I said OR, not AND!” as before, and now you are in the wrong. It is also possible to imagine examples where OR is used one way, but then the speaker permits interpretation the other way, such as when we stock up for a safari, I tell you, “You can have a Toyota, or a Ford, or a Subaru,” and you pick two, and I consider that, regardless of what I was thinking, we do have the budget for it.  Note that at the buffet, I could have said either, “You can have A, or B, or C,” or said, “You can have A, and B, and C,” but not at the car dealership, unless we were on safari, where I would have said OR, not AND.

Wittgenstein suggests, and I think he is right, that the Lord Jehovah, an objective, omniscient being that knows everything, couldn’t tell you which way we mean things if we leave things open for ourselves these ways.  Let’s say I team up with a company in China, and I say, “We need to wear purple pants at noon!” and the company representatives ask, “Do we all wear purple pants when it is noon in California, when it is noon in Shanghai, or do you wear purple pants when it is noon in California, and we wear purple pants when it is noon in Shanghai?” and I reply, “You know, I hadn’t thought that far!”  Which did I mean, and did I need to mean it one way or the other to say it, mean it, and for you to understand it as I meant it?  Many who seek formal closure in logic ignore these issues, as we all do when speaking in daily life. Notice the situation resembles the difference between inclusive and exclusive OR, with the office in Shanghai asking me to whittle down what I mean, but without thinking I left it inclusively open.

In formal logic we can’t have one symbol (for this class and in many textbooks v, a lowercase V) stand for both sorts of OR, but there is also the interest in limiting the number of symbols for simplicity’s sake, so instead of creating two symbols or more words such as NYOR, in symbolic formal logic OR is always inclusive, and you then have to state that you can’t have A and B, or B and C, or A and C, which is clunky, and not how human thought actually works if we don’t speak out all these options to ourselves, possibly because we can feel exclusivity and inclusivity out partly through feelings, like feeling familiar and included or unfamiliar and excluded.

We can similarly use AND (in this class and texts ^, pressing shift and 6 on a keyboard) in inclusive and exclusive ways in everyday life that go beyond the bounds of formal logic.  If I send you to the store to get ten sorts of vegetables and fruits for a complicated salad, saying, “Get A, and B, and C,” and you get nine of the ten, I could say you overall succeeded, and you were relatively true to my word, such that saying, “You got A, and B, and C…” is 9/10ths and thus overall true, particularly if our culture is not that picky about complicated, eclectic salads, but if I tell you to get ten parts for a computer, and you get 9, we may or may not be able to do anything.  AND is more exclusive, must entirely be true to be completely true, in the second case, but not in the first, which is more inclusive about which items can or need not be added together with AND. In formal logic, AND, unlike OR, is used exclusively, such that if you get 99 out of 100 things right, but don’t have the last one, the entire thing fails, and the whole sentence is categorically false. This is somewhat unlike life, where one error in fact does not invalidate an entire argument, nor does it prove the speaker an entire idiot.

Formal logic may not have much use for BUT, and less use for NYOR, but some claim that, in English, there is a simple set of basic conjunctions: AND, OR, NOR, FOR, SO, BUT, and YET.  I do not know if these make a perfect set, but natural semantic metalanguage theory in linguistics, one among three dominant theories, argues that there are 65 basic words found in most if not all languages, but if Everett is right about the Piranha tribe of the Amazon, the words one and two can be crossed off the list.  Some of the 65 (63?) of these, besides you, I, thing, body, kind, part, this, same, other, good, bad, big, small, think, know, want, feel, see, hear, touch, say, true, do, move, be, life die, time, before, after, long, short, now, where, here, far, near, inside, outside, very, more, like, and way, are the logical connectives of not, if, because, maybe and can, with OR and AND interwoven in the last few in ways that don’t have to universally function, but likely function in overlapping ways that stretch much as AND and OR can and do to fit a variety of situations that changes.

Notice that AND and OR are not words on the 65 list explicitly.  As mentioned with DeMorgan, we don’t actually need to say AND, if we just keep saying things like A, B, C…  Maybe and can are very much like OR, as saying, “Maybe A, maybe B,” or “A can, B can,” is much like saying, “A, or B,” considering possible options and ways. In the examples of the buffet and safari, inclusive OR and inclusive AND pass through and into each other, such that either could be said interchangeably.  In any case where we can have any number of A, or B, or C, we can also be said to, loosely and inclusively, likely have A, and B, and C. At the same time, exclusive OR and exclusive AND are used in distinct opposition to each other.  There can be no cases in which we are saying you can only have one, but not others, but you have to have them all entirely.  Isn’t it odd that such basic connectives, words that sound the same indistinguishably either way, are used in ways that are inclusively interchangeable, but also exclusively not interchangeable?

Assignment: Please email answers to the following questions by class next week.

A) Describe four examples, a thought that doesn’t use sensations (sights, sounds, etc.), that doesn’t use emotions, that doesn’t involve memories, and that doesn’t use words.  Explain your examples.

B) Describe an example of inclusive OR, exclusive OR, inclusive AND and exclusive AND, and explain your examples.

C) Describe an example where we could use either inclusive OR or inclusive AND, and explain your examples.

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