A SELECTION FROM
Sets of Concrete Propositions, proposed as Premisses for Sorites. Conclusions to be found.
with simplified statements included.
(1) Babies are illogical;
(2) Nobody is despised who can manage a crocodile;
(3) Illogical persons are despised.
Univ. "persons"; a = able to manage a crocodile; b = babies; c = despised; d = logical.
(1) My saucepans are the only things I have that are made of tin;
(2) I find all your presents very useful;
(3) None of my saucepans are of the slightest use.
Univ. "things of mine"; a = made of tin; b = my saucepans; c = useful; d = your presents.
(1) No potatoes of mine, that are new, have been boiled;
(2) All my potatoes in this dish are fit to eat;
(3) No unboiled potatoes of mine are fit to eat.
Univ. "my potatoes"; a = boiled; b = eatable; c = in this dish; d = new.
(1) There are no Jews in the kitchen;
(2) No Gentiles say 'shpoonj';
(3) My servants are all in the kitchen.
Univ. "persons"; a = in the kitchen; b Jews; c = my servants; d = saying 'shpoonj'.
(1) No ducks waltz;
(2) No officers ever decline to waltz;
(3) All my poultry are ducks.
Univ. "creatures"; a = ducks; b = my poultry; c = officers; d = willing to waltz.
(1) Every one who is sane can do Logic;
(2) No lunatics are fit to serve on a jury;
(3) None of your sons can do Logic.
Univ. "persons"; a = able to do Logic; b = fit to serve on a jury; c = sane; d = your sons.
(1) There are no pencils of mine in this box;
(2) No sugar-plums of mine are cigars;
(3) The whole of my property, that is not in this box, consists of cigars.
Univ. "things of mine"; a = cigars; b = in this box; c = pencils; d = sugar-plums.
(1) No experienced person is incompetent;
(2) Jenkins is always blundering;
(3) No competent person is always blundering.
Univ. "persons"; a = always blundering; b = competent; c = experienced; d = Jenkins.
(1) No terriers wander among the signs of the zodiac;
(2) Nothing, that does not wander among the signs of the zodiac, is a comet;
(3) Nothing but a terrier has a curly tail.
Univ. "things"; a = comets; b = curly-tailed; c = terriers; d = wandering among the signs of the zodiac.
(1) No one takes in the Times, unless he is well-educated;
(2) No hedge-hogs can read;
(3) Those who cannot read are not well-educated.
Univ. "creatures"; a = able to read; b = hedge-hogs; c = taking in the Times; d = well-educated.
(1) All puddings are nice;
(2) This dish is a pudding;
(3) No nice things are wholesome.
Univ. "things"; a = nice; b = puddings; c = this dish; d = wholesome.
(1) My gardener is well worth listening to on military subjects;
(2) No one can remember the battle of Waterloo, unless he is very old;
(3) Nobody is really worth listening to on military subjects, unless he can remember the battle of Waterloo.
Univ. "persons"; a = able to remember the battle of Waterloo; b = my gardener; c = worth listening to on military subjects; d = very old.
(1) All humming birds are richly coloured;
(2) No large birds live on honey;
(3) Birds that do not live on honey are dull in colour.
Univ. "birds"; a = humming-birds; b = large; c = living on honey; d = richly coloured.
(1) No Gentiles have hooked noses;
(2) A man who is a good hand at a bargain always makes money;
(3) No Jew is ever a bad hand at a bargain.
Univ. "persons"; a = good hands at a bargain; b = hook-nosed; c = Jews; d = making money.
(1) All ducks in this village that are branded "B", belong to Mrs. Bond;
(2) Ducks in this village never wear lace collars, unless they are branded "B";
(3) Mrs. Bond has no gray ducks in this village.
Univ. "ducks in this village"; a = belonging to Mrs. Bond; b = branded "B"; c = gray; d = wearing lace collars.
(1) All the old articles in this cupboard are cracked;
(2) No jug in this cupboard is new;
(3) Nothing in this cupboard, that is cracked, will hold water.
