11 ideas
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
| A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
| A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
| A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
| A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
| 2534 | Mindless bodies are zombies, bodiless minds are ghosts [Sturgeon] |
| Full Idea: When bodies are conceived without mind, Zombies are the topic; when mind is conceived without bodies, Ghosts are the topic. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: Personally I am not too impressed by either possibility. I doubt whether either of them are even logically possible. Can you have a magnet without its magnetism? Can you have magnetism with no magnet? |
| 2537 | Types are properties, and tokens are events. Are they split between mental and physical, or not? [Sturgeon] |
| Full Idea: The question is whether mental and physical types (which are properties) are distinct, and whether mental and physical tokens (which are events) are distinct. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: Helpful. While the first one gives us the rather dodgy notion of 'property dualism', the second one seems to imply Cartesian dualism, if the events really are distinct. It seems to me that thought is an aspect of brain events, not a distinct event. |
| 2532 | Intentionality isn't reducible, because of its experiential aspect [Sturgeon] |
| Full Idea: The link between Aboutness and consciousness, plus the latter's theoretical recalcitrance, have prevented reduction of the former. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: I remain unconvinced that Aboutness (intentionality) has to be wholly (or even partly conscious). We are more interested in our conscious mental states, because those are the ones we can report to other people, and discuss. |
| 2533 | Rule-following can't be reduced to the physical [Sturgeon] |
| Full Idea: If you can't squeeze an 'ought' from an 'is', then the feature of normativity will prevent the reduction of Aboutness. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: A dubious argument. Hume's point is that no rational inference will get you from is to ought, but you can get there on a whim. I don't see normativity as being so intrinsically magical that it is irreducible. |
| 2535 | The main argument for physicalism is its simple account of causation [Sturgeon] |
| Full Idea: The dominant empirical argument for physicalism is the Overdetermination Argument: physics is closed and complete, mind is causally efficacious, the world isn't choc-full of overdetermination, so the mind is physical as well. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: I find this argument utterly convincing. The idea that there is only one thing which is outside the interconnected causal nexus which seems to constitute the rest of reality, and that is a piece of meat inside our heads, strikes me as totally ridiculous. |
| 2536 | Do facts cause thoughts, or embody them, or what? [Sturgeon] |
| Full Idea: Does a thought relate to its truth conditions like a tree to its age, a bee dance to its target, or smoke to its cause? | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: Nice question. Is truth the purpose of thoughts, or the cause of thoughts, or the constitution(?) of thoughts? I vote for the bee….but we mustn't confuse truth with truth-conditions. |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |