32 ideas
| 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. |
| 13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
| Full Idea: The 'aggregative' objection to classical extensional mereology is that it assigns simply the wrong, set-like conditions of existence and spatio-temporal location to ordinary material objects. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 5.1) | |
| A reaction: [She attributes this to Kit Fine] The point is that there is more to a whole than just some parts, otherwise you could scatter the parts across the globe (or even across time) and claim that the object still existed. It's obvious really. |
| 13288 | Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki] |
| Full Idea: Two conceptions of logical consequence: a substitutional account, where no substitution of non-logical terms for others (of the right syntactic category) produce true premises and false conclusions; and model theory, where no interpretation can do it. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 9.3.2 n8) | |
| A reaction: [compressed] |
| 14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |
| Full Idea: 'Roses are red; therefore, roses are colored' may be necessarily truth-preserving, but it would not be classified as logically valid by standard systems of logic. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 9.3.2) |
| 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. |
| 14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
| Full Idea: Those who hold that not all mathematical questions can be concerned with structural matters can point to 'why are π or e transcendental?' or 'how are the prime numbers distributed?' as questions about particular features in the domain. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 9.3.1 n6) | |
| A reaction: [She cites Mac Lane on this] The reply would have to be that we only have those particular notions because we have abstracted them from structures, as in deriving π for circles. |
| 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. |
| 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. |
| 13289 | Structures have positions, constituent types and number, and some invariable parts [Koslicki] |
| Full Idea: Structures make available positions or places for objects, and place restraints on the type of constituent, and on their configuration. ...These lead to restrictions on the number of objects, and on which parts of the structure are invariable. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 9.6) | |
| A reaction: [compressed] That's a pretty good first shot at saying what a structure is, which I have so far not discovered any other writer willing to do. I take this to be an exploration of what Aristotle meant by 'form'. |
| 14501 | 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki] |
| Full Idea: The 'categorical' properties are roughly those that concern what goes on in the actual world; the properties excluded from that family are the 'hypothetical' ones, which concern what goes on in other worlds. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 3.2.3.1) | |
| A reaction: The awkward guest at this little party is the 'dispositional' properties, which are held to exist in the actual world, but have implications for other worlds. I'm a fan of them. |
| 14495 | I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki] |
| Full Idea: My project is to put the notion of structure or form squarely back at the center of any adequate account of the notion of part, whole and object. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], Intro) | |
| A reaction: Excellent. It is the fault of logicians, who presumably can't cope with such elusive and complex concepts, that we have ended up with objects as lists of things or properties, or quantifications over them. |
| 13264 | If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki] |
| Full Idea: If a whole is just a structure, we wonder how the guests could really be part of the dinner party seating structure, when the complex whole is fully exhausted by the structure that specifies the slots. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 4.2.2) | |
| A reaction: This cuts both ways. A dinner party may necessarily require guests, but the seating plan can be specified in the absence of any guests, who may never turn up. A seating plan is not a dinner party. Perhaps we have two objects here. |
| 14497 | The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki] |
| Full Idea: That objects are compounds of matter and form yields a solution to the Problem of Constitution: the clay is merely a proper part of the statue (viz. its matter); the 'remainder' of the statue is its formal or structural components which distinguish it. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], Info) | |
| A reaction: Thus philosophers have thought that it might consist of two objects because they have failed to grasp what an 'object' is. I would add that we need to mention 'essence', so that the statue can survive minor modifications. This is the solution! |
| 13280 | Statue and clay differ in modal and temporal properties, and in constitution [Koslicki] |
| Full Idea: The statue and the clay appear to differ in modal properties (such as being able to survive squashing), and temporal properties (coming into existence after the lump of clay), and in constitution (only the statue is constituted of the clay). | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 7.2.7.2) | |
| A reaction: I think the modal properties are the biggest problem here. You can't say a thing and its constitution are different objects, as they are necessarily connected. Structure comes into existence at t, but the structure isn't the whole object. |
| 14496 | Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki] |
| Full Idea: The notion of structure or form, far from being a mysterious and causally inert invention of philosophers, lies at the very center of many scientific and other rigorous endeavours, such as mathematics, logic, linguistics, chemistry and music. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], Intro) | |
| A reaction: This echoes my own belief exactly, and places Aristotle at the centre of the modern stage. Her list of subjects is intriguing, and will need a bit of thought. |
| 13279 | There are at least six versions of constitution being identity [Koslicki] |
