82 ideas
| 22216 | Phenomenology studies different types of correlation between consciousness and its objects [Husserl, by Bernet] |
| Full Idea: Husserl's phenomenology is the science of the intentional correlation of acts of consciousness with their objects and it studies the ways in which different kinds of objects involve different kinds of correlation with different kinds of acts. | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Rudolf Bernet - Husserl p.198 | |
| A reaction: I notice he uncritically accepts Husserl's description of it as a 'science'. My naive question is how you would distinguish one kind of 'correlation' from another. |
| 21217 | Phenomenology needs absolute reflection, without presuppositions [Husserl] |
| Full Idea: Phenomenology demands the most perfect freedom from presuppositions and, concerning itself, an absolute reflective insight. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], III.1.063), quoted by Victor Velarde-Mayol - On Husserl 3.1 | |
| A reaction: As an outsider, I would have thought that the whole weight of modern continental philosophy is entirely opposed to the aspiration to think without presuppositions. |
| 22218 | There can only be a science of fluctuating consciousness if it focuses on stable essences [Husserl, by Bernet] |
| Full Idea: How can there be a science of a Heraclitean flux of acts of consciousness? Husserl answers that this is possible only if these acts are described in respect of their invariant or essential structure. This is an 'eidetic' scence of 'pure' psychology. | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Rudolf Bernet - Husserl p.199 | |
| A reaction: This is his phenomenology in 1913, which Bernet describes as 'static'. Husserl later introduced time with his 'genetic' version of phenomenology, looking at the sources of experience (and then at history). Essentialism seems to be intuitive. |
| 22217 | Phenomenology aims to validate objects, on the basis of intentional intuitive experience [Husserl, by Bernet] |
| Full Idea: Husserl's goal is to account for the validity, the 'being-true', of objects on the basis of the way in which they are given or constituted. ...Experiences more suitable for guaranteeing objects are those which both intend and intuitively apprehend them. | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Rudolf Bernet - Husserl p.199 | |
| A reaction: [compressed] In the light of previous scepticism and idealism, the project sounds a bit optimistic. If there is a gulf between mind and world it can only be bridged by 'reaching out' from both sides. This is a mind-sided attempt. |
| 22219 | Husserl saw transcendental phenomenology as idealist, in its construction of objects [Husserl, by Bernet] |
| Full Idea: Phenomeonology is 'transcendental' in describing the correlation between phenomena and intentional objects, to show how their meaning and validity are constructed. Husserl gave this process an idealist interpretation (which Heidegger criticised). | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Rudolf Bernet - Husserl p.200 | |
| A reaction: [compressed] If the actions which produce our concepts of objects all take place 'behind' phenomenal consciousness, then it is hard to avoid sliding into some sort of idealism. It encourages direct realism about perception. |
| 22204 | Start philosophising with no preconceptions, from the intuitively non-theoretical self-given [Husserl] |
| Full Idea: Where other philosophers ...start from unclarified, ungrounded preconceptions, we start out from that which antedates all standpoints: from the totality of the intuitively self-given which is prior to any theorising reflexion. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.2.020) | |
| A reaction: This is the great aim of Phenomenology, which is obviously inspired by Hegel's similar desire to start from nothing. Hegel starts from a concept ('nothing'), but Husserl starts from raw experience. I suspect both approaches are idle dreams. |
| 22207 | Epoché or 'bracketing' is refraining from judgement, even when some truths are certain [Husserl] |
| Full Idea: In relation to every thesis we can use this peculiar epoché (the phenomenon of 'bracketing' or 'disconnecting'), a certain refraining from judgment which is compatible with the unshaken and unshakable because self-evidencing conviction of Truth. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.1.031) | |
| A reaction: This is the crucial first step of Phenomenology. It seems to me that it is best described as 'methodological scepticism'. People actually practise it all the time, while they focus on some experience, while trying to forget preconceptions. |
| 22208 | 'Bracketing' means no judgements at all about spatio-temporal existence [Husserl] |
| Full Idea: I use the 'phenomenological' epoché, which completely bars me from using any judgment that concerns spatio-temporal existence. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.1.032) | |
| A reaction: This makes bracketing (or epoché) into a sort of voluntary idealism. Put like that, it is hard to see what benefits it could bring. I am, you will notice, a pretty thorough sceptic about the project of phenomenology. What has it taught us? |
| 22210 | After everything is bracketed, consciousness still has a unique being of its own [Husserl] |
