Combining Texts

All the ideas for 'Deflationary Metaontology of Thomasson', 'Theory of Science (Wissenschaftslehre, 4 vols)' and 'Intros to 'Buddhist Scriptures''

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

12 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
7807 The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
     Full Idea: Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms.
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], §3) by George / Van Evra - The Rise of Modern Logic
     A reaction: An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797.
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618 Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
     Full Idea: Bolzano if the father of 'arithmetization', which sought to found all of analysis on the concepts of arithmetic and to eliminate geometrical notions entirely (with logicism taking it a step further, by reducing arithmetic to logic).
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by James Robert Brown - Philosophy of Mathematics Ch. 3
     A reaction: Brown's book is a defence of geometrical diagrams against Bolzano's approach. Bolzano sounds like the modern heir of Pythagoras, if he thinks that space is essentially numerical.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830 Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
     Full Idea: Bolzano began the process of eliminating intuition from analysis, by proving something apparently obvious (that as continuous function must be zero at some point). Proof reveals on what a theorem rests, and that it is not intuition.
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - Frege philosophy of mathematics Ch.6
     A reaction: Kant was the target of Bolzano's attack. Two responses might be to say that many other basic ideas are intuited but impossible to prove, or to say that proof itself depends on intuition, if you dig deep enough.
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17265 Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
     Full Idea: Mathematical proofs are philosophical in method if they do not only demonstrate that a certain mathematical truth holds but if they also disclose why it holds, that is, if they uncover its grounds.
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3
     A reaction: I aim to defend the role of explanation in mathematics, but this says that this is only if the proofs are 'philosophical', which may be of no interest to mathematicians. Oh well, that's their loss.
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
14082 No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J]
     Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it.
     From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8)
     A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it.
9. Objects / F. Identity among Objects / 6. Identity between Objects
14081 Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J]
     Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms.
     From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1)
     A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible?
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9185 Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
     Full Idea: Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms.
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3
     A reaction: This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times.
19. Language / D. Propositions / 1. Propositions
22276 Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
     Full Idea: Bolzano took the entities of which truth is predicated to be not propositions in the subjective sense but 'propositions-in-themselves' - objective entities existing independent of our apprehension.
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Emp'
     A reaction: A serious mistake. Presumably the objective propositions are all true (or there would be endless infinities of them). So what is assessed in the case of error? Something other than the objective propositions! We assess these other things!
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
17264 Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
     Full Idea: Bolzano conceived of propositions as abstract objects which are structured compounds of concepts and potential contents of judgements and assertions.
     From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3
     A reaction: Personally I think of propositions as brain events, the constituents of thought about the world, but that needn't contradict the view of them as 'abstract'.
12232 A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
     Full Idea: What I mean by 'propositions' is not what the grammarians call a proposition, namely the linguistic expression, but the mere sense of this expression, is what is meant by proposition in itself or object proposition. This sense can be true or false.
     From: Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref?)
     A reaction: This seems to be the origin of what we understand by 'proposition'. The disputes are over whether such things exists, and whether they are features of minds or features of the world (resembling facts).
19. Language / E. Analyticity / 2. Analytic Truths
12233 The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]
     Full Idea: We can find the ground of a pure conceptual truth only in other conceptual truths.
     From: Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref)
     A reaction: Elsewhere he insists that these grounds must be in 'truths', and not just in the attributes of the concepts of involved. This conflicts with Kit Fine's view, that the concepts themselves are the source of conceptual truth and necessity.
29. Religion / C. Spiritual Disciplines / 3. Buddhism
7901 'Buddha' just means a person who is fully enlightened about life [Conze]
     Full Idea: 'Buddha' is not the name of a person, but designates a type. 'Buddha' is Sanskrit for someone who is 'fully enlightened' about the nature and meaning of life.
     From: Edward Conze (Intros to 'Buddhist Scriptures' [1959], Ch.1)
     A reaction: There seems to be an unexplained rule that there is never more than one Buddha in any generation. This isn't controlled by gods, so I take it that everyone defers to the most enlightened one, even if they themselves are very advanced in enlightenment.