Univ. "things in this cupboard"; a = able to hold water; b = cracked; c = jugs; d = old.
(1) All unripe fruit is unwholesome;
(2) All these apples are wholesome;
(3) No fruit, grown in the shade, is ripe.
Univ. "fruit"; a = grown in the shade; b = ripe; c = these apples; d = wholesome.
(1) Puppies, that will not lie still, are always grateful for the loan of a skipping-rope;
(2) A lame puppy would not say "thank you" if you offered to lend it a skipping-rope;
(3) None but lame puppies ever care to do worsted-work.
Univ. "puppies"; a = caring to do worsted-work; b = grateful for the loan of a skipping-rope; c = lame; d = willing to lie still.
(1) No name in this list is unsuitable for the hero of a romance;
(2) Names beginning with a vowel are always melodious;
(3) No name is suitable for the hero of a romance, if it begins with a consonant.
Univ. "names"; a = beginning with a vowel; b = in this list; c = melodious; d = suitable for the hero of a romance.
(1) All members of the House of Commons have perfect self-command;
(2) No M.P., who wears a coronet, should ride in a donkey-race;
(3) All members of the House of Lords wear coronets.
Univ. "M.P.'s"; a = belonging to the House of Commons; b = having perfect self-command; c = one who may ride in a donkey-race; d = wearing a coronet.
(1) No goods in this shop, that have been bought and paid for, are still on sale;
(2) None of the goods may be carried away, unless labeled "sold";
(3) None of the goods are labeled "sold" unless they have been bought and paid for.
Univ. "goods in this shop"; a = allowed to be carried away; b = bought and paid for; c = labeled "sold"; d = on sale.
(1) No acrobatic feats, that are not announced in the bills of a circus, are ever attempted there;
(2) No acrobatic feat is possible, if it involves turning a quadruple somersault;
(3) No impossible acrobatic feat is ever announced in a circus bill.
Univ. "acrobatic feats"; a = announced in the bills of a circus; b = attempted in a circus; c = involving the turning of a quadruple somersault; d = possible.
(1) Nobody, who really appreciates Beethoven, fails to keep silence while the Moonlight-Sonata is being played;
(2) Guinea-pigs are hopelessly ignorant of music;
(3) No one, who is hopelessly ignorant of music, ever keeps silence while the Moonlight-Sonata is being played.
Univ. "creatures"; a = guinea-pigs; b = hopelessly ignorant of music; c = keeping silence while the Moonlight Sonata is being played; d = really appreciating Beethoven.
(1) Coloured flowers are always scented;
(2) I dislike flowers that are not grown in the open air;
(3) No flowers grown in the open air are colourless.
Univ. "flowers"; a = coloured; b = grown in the open air; c = liked by me; d = scented.
(1) Showy talkers think too much of themselves;
(2) No really well-informed people are bad company;
(3) People who think too much of themselves are not good company.
Univ. "persons"; a = good company; b = really well-informed; c = showy talkers; d = thinking too much of one's self.
(1) No boys under 12 are admitted to this school as boarders;
(2) All the industrious boys have red hair;
(3) None of the day-boys learn Greek;
(4) None but those under 12 are idle.
Univ. "boys in this school"; a = boarders; b = industrious; c = learning Greek; d = red-haired; e = under 12.
(1) The only articles of food, that my doctor allows me, are such as are not very rich;
(2) Nothing that agrees with me is unsuitable for supper;
(3) Wedding-cake is always very rich;
(4) My doctor allows me all articles of food that are suitable for supper.
Univ. "articles of food"; a = agreeing with me, h = allowed by my doctor; c = suitable for supper; d = very rich; e = wedding-cake.
(1) No discussions in our Debating-Club are likely to rouse the British Lion, so long as they are checked when they become too noisy;
(2) Discussions, unwisely conducted, endanger the peacefulness of our Debating-Club;
(3) Discussions, that go on while Tomkins is in the Chair, are likely to rouse the British Lion;
(4) Discussions in our Debating-Club, when wisely conducted, are always checked when they become too noisy.