| Full Idea: We fix our eyes steadily upon the sphere of Consciousness and study what it is that we find immanent in it. ...Consciousness in itself has a being of its own which in its absolute uniqueness of nature remains unaffected by disconnection. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.2.033) | |
| A reaction: 'Disconnection' is his 'bracketing'. He makes it sound obvious, but Schopenhauer entirely disagrees with him, and I have no idea how to arbitrate. I struggle to grasp consciousness once nature has been bracketed, but have little luck. Is it Da-sein? |
| 22215 | Phenomenology describes consciousness, in the light of pure experiences [Husserl] |
| Full Idea: Phenomenology is a pure descriptive discipline which studies the whole field of pure transcendental consciousness in the light of pure intuition. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.4.059) | |
| A reaction: When he uses the word 'pure' three times in a sentence, each applied to a different thing, you begin to wonder precisely what it means. Strictly speaking, I would probably only apply 'pure' to abstracta, and never to experiences or reality.115 |
| 22201 | The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl] |
| Full Idea: Definition cannot take the same form in philosophy as it does in mathematics; the imitation of mathematical procedure is invariably in this respect not only unfruitful, but perverse and most harmful in its consequences. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], Intro) | |
| A reaction: A hundred years of analytic philosophy has entirely ignored this warning. My heart has always sunk when I read '=def...' in a philosophy article (which is usually American). The illusion of rigour. |
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| Full Idea: Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VII.4) |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| Full Idea: A member m of M is an 'upper bound' of a subset N of M if m is not less than any member of N. A member m of M is a 'least upper bound' of N if m is an upper bound of N such that if l is any other upper bound of N, then m is less than l. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: [if you don't follow that, you'll have to keep rereading it till you do] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| Full Idea: Since combinatorial collections are enumerated, some multiplicities may be too large to be gathered into combinatorial collections. But the size of a multiplicity seems quite irrelevant to whether it forms a logical connection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| Full Idea: Many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| Full Idea: The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| Full Idea: The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| Full Idea: The Axiom of Foundation (Zermelo 1930) says 'Every (descending) chain in which each element is a member of the previous one is of finite length'. ..This forbids circles of membership, or ungrounded sets. ..The iterative conception gives this centre stage. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.4) |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| Full Idea: Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| Full Idea: The controversy was not about Choice per se, but about the correct notion of function - between advocates of taking mathematics to be about arbitrary functions and advocates of taking it to be about functions given by rules. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| Full Idea: The Peano-Russell notion of class is the 'logical' notion, where each collection is associated with some kind of definition or rule that characterises the members of the collection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.1) |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| Full Idea: The iterative conception of set was not so much as suggested, let alone advocated by anyone, until 1947. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| Full Idea: The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| Full Idea: The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) | |
| A reaction: He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far). |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| Full Idea: Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| Full Idea: A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) | |
| A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| Full Idea: Mathematics is today thought of as the study of abstract structure, not the study of quantity. That point of view arose directly out of the development of the set-theoretic notion of abstract structure. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.2) | |
| A reaction: It sounds as if Structuralism, which is a controversial view in philosophy, is a fait accompli among mathematicians. |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| Full Idea: One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.3) | |
| A reaction: That is, with rations every division operation has an answer. |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| Full Idea: The chief importance of the Continuum Hypothesis for Cantor (I believe) was that it would show that the real numbers form a set, and hence that they were encompassed by his theory. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| Full Idea: The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], 2.5) |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| Full Idea: Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], II.6) | |
