8 ideas
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
| From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
| From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
| A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
| 5044 | Reality must be made of basic unities, which will be animated, substantial points [Leibniz] |
| Full Idea: A multiplicity can only be made up of true unities, ..so I had recourse to the idea of a real and animated point, or an atom of substance which must embrace some element of form or of activity in order to make a complete being. | |
| From: Gottfried Leibniz (New System and Explanation of New System [1696], p.116) | |
| A reaction: This seems to be a combination of logical atomism and panpsychism. It has a certain charm, but looks like another example of these rationalist speculators overreaching themselves. |
| 3900 | Maybe experience is not essential to perception, but only to the causing of beliefs [Armstrong, by Scruton] |
| Full Idea: Armstrong has argued that experience, as normally understood, is not necessary to perception. To perceive is to acquire beliefs, through a causal process. | |
| From: report of David M. Armstrong (Belief Truth and Knowledge [1973]) by Roger Scruton - Modern Philosophy:introduction and survey 23.4 |
| 4253 | Externalism says knowledge involves a natural relation between the belief state and what makes it true [Armstrong] |
| Full Idea: Externalist accounts of non-inferential knowledge say what makes a true non-inferential belief a case of knowledge is some natural relation which holds between the belief state and the situation which makes the belief true. | |
| From: David M. Armstrong (Belief Truth and Knowledge [1973], 11.III.6) | |
| A reaction: Armstrong's concept is presumably a response to Quine's desire to 'naturalise epistemology'. Bad move, I suspect. It probably reduces knowledge to mere true belief, and hence a redundant concept. |
| 5045 | No machine or mere organised matter could have a unified self [Leibniz] |
| Full Idea: By means of the soul or form, there is a true unity which is called the 'I' in us; a thing which could not occur in artificial machines, nor in the simple mass of matter, however organised it may be. | |
| From: Gottfried Leibniz (New System and Explanation of New System [1696], p.120) | |
| A reaction: I think the unity of consciousness and the unified Self are different phenomena. A wonderful remark about artificial intelligence for 1696! Note the idea of functionalism contained in 'organised'. Personally I see the brain as a 'mass of matter'. |
| 5046 | The soul does know bodies, although they do not influence one another [Leibniz] |
| Full Idea: I do not admit that the soul does not know bodies, although this knowledge arises without their influencing one another. | |
| From: Gottfried Leibniz (New System and Explanation of New System [1696], Reply 11) | |
| A reaction: He couldn't very well admit this without moving into pure idealism. Presumably it is like "I know her - she'll be in Harrods this morning". I wonder if Satan could steal my body, but my mind continue to believe it was still there? |
| 5043 | To regard animals as mere machines may be possible, but seems improbable [Leibniz] |
| Full Idea: It seems to me that the opinion of those who transform or degrade the lower animals into mere machines, although it seems possible, is improbable, and even against the order of things. | |
| From: Gottfried Leibniz (New System and Explanation of New System [1696], p.116) | |
| A reaction: His target is Descartes. 'Against the order of things' seems to beg the question. What IS the order of things? Only a thorough-going dualist would worry about this question, and that isn't me. |