3. Species #1 Difference 2 Species #2 Difference 1 Genus Logical Division of a

4. A genus is divided into species by adding differences. Substance Substance having life = Organism Having life GENUS + DIFFERENCE = SPECIES DIFFERENCE

5. A difference must exclude some individual members of the genus. EXCLUDES COPPER, IRON, SALT, ET AL. Substance Substance having life = Organism Having life

6. ? Something that excludes nothing is not a difference, and so it does not divide the genus, nor does it make a species. EXCLUDES No organismEvery organism Being cellular Organism NOT A DIFFERENCE

7. Something that includes nothing is not a difference, and so it does not divide the genus, nor does it make a species. EXCLUDES Every animal Animal No animal Having leaves NOT A DIFFERENCE

8. Each part in a genus requires its own difference. having Two Legs Biped Quadruped having Four Legs Animal

9. Not all differences make good divisions. Is this a good division of the genus? Species #1 having Webbed Feet e.g. a doge.g. a duck Species #2 having Four Legs Animal

10. To which species does a snake belong? A good division is exhaustive. DEFINITION: An exhaustive division of a genus is one in which every individual of the genus falls into a species. Species #1 having Webbed Feet Species #2 having Four Legs The division is no good because it is not exhaustive. Animal

11. To which species does a frog belong? Animal A good division is exclusive. DEFINITION: An exclusive division of a genus is one in which no individual of the genus falls into two species. Species #1 having Webbed Feet Species #2 having Four Legs The division is no good because it is not exclusive.

12. neither What counter example proves this division is not exhaustive? A division is EXHAUSTIVE when every individual of that genus has a species to which it belongs. What counter example proves this division is not exclusive? having Webbed Feet having Four Legs both Animal Species #1Species #2 A division is EXCLUSIVE when no individual of that genus falls into more than one species.

13. Summary A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species. A difference must include some individual in the genus and exclude some individual in the genus. A perfect division has two qualities: it must be exhaustive and it must be exclusive. Imperfect divisions fail to be exhaustive, or exclusive, or both. A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species. A difference must include some individual in the genus and exclude some individual in the genus. A perfect division has two qualities: it must be exhaustive and it must be exclusive. Imperfect divisions fail to be exhaustive, or exclusive, or both. A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species. A difference must include some individual in the genus and exclude some individual in the genus. A perfect division has two qualities: it must be exhaustive and it must be exclusive. Imperfect divisions fail to be exhaustive, or exclusive, or both. Summary A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species. A difference must include some individual in the genus and exclude some individual in the genus. A perfect division has two qualities: it must be exhaustive and it must be exclusive. Imperfect divisions fail to be exhaustive, or exclusive, or both. A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species. A difference must include some individual in the genus and exclude some individual in the genus. A perfect division has two qualities: it must be exhaustive and it must be exclusive. Imperfect divisions fail to be exhaustive, or exclusive, or both. A difference is something added to the genus that divides off a part of a genus. The part divided off is called a species. A difference must include some individual in the genus and exclude some individual in the genus. A perfect division has two qualities: it must be exhaustive and it must be exclusive. Imperfect divisions fail to be exhaustive, or exclusive, or both.

14. What counter example proves this division is not exhaustive? Give two differences that make a division which is EXCLUSIVE but NOT EXHAUSTIVE. Why is this division exclusive? ?? Animal Species #1Species #2 Having exactly four legs Having exactly two legs

15. What counter example proves this division is not exclusive? Give two differences that make a division which is EXHAUSTIVE but NOT EXCLUSIVE. Why is this division exhaustive? ?? Animal Species #1Species #2 Water-breathing Air-breathing

16. What counter example proves this division is not exhaustive? Give two differences that make a division which is NEITHER EXCLUSIVE NOR EXHAUSTIVE. What counter example proves this division is not exclusive? ?? Animal Species #1Species #2 Four-footed Web-footed

17. Why is this division exhaustive? Give two differences that make a division which is BOTH EXCLUSIVE and EXHAUSTIVE. ?? Animal Species #1Species #2 Why is this division exclusive?

18. Species #1 Not having feathers Species #2 Having feathers To guarantee that a division is both exhaustive and exclusive, logicians divide using contradictory differences. Such a division is both exhaustive (an individual animal either has feathers or it doesn’t) and exclusive (an individual animal can’t have feathers and not have them at the same time.) Animal

19. Homework Select four different genera. Divide each one as follows: Divide genus #1 so the division is exclusive but not exhaustive. Divide genus #2 so the division is exhaustive but not exclusive. Divide genus #3 so the division is neither exclusive nor exhaustive. Divide genus #4 so the division is both exclusive and exhaustive. Give reasons for each, using complete sentences, of the following form : Division is exhaustive b/c every _______(genus) falls under one of the differences. Division isn’t exhaustive b/c ________(counter-ex.) doesn’t fall under one of the differences. Division is exclusive b/c no _______(genus) falls under two differences. Division isn’t exclusive b/c ________(c-example) does fall under two differences.

20. Division by contradictory differences is called logical dichotomy YUM “What is the essence of a banana?” Man Not having the capacity to reason Brute Having the capacity to reason Animal Man Brute “What is the meaning of life?” EAT!

21. Man Non-rational Brute Rational In division by contradictory differences, one difference is called possession, the other privation. Animal Man is a rational animal. A brute is an irrational animal. Positive Difference Privative Difference

22. One problem with logical dichotomy is that the definition of one species says not WHAT IT IS, but WHAT IT ISN’T. “What is the nature of happiness?” “What is the nature of happiness?” Abstract thinking – OH YEAH! Abstract thinking – NOT!

23. For more complex divisions, differences can be combined in a matrix. SPECIES #1SPECIES #2 SPECIES #3SPECIES #4 PossessionPrivation DIFFERENCE #1 Possession Privation DIFFERENCE #2 GENUS

24. SQUAREOBLONG RHOMBUS Quadrilateral with an unequal side and oblique angle. PossessionPrivation WITH ALL SIDES EQUAL Possession Privation WITH ALL ANGLES RIGHT QUADRI LATERAL Quadrilaterals can be divided using a matrix. NB: Species is unnamed, so we must use circumlocution to identify it. Rhomboids & Trapezia SQUARE OBLONG RHOMBUS

25. Divide a genus of your choosing using a matrix. PossessionPrivation Possession Privation

26. Homework Select four different genera. Divide each using a matrix: Do not give examples of the species, but name the species in the matrix. If a species does not have a name, identify it using circumlocution.

27. FINIS. FINIS © 2009 Peter Orlowski. All rights reserved.