Univ. "discussions in our Debating-Club"; a = checked when too noisy; b = dangerous to the peacefulness of our Debating-Club; c = going on while Tomkins is in the Chair; d = likely to rouse the British Lion; e = wisely conducted.
(1) All my sons are slim;
(2) No child of mine is healthy who takes no exercise;
(3) All gluttons, who are children of mine, are fat;
(4) No daughter of mine takes any exercise.
Univ. "my children"; a = fat; b = gluttons; c = healthy; d = sons; e = taking exercise.
(1) Things sold in the street are of no great value;
(2) Nothing but rubbish can be had for a song;
(3) Eggs of the Great Auk are very valuable;
(4) It is only what is sold in the streets that is really rubbish.
Univ. "things"; a = able to be had for a song; b = eggs of the Great Auk; c = rubbish; d = sold in the street; e = very valuable.
(1) No books sold here have gilt edges, except what are in the front shop;
(2) All the authorized editions have red labels;
(3) All the books with red labels are priced at 5s. and upwards;
(4) None but authorized editions are ever placed in the front shop.
Univ. "books sold here"; a = authorized editions; b = gilt-edged; c = having red labels; d = in the front shop; e = priced as 5s. and upwards.
(1) Remedies for bleeding, which fail to check it, are a mockery;
(2) Tincture of Calendula is not to be despised;
(3) Remedies, which will check the bleeding when you cut your finger, are useful;
(4) All mock remedies for bleeding are despicable.
Univ. "remedies for bleeding"; a = able to check bleeding; b = despicable; c = mockeries; d = Tincture of Calendula; e = useful when you cut your finger.
(1) None of the unnoticed things, met with at sea, are mermaids; e
(2) Things entered in the log, as met with at sea, are sure to be worth remembering;
(3) I have never met with anything worth remembering, when on a voyage;
(4) Things met with at sea, that are noticed, are sure to be recorded in the log.
Univ. "things met with at sea"; a = entercd in log; b = mermaids; c = met with by me; d = noticed; e = worth remembering.
(1) The only books in this library, that I do not recommend for reading, are unhealthy in tone;
(2) The bound books are all well-written;
(3) All the romances are healthy in tone;
(4) I do not recommend you to read any of the unbound books.
Univ. "books in this library"; a = bound; b = healthy in tone; c = recommended by me; d = romances; e = well-written.
(1) No birds, except ostriches, are 9 feet high;
(2) There are no birds in this aviary that belong to any one but me;
(3) No ostrich lives on mince-pies;
(4) I have no birds less than 9 feet high.
Univ. "birds"; a = in this aviary; b = living on mince-pies; c = my; d = g feet high; e = ostriches.
(1) A plum-pudding, that is not really solid, is mere porridge;
(2) Every plum-pudding, served at my table, has been boiled in a cloth;
(3) A plum-pudding that is mere porridge is indistinguishable from soup;
(4) No plum-puddings are really solid, except what are served at my table.
Univ. "plum-puddings"; a = boiled in a cloth; b = distinguishable from soup; c = mere porridge; d = really solid; e = served at my table.
(1) No interesting poems are unpopular among people of real taste;
(2) No modern poetry is free from affectation;
(3) All your poems are on the subject of soap-bubbles;
(4) No affected poetry is popular among people of real taste;
(5) No ancient poem is on the subject of soap-bubbles.
Univ. "poems"; a = affected; b = ancient; c = interesting; d = on the subject of soap-bubbles; e = popular among people of real taste; h = written by you.
(1) All the fruit at this Show, that fails to get a prize, is the property of the Committee;
(2) None of my peaches have got prizes;
(3) None of the fruit, sold off in the evening, is unripe;
(4) None of the ripe fruit has been grown in a hot-house;
(5) All fruit, that belongs to the Committee, is sold off in the evening.
