42 ideas
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
| 14480 | Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson] |
| Full Idea: It is a venerable view that analytic claims do not require truth-makers, as they place no demands on the world, but this claim has often been challenged. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.4) | |
| A reaction: She offers two challenges (bottom p.68), but I would have thought that the best response is that the meanings of the words themselves constitute truthmakers - perhaps via the essence of each word, as Fine suggests. |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: The interesting question is who is in charge - the mathematician or the logician? |
| 14471 | Analytical entailments arise from combinations of meanings and inference rules [Thomasson] |
| Full Idea: 'Analytically entail' means entail in virtue of the meanings of the expressions involved and rules of inference. So 'Jones bought a house' analytically entails 'Jones bought a building'. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 01.2) | |
| A reaction: Quine wouldn't like this, but it sounds OK to me. Thomasson uses this as a key tool in her claim that common sense objects must exist. |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| Full Idea: We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience. |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| Full Idea: Science must endeavour to make the circle of unprovable primitive truths as small as possible, for the whole of mathematics is contained in this kernel. The essence of mathematics has to be defined by this kernel of truths. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204-5) | |
| A reaction: [compressed] I will make use of this thought, by arguing that mathematics may be 'explained' by this kernel. |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| Full Idea: It is possible for a truth to be an axiom in one system and not in another. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: Frege aspired to one huge single system, so this is a begrudging concession, one which modern thinkers would probably take for granted. |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| Full Idea: The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria. |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| Full Idea: We cannot long remain content with the present fragmentation [of mathematics]. Order can be created only by a system. But to construct a system it is necessary that in any step forward we take we should be aware of the logical inferences involved. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| Full Idea: If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them. |
| 14493 | Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson] |
| Full Idea: A higher standard for saying that entities exist might require that they play an essential role in explanation, or must figure in any complete causal story, or exist according to some uniform and nonarbitrary principle of composition. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 11.2) | |
| A reaction: I am struck by the first of these three. If I am defending the notion that essence depends on Aristotle's account of explanation, then if we add that existence also depends on explanation, we get a criterion for the existence of essences. Yay. |
| 14491 | Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson] |
| Full Idea: Where there are analytic interrelations among our claims, distinct ontological claims may be true without rivalry, redundancy, or reduction. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 10) | |
| A reaction: Thus we might, I suppose, that it is analytically necessary that a lump of clay has a shape, and that a statue be made of something. Interesting. |
| 14489 | Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson] |
| Full Idea: A theory does not avoid commitment to any entities by avoiding use of certain terms or concepts. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.4) | |
| A reaction: This is a salutary warning to those who apply the notion of ontological commitment rather naively. |
| 14485 | Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson] |
| Full Idea: I do not argue that ordinary objects are indispensable, but rather that they are (nearly) unavoidable. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09) | |
| A reaction: Disappointing, given the blurb and title of the book, but put in those terms it will be hard to disagree. