Logic is the study of reasoning in general, and in the first place, it is the concern with the difference between better reasoning and worse reasoning.
Historically, this originated in people developing suspicions about the the reliability of certain patterns of reasoning, and of course this is most likely to have been in informal contexts of everyday life. Later, more structured or formalized contexts would have come along. But whether we are working in formal or informal contexts, there are certain common concepts we’ll always make use of.
First off, we have the word “argument.” We use this in a restricted sense here. It has nothing to do with a dispute or a disagreement or a fight. “Argument” is almost a synonym for “a piece of reasoning.” But let’s take that apart a little, and see what we can say about a piece of reasoning.
This is as good a time as any to watch the Monty Python “Argument Clinic” skit. (Unless you just can’t stop, or really love Monty Python, this ends at minute 4 for our purposes.)
When you reason, you move from one thing that you take to be true to something else that you take to be true as a result. Reasoning is a kind of thinking, but not all thinking is reasoning.
You are not engaging in reasoning when you simply say “The sky’s blue today.” But when you say “The sky’s blue today so it won’t rain,” you are engaged in (reporting a piece of) reasoning. You’ve reasoned that one thing is true as a result of something else.
When you represent that piece of reasoning, we say you’ve made an argument. The argument isn’t really the same thing as the reasoning, since after all, the reasoning takes place in your private experience, and quite possibly without your explicit awareness. The argument is the expressing of the reasoning in a series of statements. Two people can’t engage in the same act of reasoning, since for each of us those acts are our own only; but we can consider the same argument, the representation of the reasoning.
Many people use the words “infer” and “imply” interchangeably, as though they meant the same thing. But here we can address the difference: an inference is an act of thought, something you or I engage in (or that happens “in us”), moving from one claim to another claim (e.g., “It’s raining so I better get my umbrella”). An implication, on the other hand, is a relationship between two claims (not between two acts of thought). “Implication” means that if one claim is true, another must be (or is expected to be) true as well.
So we’ll say that an argument is a series of statements, one of which is claimed to be true as a consequence of the other(s).
This calls for more clarification. What is meant here by “statement”?
A statement is a specific kind of sentence. All sentences in a language have in common the fact that they are meaningful strings of words. But not all sentences do the same kind of thing. Some sentences assert things, some ask things, some command, and some exclaim. The ones that assert things are the ones we’re calling “statements.” Of course, we can also call them “assertions,” “declarations,” “affirmations,” or “propositions.”
This is not really news! But it is of interest, because to state or assert or affirm or declare or propose is to claim that something is true. And whenever one claims that something is true, one is either right or wrong (even if one doesn’t know which it is at the moment!). That is, statements (assertions, propositions, affirmations, declarations) are sentences that are either True or False.
The other kinds of sentences are not like this. Interrogative sentences, also known as questions, cannot be called “true” or “false.” If I say “What day is it?,” no one who knows English will think that “That’s so true” or “I’m sorry, but that’s not true” is an appropriate response.
Likewise with imperative sentences.
John and Anne were driving to the movies when she spotted a turtle in the road and said “Be careful!” John looked at her hard and said “That’s not true.” Anne replied “You’re weird.”
Same goes for exclamations. Exclamations exclaim, but they don’t exclaim that something is true or false. In response to “Wow!” or “Oh Goodness Gracious,” there are plenty of things we can say, but “That’s such a good point” isn’t one of them, because those exclamations are not asserting that anything is the case; they are expressing an emotional reaction to something. Often exclamations bring statements along with them, but then two distinct things are happening in the utterance:
“Wow! That movie was really a piece of s**t.”
“Wow! It’s almost dinnertime.”
“Wow! That’s too bad.”
As these three uses of “Wow!” show, the exclamation itself doesn’t assert anything; in fact, it’s not even always on the same end of the emotional spectrum. It can express disappointment, surprise, empathy; I’m sure you can find lots of other emotions it can express as well.
The moral of this reflection on kinds of sentences is to cultivate a sensitivity to the class we call “statements,” the kind of sentences that are either true or false. Arguments are made up of statements. Arguments attempt to convince us that something follows from something else, that something is true as a consequence of something else being true. So, just for complete clarity about what we are dealing with, it is useful to appreciate how statements differ from other kinds of sentences.