Univ. "fruit at this Show"; a = belonging to the Committee; b = getting prizes; c = grown in a hot-house; d = my peaches; e = ripe; h = sold off in the evening.
(1) Promise-breakers are untrustworthy;
(2) Wine-drinkers are very communicative;
(3) A man who keeps his promises is honest;
(4) No teetotalers are pawnbrokers;
(5) One can always trust a very communicative person.
Univ. "persons"; a = honest; b = pawnbrokers; c = promise-breakers; d = trustworthy; e = very communicative; h = wine-drinkers.
(1) No kitten, that loves fish, is unteachable.
(2) No kitten without a tail will play with a gorilla;
(3) Kittens with whiskers always love fish;
(4) No teachable kitten has green eyes;
(5) No kittens have tails unless they have whiskers.
Univ. "kittens"; a = green-eyed; b = loving fish; c = tailed; d = teachable; e = whiskered; h = willing to play with a gorilla.
(1) All the Eton men in this College play cricket;
(2) None but the Scholars dine at the higher table;
(3) None of the cricketers row;
(4) My friends in this College all come from Eton;
(5) All the Scholars are rowing-men.
Univ. "men in this College"; a = cricketers; b = dining at the higher table; c = Etonians; d = my friends; e = rowing-men; h = Scholars.
(1) There is no box of mine here that I dare open;
(2) My writing-desk is made of rose-wood;
(3) All my boxes are painted, except what are here;
(4) There is no box of mine that I dare not open, unless it is full of live scorpions;
(5) All my rose-wood boxes are unpainted.
Univ. "my boxes"; a = boxes that I dare open; b = full of live scorpions; c = here; d = made of rose-wood; e = painted; h = writing-desks.
(1) Gentiles have no objection to pork;
(2) Nobody who admires pigsties ever reads Hogg's poems;
(3) No Mandarin knows Hebrew;
(4) Every one, who does not object to pork, admires pigsties;
(5) No Jew is ignorant of Hebrew.
Univ. "persons"; a = admiring pigsties; b = Jews; c = knowing Hebrew; d = Mandarins; e = objecting to pork; h = reading Hogg's poems.
(1) All writers, who understand human nature, are clever;
(2) No one is a true poet unless he can stir the hearts of men;
(3) Shakespeare wrote "Hamlet";
(4) No writer, who does not understand human nature, can stir the hearts of men;
(5) None but a true poet could have written "Hamlet".
Univ. "writers"; a = able to stir the hearts of men; b = clever; c = Shakespeare; d = true poets; e = understanding human nature; h = writer of "Hamlet".
(1) I despise anything that cannot be used as a bridge;
(2) Everything, that is worth writing an ode to, would be a welcome gift to me;
(3) A rainbow will not bear the weight of a wheelbarrow;
(4) Whatever can be used as a bridge will bear the weight of a wheel-barrow;
(5) I would not take, as a gift, a thing that I despise.
Univ. "things"; a = able to bear the weight of a wheelbarrow; b = acceptable to me; c = despised by me; d = rainbows; e = useful as a bridge; h = worth writing an ode to.
(1) When I work a Logic-example without grumbling, you may be sure it is one that I can understand;
(2) These Sorites are not arranged in regular order, like the examples I am used to;
(3) No easy example ever makes my head ache;
(4) I can't understand examples that are not arranged in regular order, like those I am used to;
(5) I never grumble at an example, unless it gives me a headache.
Univ. "Logic-examples worked by me"; a = arranged in regular order, like the examples I am used to; b = easy ; c = grumbled at by me; d = making my head ache; e = these Sorites; h = understood by me.
(1) Every idea of mine, that cannot be expressed as a Syllogism, is really ridiculous;
(2) None of my ideas about Bath-buns are worth writing down;
(3) No idea of mine, that fails to come true, can be expressed as a Syllogism;
(4) I never have any really ridiculous idea, that I do not at once refer to my solicitor;
(5) My dreams are all about Bath-buns;
(6) I never refer any idea of mine to my solicitor, unless it is worth writing down.
