42 ideas
| 21634 | 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. |
| 21666 | '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). |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 21640 | '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'?' |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 21657 | 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. |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 21653 | 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. |
| 21636 | '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'). |
| 21637 | 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. |
| 21643 | 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. |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 21644 | 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'. |
| 21646 | 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. |
| 21665 | 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. |
| 21649 | 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. |
| 21647 | 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. |
| 21648 | 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. |
| 21664 | 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] |
| 21660 | 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. |
| 21661 | 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. |
| 21652 | 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. |
| 16079 | De re modal predicates are ambiguous [Lewis, by Rudder Baker] |
| Full Idea: Lewis is perhaps the most prominent proponent of the view that de re modal predicates are ambiguous. | |
| From: report of David Lewis (Survival and Identity, with postscript [1983]) by Lynne Rudder Baker - Why Constitution is not Identity n25 |
| 21663 | 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. |
| 21654 | 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. |
| 21641 | 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? |
| 21638 | 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? |
| 21658 | 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? |
| 21659 | '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. |
| 21655 | 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. |
| 21656 | 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. |
| 21635 | 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. |
| 21662 | 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. |
| 21645 | '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'. |
| 21639 | '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. |