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All the ideas for 'Thinking About Mathematics', 'Ontology and the Ambitions of Metaphysics' and 'Ideas: intro to pure phenomenology'

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71 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber]
     Full Idea: Metaphysics can be divided into two parts: first ontology, which is supposed to tell us what there is in general. The second part is the rest of metaphysics, which is supposed to tell us what these things are like, in various general ways.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 01.1)
     A reaction: Hofweber is a fairly sceptical guide to metaphysics, but this has been the standard view for the last decade. Before that, Quine had set an agenda of mere ontology.
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
'Fundamentality' is either a superficial idea, or much too obscure [Hofweber]
     Full Idea: The dilemma of neo-Aristotelian metaphysics is that on an ordinary reading of prioriy, 'fundamentality' won't give the intended results, and on a metaphysical reading it turns into esoteric metaphysics.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 13.4.2)
     A reaction: Hofweber is hostile to 'esoteric' metaphysics, but sympathetic to 'egalitarian' metaphysics, which anyone can understand (with a bit of effort).
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
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.
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.
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.
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.
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.
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.
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.
'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?
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?
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
2. Reason / D. Definition / 13. Against Definition
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.
3. Truth / H. Deflationary Truth / 1. Redundant Truth
'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber]
     Full Idea: 'It's true that Fido is a dog' gives rise to a contrastive focus on 'true', with the contrast class probably depending on members like 'it's false that...' or 'it's unlikely that...'.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 02.6.3)
     A reaction: If we introduce (from linguistics) the idea of a 'contrast class', then Ramsey's famous example begins to sound meaningful. It might occur in a discussion of 'did Antony actually say 'Friends, Romans. countrymen'?'
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Since properties can have properties, some theorists rank them in 'types' [Hofweber]
     Full Idea: Since properties themselves can have properties there is a well-known division in the theory of properties between those who take a typed and those who take a type-free approach.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 08.5)
     A reaction: I take this idea to be about linguistic predicates, and about semantics which draws on model theory. To see it as about actual 'properties' in the physical world makes no sense.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
     Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Maybe not even names are referential, but are just by used by speakers to refer [Hofweber]
     Full Idea: A more radical alternative which takes names not to be referring even in the broader sense, but only takes speakers to refer with uses of names.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 08.1)
     A reaction: Given that you can make up nicknames and silly nonce names for people, this seems plausible. I may say a name in a crowded room and three people look up.
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber]
     Full Idea: Being a 'singular term' is not a category in contemporary syntactic theory and it doesn't correspond to any of the notions employed there like that of a singular noun phrase or the like.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 02.3)
     A reaction: Hofweber has researched such things. This is an important objection to the reliance of modern Fregeans on the ontological commitments of singular terms (as proof that there are 'mathematical objects').
If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber]
     Full Idea: Identity between objects occurs in 'How Mary makes a chocolate cake is identical to how my grandfather used to make it', but does this show that 'how Mary makes a chocolate cake' aims to pick out an entity?
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 02.3)
     A reaction: This is a counterexample to the Fregean thought that the criterion for the existence of the referent of a singular term is its capacity to participate in an identity relation. Defenders of the Fregean view are aware of such examples.
5. Theory of Logic / G. Quantification / 1. Quantification
The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber]
     Full Idea: When we ask 'is there a number?' in its inferential role (or internalist) reading, then we ask whether or not there is a true instance of 't is a number'. When we ask in its domain conditions (externalist) reading, we ask if the world contains a number.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 03.6)
     A reaction: Hofweber's key distinction. The distinction between making truth prior and making reference prior is intriguing and important. The internalist version is close to substitutional quantification. Only the externalist view needs robust reference.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are used as singular terms, as adjectives, and as symbols [Hofweber]
     Full Idea: Number words have a singular term use, and adjectival (or determiner) use, and the symbolic use. The main question is how they relate to each other.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 05.1)
     A reaction: Thus 'the number four is even', 'there are four moons', and '4 comes after 3'.
The Amazonian Piraha language is said to have no number words [Hofweber]
     Full Idea: The now famous Piraha language, of the Amazon region in Brazil, allegedly has no number words.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 05.6)
     A reaction: Two groups can be shown to be of equal cardinality, by one-to-one matching rather than by counting. They could get by using 'equals' (and maybe unequally bigger and unequally smaller), and intuitive feelings for sizes of groups.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
     Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
     Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4)
     A reaction: The sequence is 'Cauchy' if N exists.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber]
     Full Idea: The prime numbers are more fundamental than the even numbers, and than the composite non-prime numbers. The result that all numbers uniquely decompose into a product of prime numbers is called the 'Fundamental Theorem of Arithmetic'.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 13.4.2)
     A reaction: I could have used this example in my thesis, which defended the view that essences are the fundamentals of explanation, even in abstract theoretical realms.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
How can words be used for counting if they are objects? [Hofweber]
     Full Idea: Number words as singular terms seem to refer to objects; numbers words in determiner or adjectival position are tied to counting. How these objects are related to counting is what the application problem is about.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.3)
     A reaction: You can't use stones for counting, so there must be more to numbers than the announcement that they are 'objects'. They seem to have internal relations, which makes them unusual objects.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
     Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7)
     A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
     Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
     Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate.
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
     Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicism makes sense of our ability to know arithmetic just by thought [Hofweber]
     Full Idea: Frege's tying the objectivity of arithmetic to the objectivity of logic makes sense of the fact that can find out about arithmetic by thinking alone.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.1)
     A reaction: This assumes that logic is entirely a priori. We might compare the geometry of land surfaces with 'pure' geometry. If numbers are independent objects, it is unclear how we could have any a priori knowledge of them.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber]
     Full Idea: A major flaw of the neo-Fregean program is that it is more impressed by the technical result that Peano Arithmetic can be interpreted by second-order logic plus Hume's Principle, than empirical considerations about how numbers come about.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.3)
     A reaction: This doesn't sound like a problem that would bother Fregeans or neo-Fregeans much. Deriving the Peano Axioms from various beginnings has become a parlour game for modern philosophers of mathematics.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
     Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1)
     A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
     Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names?
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1)
     A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up.
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
     Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2)
     A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare.
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
     Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2)
     A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
     Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1)
     A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
     Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1)
     A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
     Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise.
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
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.
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
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.
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Supervenience offers little explanation for things which necessarily go together [Hofweber]
     Full Idea: The results from the use of supervenience in philosophical theorising are limited. In particular, modal notions can't distinguish between things which necessarily go together. For example, that truths about numbers are grounded in truths about sets.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 13.4.1)
     A reaction: [compressed]
7. Existence / D. Theories of Reality / 3. Reality
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.
Reality can be seen as the totality of facts, or as the totality of things [Hofweber]
     Full Idea: Reality can be seen as everything that is the case - the totality of all facts that obtain - or reality can be seen as everything there is - the totality of all things that exist.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 10)
     A reaction: Things are a lot easier to specify than facts, but on the whole I prefer facts, just in order to affirm that there is more to reality than the mere 'things' that compose it. Our ontology must capture the dynamic and relational character of reality.
7. Existence / D. Theories of Reality / 4. Anti-realism
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.
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
There are probably ineffable facts, systematically hidden from us [Hofweber]
     Full Idea: We do have reason to think that there are ineffable facts, and that these facts are systematically hidden from us.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 10.2.4)
     A reaction: [Hofweber's Ch.10 is a lengthy and interesting discussion of ineffable facts] Things which are very very small, or very very remote in space seem obvious candidates. The most obvious candidates are tiny detail about the remote past.
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber]
     Full Idea: The belief that there are simples arranged chair-wise is not a perceptual belief. Our perceptual beliefs have a content about ordinary objects, not simples arranged chair-wise.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 07.3.1)
     A reaction: Hofweber gives ontological priority to 'perceptual beliefs'. I'm inclined to agree, but I hear the critical hordes swarming against the gate.
9. Objects / D. Essence of Objects / 5. Essence as Kind
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.
9. Objects / D. Essence of Objects / 9. Essence and Properties
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.
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals are essential for planning, and learning from mistakes [Hofweber]
     Full Idea: Counterfactuals are important for reasoning about the past and to plan for the future. If we want to learn from our mistakes, it is important to think about what would have happened if I had done things differently.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 13.4.1)
     A reaction: A thought also found in Tim Williamson, but not the sort of thing you hear from Lewis or Stalnaker. It is a nice example of how highly abstract and theoretical problems need to be slotted into human psychology.
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
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.
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
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.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
     Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1)
     A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
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.
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
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?
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
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.
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
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.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
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.
16. Persons / C. Self-Awareness / 2. Knowing the Self
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.
19. Language / A. Nature of Meaning / 1. Meaning
The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber]
     Full Idea: The picture of language often called the "Fido"-Fido theory of meaning says every expression in natural languages refers; they simply differ in what they refer to.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 08.2)
     A reaction: It seems obvious that at least there are syncategorematic terms like 'not' and 'or' and 'maybe' that are internal to language. I'm inclining to the opposite view of Paul Pietroski. Hofweber says if all words are names, they can't add up to truth.