Univ. "my idea"; a = able to be expressed as a Syllogism; b = about Bath-buns; c = coming true; d = dreams; e = really ridiculous; h = referred to my solicitor; k = worth writing down.
(1) None of the pictures here, except the battle-pieces, are valuable;
(2) None of the unframed ones are varnished;
(3) All the battle-pieces are painted in oils;
(4) All those that have been sold are valuable;
(5) All the English ones are varnished;
(6) All those in frames have been sold.
Univ. "the pictures here"; a = battle-pieces; b = English; c = framed; d = oil-paintings; e = sold; h = valuable; k = varnished.
(1) Animals, that do not kick, are always unexcitable;
(2) Donkeys have no horns;
(3) A buffalo can always toss one over a gate;
(4) No animals that kick are easy to swallow;
(5) No hornless animal can toss one over a gate;
(6) All animals are excitable, except buffaloes.
Univ. "animals"; a = able to toss one over a gate; b = buffaloes; c = donkeys; d = easy to swallow; e = excitable; h = horned; k = kicking.
(1) No one, who is going to a party, ever fails to brush his hair;
(2) No one looks fascinating, if he is untidy;
(3) Opium-eaters have no self-command;
(4) Every one, who has brushed his hair, looks fascinating;
(5) No one wears white kid gloves, unless he is going to a party;
(6) A man is always untidy, if he has no self-command.
Univ. "persons"; a = going to a party; b = having brushed one's hair; c = having self-command; d = looking fascinating; e = opium-eaters; h = tidy; k = wearing white kid gloves.
(1) No husband, who is always giving his wife new dresses, can be a cross-grained man;
(2) A methodical husband always comes home for his tea;
(3) No one, who hangs up his hat on the gas-jet, can be a man that is kept in proper order by his wife;
(4) A good husband is always giving his wife new dresses;
(5) No husband can fail to be cross-grained, if his wife does not keep him in proper order;
(6) An unmethodical husband always hangs up his hat on the gas-jet.
Univ. "husbands"; a = always coming home for his tea; b = always giving his wife new dresses; c = cross-grained; d = good; e = hanging up his hat on the gas-jet; h = kept in proper order; k = methodical.
(1) Everything, not absolutely ugly, may be kept in a drawing-room;
(2) Nothing, that is encrusted with salt, is ever quite dry;
(3) Nothing should be kept in a drawing-room, unless it is free from damp;
(4) Bathing-machines are always kept near the sea;
(5) Nothing, that is made of mother-of-pearl, can be absolutely ugly;
(6) Whatever is kept near the sea gets encrusted with salt.
Univ. "things"; a = absolutely ugly; b = bathing machines; c = encrusted with salt; d = kept near the sea; e = made of mother-of-pearl; h = quite dry; k = things that may be kept in a drawing-room.
(1) I call no day "unlucky", when Robinson is civil to me;
(2) Wednesdays are always cloudy;
(3) When people take umbrellas, the day never turns out fine;
(4) The only days when Robinson is uncivil to me are Wednesdays;
(5) Everybody takes his umbrella with him when it is raining;
(6) My "lucky" days always turn out fine.
Univ. "days"; a = called by me "lucky"; b = cloudy; c = days when people take umbrellas; d = days when Robinson is civil to me; e = rainy; h = turning out fine; k = Wednesdays.
(1) No shark ever doubts that it is well fitted out;
(2) A fish, that cannot dance a minuet, is contemptible;
(3) No fish is quite certain that it is well fitted out, unless it has three rows of teeth;
(4) All fishes, except sharks, are kind to children;
(5) No heavy fish can dance a minuet;
(6) A fish with three rows of teeth is not to be despised.
Univ. "fishes"; a = able to dance a minuet; b = certain that he is well fitted out; c = contemptible; d = having 3 rows of teeth; e = heavy; h = kind to children; k = sharks.