| Full Idea: The view that constitution is identity has many versions: eliminativism (van Inwagen), identity relative to time (Gallois), identity relativized to sort (Geach), four-dimensionalism (Lewis, Sider), contingent identity (Gibbard), dominant kinds (Burke). | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 7.2.7.2 n17) | |
| A reaction: [she offers other names- useful footnote] Eliminativism says there is no identity. Gallois's view is Heraclitus. Geach seems to deny nature, since sorts are partly conventional. 4-D, nah! Gibbard: it could be the thing but lack its identity? Kinds wrong. |
| 14498 | For three-dimensionalist parthood must be a three-place relation, including times [Koslicki] |
| Full Idea: Parthood (for the three-dimensionalist) must be a three-place relation between pairs of objects and times, not the timeless two-place relation at work in the original Calculus of Individuals. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 2.2) |
| 13283 | The parts may be the same type as the whole, like a building made of buildings [Koslicki] |
| Full Idea: A building may be composed of proper parts which are themselves buildings; a particular pattern may be composed of proper parts which are themselves patterns (even the same pattern, on a smaller scale). | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 7.2.12) | |
| A reaction: This strikes me as a rather important observation, if you are (erroneously) trying to establish the identity of a thing simply by categorising its type. |
| 13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
| Full Idea: The modern theory of parts and wholes was intended primarily to replace set theory; in this way, wholes came out looking as much like sets as they possibly could, without set theory's commitment to an infinite hierarchy of abstract objects. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], Intro) | |
| A reaction: A very nice clarificatory remark, which explains well this rather baffling phenomenon of people who think there is nothing more to a whole than a pile of parts, as if a scrap heap were the same as a fleet of motor cars. |
| 14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
| Full Idea: A commitment to wholes is a commitment to entities that are numerically distinct from their parts (by Leibniz's Law, they don't share all of their properties - the parts typically exist, but the whole doesn't, prior to its creation). | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 3.1) | |
| A reaction: Presumably in classical mereology no act of 'creation' is needed, since all the parts in the universe already form all the possible wholes into which they might combine, however bizarrely. |
| 13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
| Full Idea: In my approach (as in that of Plato and Aristotle), wholes are in no way identified with parts; rather, a commitment to wholes is a commitment to entities numerically distinct from their proper parts. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 7.2.11) | |
| A reaction: Calling the whole an 'entity' doesn't seem to capture it. She seems to think there are some extra parts, in addition to the material parts, that make something a whole. I think this might be a category mistake. A structure is an abstraction. |
| 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. |
| 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! |
| 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). |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 14504 | The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki] |
| Full Idea: Theoretical terms such as 'mass', 'force', 'motion', 'species' and 'phlogiston' seem to indicate that the Kripke/Putnam approach to natural kind terms is committed to an excessive amount of stability in the meaning and reference of such expressions. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 8.6.2) | |
| A reaction: This sounds right to me. The notion of 'rigid' designation gives a nice framework for modal logic, but it doesn't seem to fit the shifting patterns of scientific thought. |
| 13285 | Natural kinds support inductive inferences, from previous samples to the next one [Koslicki] |
| Full Idea: Natural kinds are said to stand out from other classifications because they support legitimate inductive inferences ...as when we observe that past samples of copper conduct electricity and infer that the next sample will too. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 8.3.1) | |
| A reaction: A slightly more precise version of the Upanishad definition of natural kinds which I favour (Idea 8153). If you can't predict the next one from the previous one, it isn't a natural kind. You can't quite predict the next tiger from the previous one. |
| 13287 | Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki] |
| Full Idea: Candidate species concepts can be intrinsic: morphological, physiological or genetic similarity; or relational: biology such as interbreeding and reproductive isolation, ecology, such as mate recognition in a niche, or phylogenetics (ancestor relations). | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 8.4.1) | |
| A reaction: She says the relational ones are more popular, but I gather they all hit problems. See John Dupré on the hopelessness of the whole task. |
| 13284 | Should vernacular classifications ever be counted as natural kind terms? [Koslicki] |
| Full Idea: It is controversial whether classificatory expressions from the vernacular should ever really be counted as genuine natural kind terms. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 8.2) | |
| A reaction: This is a similar confrontation between the folk and the scientific specialist as we find in folk psychology. There are good defences of folk psychology, and it looks plausible to defend the folk classifications as having priority. |
| 13286 | There are apparently no scientific laws concerning biological species [Koslicki] |
| Full Idea: It has been observed that there are apparently no scientific laws concerning biological species. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 8.4.1) | |
| A reaction: The central concept of biology I take to be a 'mechanism'. and I suspect that this view of science is actually applicable in physics and chemistry, with so-called 'laws' being a merely superficial description of what is going on. |