Combining Philosophers

All the ideas for Eucleides, George Boole and Peter John Olivi

unexpand these ideas     |    start again     |     specify just one area for these philosophers

10 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
8083 Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
     Full Idea: Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought.
     From: report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3
     A reaction: The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one.
7727 Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
     Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once.
     From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege
     A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven?
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
8686 Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
     Full Idea: Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning.
     From: report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics
     A reaction: The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet.
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
22277 Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
     Full Idea: Boole's work was an early example of the axiomatic method, whereby intellectual economy is achieved by studying a set of axioms in which the primitive terms have multiple interpretations.
     From: report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole'
     A reaction: Unclear about this. I suppose the axioms are just syntactic, and a range of semantic interpretations can be applied. Are De Morgan's Laws interpretations, or implications of the syntactic axioms? The latter, I think.
8. Modes of Existence / A. Relations / 1. Nature of Relations
16659 Relations do not add anything to reality, though they are real aspects of the world [Olivi]
     Full Idea: It does not seem that a relation adds anything real to that on which it is founded, but only makes for another real aspect belonging to the same thing. It is real since an aspect exists in re, not solely in the intellect, but it is not another thing.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], II.54), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.4
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16672 Quantity is the quantified parts of a thing, plus location and coordination [Olivi]
     Full Idea: Quantity refers to nothing other than the parts of the thing quantified, together with their location or position, being extrinsically coordinated with each other.
     From: Peter John Olivi (Treatise on Quantity [1286], f. 49vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.1
     A reaction: I'm not sure I understand 'extrinsically'. Is there some external stretching force? God spends his time spreading out his stuff? It is nice that being spread out isn't taken for granted. We take much more for granted than they did. Motion, for example.
16673 Quantity just adds union and location to the extension of parts [Olivi]
     Full Idea: Quantity or extension adds absolutely nothing really distinct to the quantified matter or to the extended and quantified form, except perhaps the union and location and position of those parts.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], II:58,II:440), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.1
     A reaction: Other views seem to say that the Quantity provides the extension, but he seems to take that as given.
19. Language / B. Reference / 1. Reference theories
1757 The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius]
     Full Idea: The 'Electra': Electra knows that Orestes is her brother, but not that this man is Orestes, so she knows and does not know her brother simultaneously.
     From: report of Eucleides (fragments/reports [c.410 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Eu.4
     A reaction: Hence we distinguish 'know of', 'know that' and 'know how'. Hence Russell makes 'knowledge by acquaintance' fundamental, and descriptions come later.
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
3028 The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides]
     Full Idea: The chief good is unity, which is known by several names, for at one time people call it prudence, at another time God, at another intellect, and so on.
     From: Eucleides (fragments/reports [c.410 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.9.2
     A reaction: So the chief good is what unites and focuses our moral actions. Kant calls that 'the will'.
27. Natural Reality / G. Biology / 5. Species
16663 Things are limited by the species to certain modes of being [Olivi]
     Full Idea: A subject is limited by its species to certain modes of being.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], I:586-7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.2
     A reaction: I think this is so very the wrong way round. Species characteristics are generalisations about similar individual creatures. The 'species' doesn't do anything at all. It is a classification. See ring species, for example.