Google ngram Aristotelian Syllogisms · 2020. 9. 30. · Socrates is a man All men are mortal ∴...
Transcript of Google ngram Aristotelian Syllogisms · 2020. 9. 30. · Socrates is a man All men are mortal ∴...
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Aristotelian Syllogisms
Euler diagrams
Aristotle 384-322 BC
INF1Afrom
Aristotle to Euler
Google ngram
inf1a-cl September 2020
Michael Fourman
Euler 1707-1783
a b c a b c
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Socrates is a man All men are mortal ∴ Socrates is mortal
A deduction is speech (logos) in which, certain things having been supposed, something, different from those supposed, results, of necessity, because of their being so.
AristotleAristotle
384-322 BC
INF1Adeduction
a b c a b c
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Socrates is a man All men are mortal ∴ Socrates is mortal
INF1Asyllogism
{x | x = Socrates} ✓ {x | isaMan x}{x | isaMan x} ✓ {x | isaMortal x}
))) {x | x = Socrates} ✓ {x | isaMortal x}
isSocrates x =def x = Socrates
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isSocrates ✏ isaMan isaMan ✏ isaMortalisSocrates ✏ isaMortal
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a ✏ b b ✏ ca ✏ c
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afz7DyJTbcs=</latexit>
Euler diagram
a b c
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Aristotelian Syllogisms
Venn diagrams
Aristotle 384-322 BC
John Venn 1834–1923
INF1AAristotle via Venn
Google ngram
inf1a-cl September 2020
Michael Fourman
Venn 1834—1923
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every red triangle is small
every small triangle is red
some big triangle is amber
some small disc is red
no red thing is blue
✔
❌
❓
❓
❓
redtriangle
small
Nothing here
INF1A-CLuniversal
affirmative
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INF1Afrom Venn to Euler
Euler 1707-1783
John Venn 1834–1923
¿?¿?
-
INF1Afrom Venn to Euler
Euler 1707-1783
a b c a b c
John Venn 1834–1923 every a is b no a is c
a ✏ b
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a ✏ ¬c
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-
INF1Afrom Euler
to Venna b c a b c
John Venn 1834–1923
¿?¿?
-
INF1Afrom Euler
to Venna b c a b c
John Venn 1834–1923
-
a ^ 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
a ^ ¬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
¬a ^ ¬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
¬a ^ 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
not ¬, and ^, or _AAAEXXicbVNNb9QwEHXbLZSllLYcOHCJqCpxqFa7/RBcVqpAQj1wKIJ+SM2qcpxJ1opjB3uyH4ryQ/g1XOEncOKvMM5upe62Po3eG/vNzPNEhZIOu92/K6trrfUnTzeetZ9vvth6ub2ze+lMaQVcCKOMvY64AyU1XKBEBdeFBZ5HCq6i7JPnr0ZgnTT6O04LGOQ81TKRgiNBt9tHIcIEq0AbDOpQQ3owB7iOCRhDnMIdZCwhI4Db7b1up9uc4GHQmwd7bH7Ob3fWdsPYiDIHjUJx52563QIHFbcohYK6HZYOCi4ynsINhZrn4AZV010d7BMSBwmpJ0Zj0KD3b1Q8d26aR5SZcxy6Zc6Dj3Kx5KmlhCV9TD4MKqmLEkGLmXxSqgBN4AcYxNKCQDWlgAsrqYNADLnlAmnMC+9PZg0sYIU1JlmEHObcTm28hGY8I0TDWJg8JzeqsDBjkgCsq9By6SAyk6rTOwnv/HeZLIhT3KYQgnalBd90FY6Luqa3vItjGeOwfyzyBbGy+FEahAOfQXLFYin+G0qd+jkph1QR6JG0Rns7yaSYDKw8Q6VV9X47CELhvIUBYaffAD9L6/ALj0BRVfGM81fuZ/ERPJ529zA9q7hOSyqof8ZdBkoRdBCAE7wA70A/3G+QeTN9tCU0QAZQOGoG3H1sOjY2djhV0A8bo6pIlSToWZqoFHMOMeG5VNOGoMQy165PH0IlCiaS9qwh3NCMHVo/pplSwpWbURMFibc4lbrf7ZxA3q7b7XZAW9Rb3pmHweVhp3fUOfx6vHf6cb5PG+wNe8vesR57z07ZGTtnF0ywn+wX+83+rP1rrbc2W1uz1NWV+Z1XbOG0Xv8HleV3Hg==
INF1Acombinations
a Venn diagram represents all imaginable combinations
for two predicates there are four combinations
-
John Venn 1834–1923
000
0
0011
010
2
011
3
1004
101
5
110
6 111
7
a b c
INF1Acombinations
-
rotationally symmetric Venn diagrams for n predicates exist if and only if n is a prime number.
-
000
0
0011
010
2
011
3
1004
101
5
110
6 111
7
bINF1A
Venn diagram
every a is b no a is ca ✏ b
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a b c
a c
a ✏ ¬c
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