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Inferential role semantics is an alternative to semantics that connects to the world [Hofweber]
     Full Idea: An inferential role semantics is generally seen as a large-scale alternative to a semantics based on reference and other language-world relations.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 03.4.5)
     A reaction: Presumably the other obvious language-world relation is truth. Being a robust realist, I take it I have to be strongly committed to semantics which connects to the world - or do I? Reality is robust, but our talk about it is evasive?
19. Language / C. Assigning Meanings / 1. Syntax
Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber]
     Full Idea: Syntactic form is not only related to the truth conditions of a sentence; it is also related to what focus an utterance of a sentence will have.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 02.5.2)
     A reaction: Hofweber has commendably studied some linguistics. The idea of mental and linguistic 'focus' increasingly strikes me as of importance in many areas of philosophy. E.g. in the scope of ethics, on whom should you focus?
19. Language / C. Assigning Meanings / 3. Predicates
Properties can be expressed in a language despite the absence of a single word for them [Hofweber]
     Full Idea: Simply because there is no single word in a certain language for a certain property doesn't mean that it isn't expressible in that language.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 09.1.1)
     A reaction: Good. For example a shade of blue for which there is no label might be 'the next darkest discriminable shade of blue adjacent to the one we are looking at'. And then the one after that... But 'tastes better than Diet Pepsi' in ancient Greek?
'Being taller than this' is a predicate which can express many different properties [Hofweber]
     Full Idea: It is said that not every property can be expressed because there are more properties than there are predicates. ...But the same predicate can be used to express many different properties: 'being taller than this' depends on what 'this' refers to.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 09.2)
     A reaction: A good example, but being a comparative and relying on a demonstrative indexical makes it a favourable example. 'Being made of iron' doesn't have much scope for expressing many properties.
19. Language / C. Assigning Meanings / 4. Compositionality
Compositonality is a way to build up the truth-conditions of a sentence [Hofweber]
     Full Idea: Compositional semantics assigns semantic values to various expressions in order to generate the truth conditions of the sentences in which they can occur correctly, ...thus leading to the truth-conditions of the sentence.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 08.3)
     A reaction: I favour both the compositional and the truth-conditional accounts of semantics, but I am not sure how to fit the pragmatic and contextual ingredient into that picture. You can't leave out psychology.
19. Language / D. Propositions / 1. Propositions
Proposition have no content, because they are content [Hofweber]
     Full Idea: If there propositions then they do not have content, because they are content.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 08.4)
     A reaction: This sounds right. A rather obvious regress threatens if you say otherwise.
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Without propositions there can be no beliefs or desires [Hofweber]
     Full Idea: If there are no propositions, then there are no contents, and thus there are no beliefs and desires.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 01.4.3)
     A reaction: A simple but powerful point. Those who claim that there are only sentences (and no propositions) can hardly claim that you must formulate a sentence every time you have a specific belief or desire.
19. Language / D. Propositions / 3. Concrete Propositions
Do there exist thoughts which we are incapable of thinking? [Hofweber]
     Full Idea: Might there be some thought token that has a different content than any such token we can in principle have?
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 10.3.3)
     A reaction: For me the idea that a thought might exist which can never be thought is an absurdity, but people who believe in the external existence of parts of reality called 'propositions' seem committed to it. A baffling view.
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber]
     Full Idea: 'Semantic type coercion' is where an expression of variable type is forced to take a particular type on a particular occasion so that the sentence as a whole in which it occurse is semantically interpretable.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 05.4.4)
     A reaction: He compares 'and' in 'John sang and Mary danced' with 'John and Mary danced together', where 'and' can vary in type, and we adopt the reading that makes sense. Hofweber says we do this with number language. He favours 'cognitive need'.
19. Language / F. Communication / 5. Pragmatics / b. Implicature
'Background deletion' is appropriately omitting background from an answer [Hofweber]
     Full Idea: 'Background deletion' is the pheomenon that what isn't focused in an answer, what is the background, can be left out of the answer, with the resulting sub-sentential answer nonetheless being appropriate.
     From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 02.6.2)
     A reaction: [I'm struck by the verbosity of this sentence, from an over-long book] It is not unreasonable to think that each conversational exchange has an implicit and agreed domain of quantification. Well, 'focus', then.
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
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]