| A reaction: Thus there is the problem of whether the contents of the gap are one unique thing, or many. |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| Full Idea: Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Cantor didn't mean that you could literally count the set, only in principle. |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| Full Idea: The indiscernibility of indefinitely large sizes will be a critical part of the theory of indefinitely large sizes. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| Full Idea: My proposal is that the concept of the infinite began with an extrapolation from the experience of indefinitely large size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) | |
| A reaction: I think it might be better to talk of an 'abstraction' than an 'extrapolition', since the latter is just more of the same, which doesn't get you to concept. Lavine spends 100 pages working out his proposal. |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| Full Idea: The intuitionist endorse the actual finite, but only the potential infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| Full Idea: The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.3) |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| Full Idea: The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'! |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| Full Idea: The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| Full Idea: The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| Full Idea: Every theorem of mathematics has a counterpart with set theory - ...but that theory cannot serve as a basis for the notion of proof. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| Full Idea: In modern mathematics virtually all work is only up to isomorphism and no one cares what the numbers or points and lines 'really are'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: At least that leaves the field open for philosophers, because we do care what things really are. So should everybody else, but there is no persuading some people. |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| Full Idea: Intuitionism in philosophy of mathematics rejects set-theoretic foundations. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3 n33) |
| 22209 | Our goal is to reveal a new hidden region of Being [Husserl] |
| Full Idea: We could refer to our goal as the winning of a new region of Being, the distinctive character of which has not yet been defined. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.2.033) | |
| A reaction: The obvious fruit of this idea, I would think, is Heidegger's concept of Da-sein, which claims to be a distinctively human region of Being. I'm not sure I can cope with the claim that Being itself (a very broad-brush term) has hidden regions. |
| 22211 | As a thing and its perception are separated, two modes of Being emerge [Husserl] |
| Full Idea: We are left with the transcendence of the thing over against the perception of it, ...and thus a basic and essential difference arises between Being as Experience and Being as Thing. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.2.042) | |
| A reaction: I'm thinking that this is not just the germ of Heidegger's concept of Da-sein, but it actually IS his concept, without the label. Husserl had said that he hoped to reveal a new region of Being. |
| 22202 | The World is all experiencable objects [Husserl] |
| Full Idea: The World is the totality of objects that can be known through experience. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.1.001) | |
| A reaction: I think this is the 'Nature' which has to be 'bracketed', when pursuing Phenomenology. It sounds like anti-realist empiricism, which has no place for unobservables. |
| 22213 | Absolute reality is an absurdity [Husserl] |
| Full Idea: An absolute reality is just as valid as a round square. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.3.055) | |
| A reaction: Husserl distances himself from 'Berkeleyian' idealism, but his discussion keeps flirting with, perhaps in some sort of have-your-cake-and-eat-it Hegelian way. Perhaps it is close to Dummett's Anti-Realism. |
| 21218 | The sense of anything contingent has a purely apprehensible essence or Eidos [Husserl] |
| Full Idea: It belongs to the sense of anything contingent to have an essence and therefore an Eidos which can be apprehended purely. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.1.002), quoted by Victor Velarde-Mayol - On Husserl 3.2.2 | |
| A reaction: This is the quirky idea that we can know necessary categorial essences a priori, even if the category is currently empty. Crops us in Lowe. Husserl says grasping the corresponding individuals must be possible. Third Man question. |
| 19263 | Imagine an object's properties varying; the ones that won't vary are the essential ones [Husserl, by Vaidya] |
| Full Idea: Husserl's 'eidetic variation' implies that we can judge the essential properties of an object by varying the properties of the object in imagination, and seeing which vary and which do not. | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Anand Vaidya - Understanding and Essence 'Knowledge' | |
