Quiz: Science of Logic

All 50 questions. A perfect score earns the gold medal; 80% earns silver.

1. 1. What fact does Hegel cite as showing how external and mechanical arithmetic is?

   Pythagoras expressed his whole philosophy in numbers Children learn the multiplication tables by heart at school Geometry can define a circle without counting anything Machines have been built that perform its operations
2. 2. How, in the story Hegel tells, did Diogenes answer a dialectician who demonstrated the contradiction in motion?

   He conceded that motion was impossible He wrote a refutation in verse He appealed to Aristotle’s Physics He silently walked up and down
3. 3. What is Hegel’s verdict on Newton’s derivation of the differential of a product?

   It is the most correct determination of the infinite ever given It is valid only for straight-line functions It is correct but relies on motion and velocity It is incorrect, since the difference it computes is not the increment from xy to (x + dx)(y + dy)
4. 4. What does Hegel give as the more valid example of a negatively infinite judgment?

   The judgment “the rose is not red” The judgment “all men are mortal” A crime, which negates not just a particular right but law as such A civil lawsuit over disputed property
5. 5. In the chapter on Life, what does Hegel call “the privilege of living natures”?

   Self-consciousness Pain Death Reproduction
6. 6. What example does Hegel give of a formal syllogism whose correct conclusion can still be false?

   A stick that looks bent when half under water A swan judged white because all observed swans are white A coin assumed fair because it has two sides A canvas painted blue that is also covered with yellow, and so is green
7. 7. Why, according to Hegel, must the science begin with pure being?

   Tradition since Aristotle has always begun logic with being Since it must presuppose nothing, it can have no content Pure being is the richest and most concrete concept Being is the most certain fact of self-consciousness, as Descartes held
8. 8. How long does Hegel say it takes to learn the whole theory of the differential calculus by heart?

   Several years of study A full university course About half an hour It cannot be learned by rote at all
9. 9. Which German word does Hegel say language has preserved in gewesen (“been”)?

   Wesen (Essence) Schein (Show) Grund (Ground) Dasein (Determinate Being)
10. 10. According to Hegel’s Observation, what fault does he find in Spinoza’s treatment of the attributes?

    Spinoza makes Extension the only attribute and reduces Thought to it Spinoza derives the attributes from the Mode, reversing their true order Of infinite attributes, only Thought and Extension appear, taken up empirically Spinoza denies that substance has any attributes, admitting only modes
11. 11. Which example from physics does Hegel give of a merely formal, tautological ground?

    Friction as the ground of the rest of moving bodies Light as the ground of the colours of things Heat as the ground of the expansion of bodies Attractive force as ground of planetary motion
12. 12. Which ancient doctrine does Hegel identify with the stage of the One and the Void?

    Pythagorean number theory Stoic physics Eleatic monism Atomism
13. 13. Which German word does Hegel connect with positedness (Gesetztsein) when discussing the law of appearance?

    Ding (thing) Grund (ground) Gesetz (law) Wesen (essence)
14. 14. How does the Introduction describe the content of Logic?

    A preparatory exercise for students before philosophy proper God in his eternal essence, before nature and finite spirit The rules that the human mind must follow to avoid error in reasoning The most general laws of nature discovered by experiment
15. 15. Why, according to Hegel, are liabilities not negative “in and for themselves”?

    They exist only on paper, not in real goods Money as such can never be negative For the creditor they are a positive asset They are always cancelled by equal assets
16. 16. What, according to Hegel, does the philosophy of Kant and Fichte treat as the highest point of resolving the contradictions of reason?

    The Ought Sense-certainty The thing-in-itself The absolute idea
17. 17. With what sentence does Hegel open the second section of the Doctrine of Essence?

    “Essence is hidden behind appearance.” “Essence must appear.” “Whatever is, is rational.” “Appearance is mere illusion.”
18. 18. According to Hegel, how must Spinoza’s system be refuted?

    By proving it false throughout from premises outside the system By opposing to it the self-evident freedom of the individual subject By showing that its definitions contain arithmetical errors By recognising its standpoint as necessary and then showing that it leads beyond itself to a higher one
19. 19. What double meaning of aufheben (“to transcend”) does Hegel point out?

    To affirm a thing and to doubt it To begin anew and to bring to an end To preserve and to make to cease To create something and to destroy it
20. 20. How does Hegel respond to Kant’s claim that 7 + 5 = 12 is a synthetic proposition?

    He agrees, and calls it proof of the power of pure intuition in arithmetic He claims it is learnt only from experience Counting on is a mechanical joining, so the “synthesis” is analytical He argues that the sum must be derived from the law of contradiction alone
21. 21. How does Hegel describe the shape of the science at the end of the Logic?

    A pyramid resting on self-evident axioms A straight line advancing to infinity A tree branching from a single root without return A circle of circles
22. 22. How does Hegel describe the difficulty of the Doctrine of the Notion compared with the first two Books?

    It must build from nothing, since no one had written on the Notion before It must reshape a finished, “ossified” body of logic, like giving a new plan to an old, inhabited city It must reconcile the Notion with the results of experimental psychology It must translate Aristotle’s logic into German for the first time
23. 23. What does Hegel say about water cooled to its freezing point?

    It passes gradually through a paste-like consistency before freezing It hardens little by little from the surface down towards the bottom It cannot be cooled to freezing point unless it is first boiled Left still it may stay liquid; a slight shake hardens it at once
24. 24. What anecdote does Hegel tell to illustrate the proposition that no two things are alike?

    Court ladies looked for two identical leaves Spinoza ground two identical lenses Newton counted the leaves on an apple tree at Woolsthorpe Kant compared snowflakes on his daily walk through Königsberg
25. 25. Which doctrine of the Critique of Pure Reason does Hegel call one of its profoundest and most correct discoveries?