What is meant by “a series of statements”? It means “at least two statements.” No single statement by itself can be an argument. Not only that, but the various statements have clearly different roles: one of them is providing evidence, the other one is claiming that something follows from that evidence. In other words, one is what’s called a premise, the other is what’s called a conclusion. It’s important to appreciate that no statement by itself is either a premise or a conclusion; these are roles that any statement can play. In fact, the very same statement can be a premise in one argument and the conclusion in another. One more note on this “series” bit: a statement is not necessarily a single grammatical sentence. We very often combine several statements together in one sentence, thanks to words like “and” and “or,” “if” and “then.” So we can very well have a series of statements without having more than one sentence.
The most important feature of the definition of “argument” I’m commenting on is the verb “claims to.” A conclusion claims to follow from the premises; the premises claim to establish the conclusion; the argument claims that the conclusion follows.
The question is: DOES it follow? If we were to leave out the “claims to” in defining “argument,” we would be defining all arguments as good ones: An argument is a series of statements, one of which follows from the other(s). If all arguments were good arguments, there’d be no possible need for the study of good reasoning, no need for Logic. Likewise, if cars couldn’t break down, there’d be no need for mechanics.
Luckily for us, reasoning has the capacity of breaking down, and in quite an interesting variety of ways. So we’ll have something to do in this course!
Following this page, you will find an Exercises page, on which there are a number of passages for you to consider. All of them are arguments in the sense in which we use the word here. Your task is simple enough: read each and identify what the conclusion is, and how many premises each contains.
This link will open a Powerpoint that reviews the material in this section: 1 Argument
Pasted below you will find a chapter from Lewis Carroll’s Through the Looking Glass. Perhaps you have already read this, but I’ve been surprised at the number of college students who never have. And even if you have, I’d like you to read this chapter, as a way of tuning you in to a distinction I’ve been obeying in the preceding discussion, that’s quite important in philosophy in general, and in logic in particular. It’s a distinction that has to do with punctuation. As you read this, see if you can tell what it is. We’ll give it name in a bit, but whatever it’s called, it’s a distinction that you need to appreciate and begin making in a systematic way. As you read this, you’ll find HD making an argument, about which he then says “There’s glory for you.” What are the premises and conclusion of this argument?
(Don’t feel obliged to read the whole thing if you find it tiresome, especially the commentary on all the words in Jabberwocky –but the poem about the fishies at the end is good.) We’ll talk about the philosophical issues in the selections at our next meeting.
However, the egg only got larger and larger, and more and more human: when she had come within a few yards of it, she saw that it had eyes and a nose and mouth; and when she had come close to it, she saw clearly that it was HUMPTY DUMPTY himself. `It can’t be anybody else!’ she said to herself. `I’m as certain of it, as if his name were written all over his face.’
It might have been written a hundred times, easily, on that enormous face. Humpty Dumpty was sitting with his legs crossed, like a Turk, on the top of a high wall — such a narrow one that Alice quite wondered how he could keep his balance — and, as his eyes were steadily fixed in the opposite direction, and he didn’t take the least notice of her, she thought he must be a stuffed figure after all.
`And how exactly like an egg he is!’ she said aloud, standing with her hands ready to catch him, for she was every moment expecting him to fall.
`It’s VERY provoking,’ Humpty Dumpty said after a long silence, looking away from Alice as he spoke, `to be called an egg — VERY!’
`I said you LOOKED like an egg, Sir,’ Alice gently explained. `And some eggs are very pretty, you know, she added, hoping to turn her remark into a sort of a compliment.
`Some people,’ said Humpty Dumpty, looking away from her as usual, `have no more sense than a baby!’
Alice didn’t know what to say to this: it wasn’t at all like conversation, she thought, as he never said anything to HER; in fact, his last remark was evidently addressed to a tree — so she stood and softly repeated to herself: —
`Humpty Dumpty sat on a wall:
Humpty Dumpty had a great fall
All the King’s horses and all the King’s men
Couldn’t put Humpty Dumpty in his place again.’
`That last line is much too long for the poetry,’ she added, almost out loud, forgetting that Humpty Dumpty would hear her.
`Don’t stand there chattering to yourself like that,’ Humpty Dumpty said, looking at her for the first time,’ but tell me your name and your business.’
`My NAME is Alice, but — ‘
`It’s a stupid name enough!’ Humpty Dumpty interrupted impatiently. `What does it mean?’
`MUST a name mean something?’ Alice asked doubtfully.
`Of course it must,’ Humpty Dumpty said with a short laugh: `MY name means the shape I am — and a good handsome shape it is, too. With a name like yours, you might be any shape, almost.’
`Why do you sit out here all alone?’ said Alice, not wishing to begin an argument.
`Why, because there’s nobody with me!’ cried Humpty Dumpty. `Did you think I didn’t know the answer to THAT? Ask another.’