| A reaction: The problem with this is that there are trivial or highly general necessary properties which are obviously not essential to the thing. Vaidya says [822] you can't perform the experiment without prior knowledge of the essence. |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 21220 | The physical given, unlike the mental given, could be non-existing [Husserl] |
| Full Idea: Anything physical which is given in person can be non-existing, no mental process which is given in person can be non-existing. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.2.046), quoted by Victor Velarde-Mayol - On Husserl 3.3.5 | |
| A reaction: This endorsement of Descartes shows how strong the influence of the Cogito remained in later continental philosophy. Phenomenology is a footnote to Descartes. |
| 22205 | Feelings of self-evidence (and necessity) are just the inventions of theory [Husserl] |
| Full Idea: So-called feelings of self-evidence, of intellectual necessity, and however they may otherwise be called, are just theoretically invented feelings. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.2.021) | |
| A reaction: This seems to be a dismissal of the a priori necessary on the grounds that it is 'theory-laden' - which is why it has to be bracketed in order to do phenomenology. |
| 21221 | Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl] |
| Full Idea: Immediate 'seeing', not merely sensuous, experiential seeing, but seeing in the universal sense as an originally presenting consciousness of any kind whatsoever, is the ultimate legitimising source of all rational assertions. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.2.019), quoted by Victor Velarde-Mayol - On Husserl 3.3.5 | |
| A reaction: Husserl is (I gather from this) a classic rationalist. Just like Descartes' judgement of the molten wax. |
| 22220 | The phenomena of memory are given in the present, but as being past [Husserl, by Bernet] |
| Full Idea: In Husserl's phenomenology, the intentional object of a memory is the object of a past experience, which is intuitively given to me in the present, not, however, as being present but as being past. | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Rudolf Bernet - Husserl p.203 | |
| A reaction: I certainly don't have to assess my mental events, and judge which are past, which are now, and which are future imaginings. I suppose Fodor would say they are memories because we find them in the memory-box. How else could it work? |
| 22206 | Natural science has become great by just ignoring ancient scepticism [Husserl] |
| Full Idea: Natural science has grown to greatness by pushing ruthlessly aside the rank growth of ancient skepticism and renouncing the attempt to conquer it. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.2.026) | |
| A reaction: This may be because scepticism is boring, or it may be because science 'brackets' scepticism, leaving philosophers to worry about it. |
| 22221 | We know another's mind via bodily expression, while also knowing it is inaccessible [Husserl, by Bernet] |
| Full Idea: Another person's consciousness is given to me through the expressive stratum of her body, which gives me access to her experience while making me realise that it is inaccessible to me. Empathy is a presentation of what is absent. | |
| From: report of Edmund Husserl (Ideas: intro to pure phenomenology [1913]) by Rudolf Bernet - Husserl p.203 | |
| A reaction: This is the phenomenological approach to the problem of other minds, by examining the raw experience of encountering another person. It is true that we seem to both know and not know another person's mind when we encounter them. |
| 22212 | Pure consciousness is a sealed off system of actual Being [Husserl] |
| Full Idea: Consciousness, considered in its 'purity', must be reckoned as a self-contained system of Being, a system of actual Being, into which nothing can penetrate, and from which nothing can escape. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.3.049) | |
| A reaction: Recorded without comment, to show that among phenomenologists there is a way of thinking about consciousness which is a long way from analytic discussions of the topic. |
| 22214 | We never meet the Ego, as part of experience, or as left over from experience [Husserl] |
| Full Idea: We never stumble across the pure Ego as an experience within the flux of manifold experiences which survives as transcendental residuum; nor do we meet it as a constitutive bit of experience appearing with the experience of which it is an integral part. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], II.4.057) | |
| A reaction: It seems that he agrees with David Hume. Sartre's 'Transcendence of the Ego' follows up this idea. However, Husserl goes on to assert the 'necessity' of the permanent Ego, which sounds like Kant's view. |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 22203 | Only facts follow from facts [Husserl] |
| Full Idea: From facts follow always nothing but facts. | |
| From: Edmund Husserl (Ideas: intro to pure phenomenology [1913], I.1.008) | |
| A reaction: I presume objective possibilities follow from facts, so this doesn't sound strictly correct. I sounds like a nice slogan for those desiring to keep facts separate from values. [on p.53 he comments on fact/value] |