23 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. |
| 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. |
| 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. |
| 12132 | Indiscernibility is a necessary and sufficient condition for identity [Brody] |
| Full Idea: Enduring objects should be taken as fundamental in an ontology, and for all such objects indiscernibility is both a necessary and sufficient condition for identity. | |
| From: Baruch Brody (Identity and Essence [1980], 3) | |
| A reaction: Brody offers a substantial defence, but I don't find it plausible. Apart from Black's well known twin spheres example (Idea 10195), discernibility is relative to the powers of the observer. Two similar people in the mist aren't thereby identical. |
| 15834 | Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P] |
| Full Idea: Brody bases sortal essentialism on the notion of a property that an individual must possess throughout its existence if it possesses it at any time in its existence. | |
| From: report of Baruch Brody (Identity and Essence [1980]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: Brody tends to treat categories as properties, which I dislike. How do you assess 'must' here? A person may possess a mole throughout life without it being essential. |
| 12140 | Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody] |
| Full Idea: The modern emphasis has been on the connection between essential properties and the properties that an object must have essentially. But traditionally there is also the connection between essential properties and the sort of thing that it is. | |
| From: Baruch Brody (Identity and Essence [1980], 5.6) | |
| A reaction: These are the modal essence and the definitional essence. My view is that he has missed out a crucial third (Aristotelian) view, which is that essences are explanatory. This third view can subsume the other two. |
| 11895 | A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P] |
| Full Idea: Brody bases sortal essentialism on the notion of a property that an individual must possess throughout its existence if it possesses it at any time in its existence. ...'Once an F, always an F'. ...Being a parrot is not a temporary occupation. | |
| From: report of Baruch Brody (Identity and Essence [1980]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: Hm. Would being less than fifty metres tall qualify as a sortal essence, for a giraffe or a uranium rod? If there is one thing an essential property should be, it is important. How do we assess importance? By explanatory power! Watch this space. |
| 12141 | Maybe essential properties are those which determine a natural kind? [Brody] |
| Full Idea: We can advance the thesis that all essential properties either determine a natural kind or are part of an essential property that does determine a natural kind. | |
| From: Baruch Brody (Identity and Essence [1980]) | |
| A reaction: A useful clear statement of the view. I am opposed to it, because I take it to be of the essence of Socrates that he is philosophical, but humans are not essentially philosophical, and philosophers are unlikely to be a natural kind. |
| 12137 | De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody] |
| Full Idea: To say that an object a has a property P essentially is to say that it has P, and in all of certain worlds (all possible, all in which something identical with it exists, ...) the object identical with it has P. This is the standard de re interpretation. | |
| From: Baruch Brody (Identity and Essence [1980], 5.4) | |
| A reaction: This view always has to be qualified by excluding trivially necessary properties, but that exclusion shows clearly that the notion of essential is more concerned with non-triviality than it is with necessity. |
| 12142 | Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody] |
| Full Idea: 'a has property P essentially' means 'a has P, a always had P, there is no possible past in which P exists without P, and there is no moment of time at which a has had P and at which there is a possible future in which a exists without P' | |
| From: Baruch Brody (Identity and Essence [1980], 6) | |
| A reaction: This is Brody's own final account of essentialism. This is a carefully qualified form of the view that essential properties are, on the whole, the necessary properties, which view I take to be fundamentally mistaken. |
| 12143 | An object having a property essentially is equivalent to its having it necessarily [Brody] |
| Full Idea: An object having a property essentially is equivalent to its having it necessarily. | |
| From: Baruch Brody (Identity and Essence [1980], 6.1) | |
| A reaction: This strikes me as blatantly false. Personally I am toying with the very unorthodox view that essential properties are not at all necessary, and that something can retain its identity while changing its essential character. A philosopher with Alzheimers. |
| 12144 | Essentialism is justified if the essential properties of things explain their other properties [Brody] |
| Full Idea: The reasonableness of the essentialist hypothesis will be proportional to the extent that we can, as a result, use a's possession of P to explain a's other properties, ...and there is an inability to explain otherwise why a has P. | |
| From: Baruch Brody (Identity and Essence [1980], 6.3) | |
| A reaction: Brody as a rather liberal notion of properties. I would hope that we can do rather more than explain a's non-essential properties. If the non-essential properties were entailed by the essential ones, would they not then also be essential? |
| 12139 | Mereological essentialism says that every part that ensures the existence is essential [Brody] |
| Full Idea: Mereological essentialism (whose leading advocate is Chisholm) says that for every x and y, if x is ever part of y, then y is necessarily such that x is part of y at any time that y exists. | |
| From: Baruch Brody (Identity and Essence [1980], 5.6) | |
| A reaction: This sounds implausible, especially given the transitivity of parthood. Not only are the planks that constitute Theseus's Ship now essential to it, but all the parts of the planks, every last chip, are as well. |
| 12135 | Interrupted objects have two first moments of existence, which could be two beginnings [Brody] |
| Full Idea: If 'beginning of existence' meant 'first moment of existence after a period of nonexistence', then objects with interrupted existence have two beginnings of existence. | |
| From: Baruch Brody (Identity and Essence [1980], 4.1) | |
| A reaction: One might still maintain that the first beginning was essential to the object, since that is the event that defined it - and that would clarify the reason why we are supposed to think the origins are essential. I say the origin explains it. |
| 12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
| Full Idea: Suppose that a and b have all of their properties in common. a certainly has the property of-being-identical-with-a. So, by supposition, does b. Then a = b. | |
| From: Baruch Brody (Identity and Essence [1980], 1.2) | |
| A reaction: Brody defends this argument, and seems to think that it proves the identity of indiscernibles. As far as I can see it totally begs the question, since we can only assume that both have the property of being-identical-with-a if we have assumed a = b. |
| 12138 | Identity across possible worlds is prior to rigid designation [Brody] |
| Full Idea: Identity across possible worlds is prior to rigid designation. | |
| From: Baruch Brody (Identity and Essence [1980], 5.4) | |
| A reaction: An interesting view. We might stipulate that any possible Aristotle is 'our Aristotle', but you would still need criteria for deciding which possible Aristotle's would qualify. Long-frozen Aristotles, stupid Aristotles, alien Aristotle's, deformed... |
| 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'). |