`Don’t you think you’d be safer down on the ground?’ Alice went on, not with any idea of making another riddle, but simply in her good-natured anxiety for the queer creature. `That wall is so VERY narrow!’
`What tremendously easy riddles you ask!’ Humpty Dumpty growled out. `Of course I don’t think so! Why, if ever I DID fall off – – which there’s no chance of — but IF I did — ‘ Here he pursed his lips and looked so solemn and grand that Alice could hardly help laughing. `IF I did fall,’ he went on, `THE KING HAS PROMISED ME — WITH HIS VERY OWN MOUTH — to — to — ‘
`To send all his horses and all his men,’ Alice interrupted, rather unwisely.
`Now I declare that’s too bad!’ Humpty Dumpty cried, breaking into a sudden passion. `You’ve been listening at doors — and behind trees — and down chimneys — or you couldn’t have known it!’
`I haven’t, indeed!’ Alice said very gently. `It’s in a book.’
`Ah, well! They may write such things in a BOOK,’ Humpty Dumpty said in a calmer tone. `That’s what you call a History of England, that is. Now, take a good look at me! I’m one that has spoken to a King, I am: mayhap you’ll never see such another: and to show you I’m not proud, you may shake hands with me!’ And he grinned almost from ear to ear, as he leant forwards (and as nearly as possible fell off the wall in doing so) and offered Alice his hand. She watched him a little anxiously as she took it. `If he smiled much more, the ends of his mouth might meet behind,’ she thought: `and then I don’t know what would happen to his head! I’m afraid it would come off!’
`Yes, all his horses and all his men,’ Humpty Dumpty went on. `They’d pick me up again in a minute, THEY would! However, this conversation is going on a little too fast: let’s go back to the last remark but one.’
`I’m afraid I can’t quite remember it,’ Alice said very politely.
`In that case we start fresh,’ said Humpty Dumpty, `and it’s my turn to choose a subject — ‘ (`He talks about it just as if it was a game!’ thought Alice.) `So here’s a question for you. How old did you say you were?’
Alice made a short calculation, and said `Seven years and six months.’
`Wrong!’ Humpty Dumpty exclaimed triumphantly. `You never said a word like it!’
`I thought you meant “How old ARE you?”‘ Alice explained.
`If I’d meant that, I’d have said it,’ said Humpty Dumpty.
Alice didn’t want to begin another argument, so she said nothing.
`Seven years and six months!’ Humpty Dumpty repeated thoughtfully. `An uncomfortable sort of age. Now if you’d asked MY advice, I’d have said “Leave off at seven” — but it’s too late now.’
`I never ask advice about growing,’ Alice said indignantly.
`Too proud?’ the other inquired.
Alice felt even more indignant at this suggestion. `I mean,’ she said, `that one can’t help growing older.’
`ONE can’t, perhaps,’ said Humpty Dumpty, `but TWO can. With proper assistance, you might have left off at seven.’
`What a beautiful belt you’ve got on!’ Alice suddenly remarked. (They had had quite enough of the subject of age, she thought: and if they really were to take turns in choosing subjects, it was her turn now.) `At least,’ she corrected herself on second thoughts, `a beautiful cravat, I should have said — no, a belt, I mean — I beg your pardon!’ she added in dismay, for Humpty Dumpty looked thoroughly offended, and she began to wish she hadn’t chosen that subject. `If I only knew,’ the thought to herself, ‘which was neck and which was waist!’
Evidently Humpty Dumpty was very angry, though he said nothing for a minute or two. When he DID speak again, it was in a deep growl.
`It is a — MOST — PROVOKING — thing,’ he said at last, `when a person doesn’t know a cravat from a belt!’
`I know it’s very ignorant of me,’ Alice said, in so humble a tone that Humpty Dumpty relented.
`It’s a cravat, child, and a beautiful one, as you say. It’s a present from the White King and Queen. There now!’
`Is it really?’ said Alice, quite pleased to find that she HAD chosen a good subject, after all.
`They gave it me,’ Humpty Dumpty continued thoughtfully, as he crossed one knee over the other and clasped his hands round it, `they gave it me — for an un-birthday present.’
`I beg your pardon?’ Alice said with a puzzled air.
`I’m not offended,’ said Humpty Dumpty.
`I mean, what IS an un-birthday present?’
`A present given when it isn’t your birthday, of course.’
Alice considered a little. `I like birthday presents best,’ she said at last.
`You don’t know what you’re talking about!’ cried Humpty Dumpty. `How many days are there in a year?’
`Three hundred and sixty-five,’ said Alice.
`And how many birthdays have you?’
