Hume’s Arguments in Part 1, section 7

The main question of the section is “whether [abstract ideas] be general or particular in the minds conception of them.” Hume wants to justify Berekely’s principle that “all general ideas are nothing but particular ones, annexed to a certain term.” He poses a dilemma : abstract ideas represent all degrees and qualities, or they represent no particular one at all. The philosophical tradition Hume is writing has opted for the 2nd horn of this dilema, calling the first absurd, as it implies an infinite capacity of the mind.  Hume rejects the tradition of indeterminate ideas. He first gives a negataive argument (i) its impossible to conceive of any quantity or quality without forming a precise notion of its degrees. Then gives a positive account of how abstract ideas work (ii) that the mind need not be infinite to form a notion of all possible degree’s of quantity and quality to apply ideas beyond their nature as particulars.

The first argument is proved in 3 stages. Note how each argument centers one each piece of the puzzle: the first is concerned with the idea, the second impressions, and the third objects.

A) The question of whether abstraction implies separation. That is, are the circumstances which we abstract from in our general ideas, distinguishable and different from the ideas we retain?

  1. If an idea of quantity and quality are not separable from the idea of an object, then quantity and quality are conjoined with the idea in conception
  2. If an idea is separable, then it is distinguishable.
  3. If the idea is distinguishable, then it is different.
  4. The precise degree of quantity or quality in the idea of the object is not different from the idea of object(e.g. just as the precise length of the line is not different from the line itself).
  5. The degree of quantity or quality of the idea of the object is not distinguishable from the idea of the object.(modus tollens 3+4).
  6. The idea of degree of quantity and quality are not separable from the idea of the object( modus tollens 5+2).
  7. Quantity and quality are conjoined with an idea in conception(modus ponens 6+1)

B) Abstraction, Hume argued, does not imply separation, now the question is whether the ultimate source of ideas is fully determined impressions

  1. If ideas are only copies and representations of impressions, then what is true of impressions, is true of ideas.
  2. Ideas are copies and representations of impressions
  3. What is true of impressions, is true of ideas(modus ponens 1+2)
  4. If what is true of impressions, is true of ideas, then every idea must have a determined quantity and quality,  if impressions have a determinate quantity and quality.
  5. If every impression has a determinate quantity and quality, then every idea must have a determined quantity and quality(modus ponens3 +4).
  6. Every impression has a determinate quantity and quality
  7. Therefore, the idea must have a determined quantity and quality(modus ponens 5+6).

C) If Locke’s principle holds, and quantity and quality are part of the conception of the idea(as Hume argued in (A), and ideas must have the determined quantity and quality of their impressions(as argued in (B), then for ideas to be general, object themselves must be general and indeterminate, which Hume here argues is absurd.

  1. Either (i) ideas represent generally because the objects which cause them are general and inderminate, or (ii) ideas represent generally because the mind applies them beyond their particular nature.
  2. Assume (i) for reductio ab adsurdum
  3. Its absurd to assume an object in reality∗, say a triangle, that has no precise degree of quantity and quality.
  4. If to form the clear and distinct idea of an object, is the same as forming a clear and distinct idea, then forming a clear and distinct idea of the absurd triangle, is to form a clear and distinct idea.
  5. To form the clear and distinct idea of an object, is the same as forming a clear and distinct idea.
  6. Forming a clear and distinct idea of the absurd triangle, is to form a clear and distinct idea(modus ponens 4+5).
  7. It is impossible it for an absurd idea to be clear and distinct(rationalist principle).
  8. The idea of the absurd triangle is both clear and distinct and not clear and distinct(Conjunctin of 6+7) which is a contradiction.
  9. If this his reductio will apply to any object said to have no particular degree of quantity and quality, and any object not limited in either quantity or quality, then not (i).
  10. This his reductio will apply to any object said to have no particular degree of quantity and quality, and any object not limited in either quantity or quality.
  11. Thus, not (i)(modus ponens 9+10)
  12. Therefore, (ii) represent generally because the mind applies them beyond their particular nature(disjunctive syllogism 1+11).

I’ll try and get the second  argument up soon
∗The absurdity of the object in reality is not question begging with regards to the reductio. Rather, it is a point about the formation of clear and distinct ideas. One could simply reject clear and distinct ideas while holding onto the absurd object in reality, and the reductio would fail. Clear and distinct ideas was a principle that had been in use since Descartes, so Hume recognized it as something the philosophers he was arguing against needed to hold onto to justify their epistemology.

 

 

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