(1) All the human race, except my footmen, have a certain amount of common sense;
(2) No one, who lives on barley-sugar, can be anything but a mere baby;
(3) None but a hop-scotch player knows what real happiness is;
(4) No mere baby has a grain of common sense;
(5) No engine-driver ever plays hop-scotch;
(6) No footman of mine is ignorant of what true happiness is.
Univ. "human beings"; a = engine-drivers; b = having common sense; c = hop-scotch players; d = knowing what real happiness is; e = living on barley-sugar; h = mere babies; k = my footmen.
(1) I trust every animal that belongs to me;
(2) Dogs gnaw bones;
(3) I admit no animals into my study, unless they will beg when told to do so;
(4) All the animals in the yard are mine;
(5) I admit every animal, that I trust, into my study;
(6) The only animals, that are really willing to beg when told to do so, are dogs.
Univ. "animals"; a = admitted to my study; b = animals that I trust; c = dogs; d = gnawing bones; e = in the yard; h = my; k = willing to beg when told.
(1) Animals are always mortally offended if I fail of notice them;
(2) The only animals that belong to me are in that field;
(3) No animal can guess a conundrum, unless it has been properly trained in a Board-School;
(4) None of the animals in that field are badgers;
(5) When an animal is mortally offended, it always rushes about wildly and howls;
(6) I never notice any animal, unless it belongs to me;
(7) No animal, that has been properly trained in a Board-School, ever rushes about wildly and howls.
Univ. "animals"; a = able to guess a conundrum; b = badgers; c = in that field; d = mortally offended if I fail to notice them; e = my; h = noticed by me; k = properly trained in a Board-School; l = rushing about wildly and howling.
(1) I never put a cheque, received by me, on that file, unless I am anxious about it;
(2) All the cheques received by me, that are not marked with a cross, are payable to bearer;
(3) None of them are ever brought back to me, unless they have been dishonoured at the Bank;
(4) All of them, that are marked with a cross, are for amounts of over ?100;
(5) All of them, that are not on that file, are marked "not negotiable";
(6) No cheque of yours, received by me, has ever been dishonoured;
(7) I am never anxious about a cheque, received by me, unless it should happen to be brought back to me;
(8) None of the cheques received by me, that are marked "not negotiable", are for amounts of over ?100.
Univ. "cheques received by me"; a = brought back to me; b = cheques that I am anxious about; c = honoured;
d = marked with a cross; e = marked "not negotiable"; h = on that file; k = over ?100; l = payable to bearer; m = your.
(1) All the dated letters in this room are written on blue paper;
(2) None of them are in black ink, except those that are written in the third person;
(3) I have not filed any of them that I can read;
(4) None of them, that are written on one sheet, are undated;
(5) All of them, that are not crossed, are in black ink;
(6) All of them, written by Brown, begin with "Dear Sir";
(7) All of them, written on blue paper, are filed;
(8) None of them, written on more than one sheet, are crossed;
(9) None of them, that begin with "Dear Sir", are written in the third person.
Univ. "letters in this room"; a = beginning with "Dear Sir"; b = crossed; c = dated; d = filed; e = in black ink; h = in third person; k = letters that I can read; l = on blue paper; m = on one sheet; n = written by Brown.
(1) The only animals in this house are cats;
(2) Every animal is suitable for a pet, that loves to gaze at the moon;
(3) When I detest an animal, I avoid it;
(4) No animals are carnivorous, unless they prowl at night;
(5) No cat fails to kill mice;
(6) No animals ever take to me, except what are in this house;
(7) Kangaroos are not suitable for pets;
(8) None but carnivora kill mice;
(9) I detest animals that do not take to me;
(10) Animals, that prowl at night, always love to gaze at the moon.
Univ. "animals"; a = avoided by me; b = carnivora; c = cats; d = detested by me; e = in this house; h = kangaroos; k = killing mice; l = loving to gaze at the moon; m = prowling at night; n = suitable for pets, r = taking to me.
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