`And if you take one from three hundred and sixty-five, what remains?’
`Three hundred and sixty-four, of course.’
Humpty Dumpty looked doubtful. `I’d rather see that done on paper,’ he said.
Alice couldn’t help smiling as she took out her memorandum- book, and worked the sum for him:
365 – 1 = 364
Humpty Dumpty took the book, and looked at it carefully. `That seems to be done right — ‘ he began.
`You’re holding it upside down!’ Alice interrupted.
`To be sure I was!’ Humpty Dumpty said gaily, as she turned it round for him. `I thought it looked a little queer. As I was saying, that SEEMS to be done right — though I haven’t time to look it over thoroughly just now — and that shows that there are three hundred and sixty-four days when you might get un-birthday presents — ‘
`Certainly,’ said Alice.
`And only ONE for birthday presents, you know. There’s glory for you!’
`I don’t know what you mean by “glory,”‘ Alice said.
Humpty Dumpty smiled contemptuously. `Of course you don’t — till I tell you. I meant “there’s a nice knock-down argument for you!”‘
`But “glory” doesn’t mean “a nice knock-down argument,”‘ Alice objected.
`When I use a word,’ Humpty Dumpty said in rather a scornful tone, `it means just what I choose it to mean — neither more nor less.’
`The question is,’ said Alice, `whether you CAN make words mean so many different things.’
`The question is,’ said Humpty Dumpty, `which is to be master – – that’s all.’
Alice was too much puzzled to say anything, so after a minute Humpty Dumpty began again. `They’ve a temper, some of them — particularly verbs, they’re the proudest — adjectives you can do anything with, but not verbs — however, I can manage the whole of them! Impenetrability! That’s what I say!’
`Would you tell me, please,’ said Alice `what that means?`
`Now you talk like a reasonable child,’ said Humpty Dumpty, looking very much pleased. `I meant by “impenetrability” that we’ve had enough of that subject, and it would be just as well if you’d mention what you mean to do next, as I suppose you don’t mean to stop here all the rest of your life.’
`That’s a great deal to make one word mean,’ Alice said in a thoughtful tone.
`When I make a word do a lot of work like that,’ said Humpty Dumpty, `I always pay it extra.’
`Oh!’ said Alice. She was too much puzzled to make any other remark.
`Ah, you should see `em come round me of a Saturday night,’ Humpty Dumpty went on, wagging his head gravely from side to side: `for to get their wages, you know.’
(Alice didn’t venture to ask what he paid them with; and so you see I can’t tell YOU.)
`You seem very clever at explaining words, Sir,’ said Alice. `Would you kindly tell me the meaning of the poem called “Jabberwocky”?’
`Let’s hear it,’ said Humpty Dumpty. `I can explain all the poems that were ever invented — and a good many that haven’t been invented just yet.’
This sounded very hopeful, so Alice repeated the first verse:
`Twas brillig, and the slithy toves
Did gyre and gimble in the wabe
All mimsy were the borogoves,
And the mome raths outgrabe.
`That’s enough to begin with,’ Humpty Dumpty interrupted: `there are plenty of hard words there. “BRILLIG” means four o’clock in the afternoon — the time when you begin BROILING things for dinner.’
`That’ll do very well,’ said Alice: and “SLITHY”?’
`Well, “SLITHY” means “lithe and slimy.” “Lithe” is the same as “active.” You see it’s like a portmanteau — there are two meanings packed up into one word.’
`I see it now,’ Alice remarked thoughtfully: `and what are “TOVES”?’
`Well, “TOVES’ are something like badgers — they’re something like lizards — and they’re something like corkscrews.’
`They must be very curious looking creatures.’
`They are that,’ said Humpty Dumpty: `also they make their nests under sun-dials — also they live on cheese.’
`And what’s to “GYRE” and to “GIMBLE”?’
`To “GYRE” is to go round and round like a gyroscope. To “GIMBLE” is to make holes like a gimblet.’
`And “THE WABE” is the grass-plot round a sun-dial, I suppose?’ said Alice, surprised at her own ingenuity.
`Of course it is. It’s called “WABE,” you know, because it goes a long way before it, and a long way behind it — ‘
`And a long way beyond it on each side,’ Alice added.
`Exactly so. Well, then, “MIMSY” is “flimsy and miserable” (there’s another portmanteau for you). And a “BOROGOVE” is a thin shabby-looking bird with its feathers sticking out all round — something like a live mop.’
`And then “MOME RATHS”?’ said Alice. `I’m afraid I’m giving you a great deal of trouble.’
`Well, a “RATH” is a sort of green pig: but “MOME” I’m not certain about. I think it’s short for “from home” — meaning that they’d lost their way, you know.’
`And what does “OUTGRABE” mean?’
`Well, “OUTGRIBING” is something between bellowing and whistling, with a kind of sneeze in the middle: however, you’ll hear it done, maybe — down in the wood yonder — and when you’ve once heard it you’ll be QUITE content. Who’s been repeating all that hard stuff to you?’
`I read it in a book,’ said Alice. `But I had some poetry repeated to me, much easier than that, by — Tweedledee, I think it was.’
`As to poetry, you know,’ said Humpty Dumpty, stretching out one of his great hands, `I can repeat poetry as well as other folk, if it comes to that — ‘
`Oh, it needn’t come to that!’ Alice hastily said, hoping to keep him from beginning.
`The piece I’m going to repeat,’ he went on without noticing her remark,’ was written entirely for your amusement.’
Alice felt that in that case she really OUGHT to listen to it, so she sat down, and said `Thank you’ rather sadly.
`In winter, when the fields are white,
I sing this song for your delight
–only I don’t sing it,’ he added, as an explanation.
`I see you don’t,’ said Alice.
`If you can SEE whether I’m singing or not, you’re sharper eyes than most.’ Humpty Dumpty remarked severely. Alice was silent.
`In spring, when woods are getting green,
I’ll try and tell you what I mean.’
`Thank you very much,’ said Alice.
`In summer, when the days are long,
Perhaps you’ll understand the song:
In autumn, when the leaves are brown,
Take pen and ink, and write it down.’
`I will, if I can remember it so long,’ said Alice.
`You needn’t go on making remarks like that,’ Humpty Dumpty said: `they’re not sensible, and they put me out.’
`I sent a message to the fish:
I told them “This is what I wish.”
The little fishes of the sea,
They sent an answer back to me.
The little fishes’ answer was
“We cannot do it, Sir, because —
`I’m afraid I don’t quite understand,’ said Alice.
`It gets easier further on,’ Humpty Dumpty replied.
`I sent to them again to say
“It will be better to obey.”
The fishes answered with a grin,
“Why, what a temper you are in!”
I told them once, I told them twice:
They would not listen to advice.
I took a kettle large and new,
Fit for the deed I had to do.
My heart went hop, my heart went thump;
I filled the kettle at the pump.
Then some one came to me and said,
“The little fishes are in bed.”
I said to him, I said it plain,
“Then you must wake them up again.”
I said it very loud and clear;
I went and shouted in his ear.’
Humpty Dumpty raised his voice almost to a scream as he repeated this verse, and Alice thought with a shudder, `I wouldn’t have been the messenger for ANYTHING!’
`But he was very stiff and proud;
He said “You needn’t shout so loud!”
And he was very proud and stiff;
He said “I’d go and wake them, if —
I took a corkscrew from the shelf:
I went to wake them up myself.
And when I found the door was locked,
I pulled and pushed and knocked.
And when I found the door was shut,
I tried to turn the handle, but — ‘
There was a long pause.
`Is that all?’ Alice timidly asked.
`That’s all,’ said Humpty Dumpty. Good-bye.’
This was rather sudden, Alice thought: but, after such a VERY strong hint that she ought to be going, she felt that it would hardly be civil to stay. So she got up, and held out her hand. `Good-bye, till we meet again!’ she said as cheerfully as she could.
`I shouldn’t know you again if we DID meet,’ Humpty Dumpty replied in a discontented tone, giving her one of his fingers to shake; `you’re so exactly like other people.’
`The face is what one goes by, generally,’ Alice remarked in a thoughtful tone.
`That`s just what I complain of,’ said Humpty Dumpty. `Your face is the same as everybody has — the two eyes, so — ‘ (marking their places in the air with this thumb) `nose in the middle, mouth under. It’s always the same. Now if you had the two eyes on the same side of the nose, for instance — or the mouth at the top — that would be SOME help.’
`It wouldn’t look nice,’ Alice objected. But Humpty Dumpty only shut his eyes and said `Wait till you’ve tried.’
Alice waited a minute to see if he would speak again, but as he never opened his eyes or took any further notice of her, she said `Good-bye!’ once more, and, getting no answer to this, she quietly walked away: but she couldn’t help saying to herself as she went, `Of all the unsatisfactory — ‘ (she repeated this aloud, as it was a great comfort to have such a long word to say) `of all the unsatisfactory people I EVER met — ‘ She never finished the sentence, for at this moment a heavy crash shook the forest from end to end.