    That reason’s ideas are merely regulative That notions without intuition are empty, intuitions without notions blind That things in themselves cannot be known by theoretical reason The unity of the Notion as the synthetic unity of apperception
26. 26. Whose idealism does Hegel describe as having presentations that “arise in it like bubbles”?

    Kant’s phenomenon Berkeley’s mind Fichte’s Ego Leibniz’s monad
27. 27. According to Hegel, what limits the many ones in the number one hundred?

    All of them equally, since each is equally the hundredth The first one, which is the principle of all number Nothing, since numbers as such have no limit at all The hundredth one alone, which closes the series and bounds the rest
28. 28. Whose picture of atoms filling the interstices of a solvent does Hegel criticise in Real Measure?

    Antoine-Laurent Lavoisier Joseph Louis Gay-Lussac Robert Boyle Jöns Jakob Berzelius
29. 29. According to the Aristotle passage Hegel quotes, why did mathematics develop early in Egypt?

    Its kings paid philosophers The Nile floods required land surveys Its priestly caste had leisure Egyptian merchants needed accounts
30. 30. According to Hegel, how many useful syllogistic forms did Leibniz find among the 2,048 possible combinations?

    24 19 256 64
31. 31. Why does Hegel say the means can be higher than the finite ends it serves?

    Ends are always mechanical, while means are always free The tool is preserved, while the enjoyments it procures pass away and are forgotten The tool costs more labour to make than the goods it produces Tools are given by God, while ends are chosen by man
32. 32. Which explanation of elliptical planetary motion does Hegel attack in the Becoming of Essence?

    Vortices in a celestial aether, as Descartes taught Epicycles turning on deferent circles The planets’ own souls steering them Opposed centripetal and centrifugal forces
33. 33. What, according to Hegel, is the real merit of Haller’s description of eternity?

    Its proof that time had a beginning and so must have an end Haller drops the vain heaping of numbers, and only then does eternity appear Its vivid portrayal of an endlessly growing magnitude that thought cannot exhaust Its use of the Pythagorean tetraktys to measure the ages
34. 34. What image does Hegel give for the true infinite, as against the straight line of the “progress to infinity”?

    The circle The spiral The point The parabola
35. 35. What does Hegel say about the worst state, whose reality least corresponds to its concept?

    It is a goal to be approached by endless progress It is pure appearance, like the thing-in-itself It is not a state at all and has no share in the Idea It is still Idea in so far as it exists, since its members still obey a ruling concept
36. 36. How does Hegel explain the fact that in nature a genus has more than two species?

    As the impotence of nature to hold fast to the Notion As an error of naturalists’ classification that will be corrected As the result of species changing into one another over time As proof that the Notion itself requires many particular species
37. 37. How does Hegel describe the perishing of finite things?

    Perishing belongs to their being: their birth is the hour of their death It is merely contingent, so in principle they could exist without perishing It is an illusion of the understanding It is caused entirely by external forces that act on them from outside
38. 38. What example does Hegel give to show that the rule “a classification must exhaust the Notion” is empty?

    The division of triangles into right-angled and other triangles The discovery of new planets beyond Uranus The classification of states into monarchies and republics A further dozen species added to the existing sixty-seven species of parrots
39. 39. What example does Hegel give of the weak being secure against what is incomparably stronger?

    A small boat rides out a wave that sinks a ship A linen cloth hanging freely in the air is not pierced by a bullet A feather falls unharmed from a great height A reed bends in a storm that breaks an oak
40. 40. Which ancient puzzles does Hegel use to show quantitative change turning into qualitative change?

    The Ship of Theseus The Liar and the Veiled Man The Bald Man and the Heap Achilles and the Tortoise
41. 41. In chemism, what serves as the neutral medium of communication in matter and in spirit?

    Electricity in matter, and money as currency in spirit Water in matter, and language in spirit Fire in matter, and the state with its laws in spirit Air in matter, and feeling or sympathy in spirit
42. 42. Whose method of finding normals and tangents does Hegel praise as “the brilliant device of a true analytic mind”?

    Pierre de Fermat Gottfried Leibniz René Descartes Isaac Barrow
43. 43. What example does Hegel use to argue that finite causality is tautological?

    Rain causing dampness The sun causing the day A spark causing an explosion A seed causing the plant
44. 44. In the first preface, what image does Hegel use for a cultured people without metaphysics?

    A ship without a rudder or a pilot A body without a head to rule it A library with all its shelves standing empty A temple lacking its Holy of Holies
45. 45. What does Hegel say the claim that the whole is equal to its parts really expresses?

    The superiority of the parts over the whole A tautology: the whole is equal to the whole The infinite divisibility of matter into parts A law of nature discovered by experiment and measurement
46. 46. Which proposition does Hegel attribute to Spinoza and call “a proposition of infinite importance”?

    All determination is negation The infinity of a thing is its negation Being and nothing are the same God is the sum-total of all realities
47. 47. Why is “Aristotle died in his seventy-third year” a sentence rather than a Judgment for Hegel?

    Its predicate only states an individual fact instead of relating the subject to a universal It concerns a historical person rather than a concept It contains numbers, which cannot express a Notion It is negative in form
48. 48. Which mark, after Blumenbach, does Hegel cite as a formally correct but empty way of defining physical man?

    The lobe of the ear The size of the brain The upright posture The opposable thumb
49. 49. Which determination does Hegel call “the root of all movement and life”?

    Variety of things Contradiction Absolute difference Identity with itself
50. 50. Which example from Kant does Hegel discuss when defending the identity of being and nothing?

    A hundred thalers, real or merely imagined A straight line as the shortest distance between two points A ship drifting downstream A house seen from different sides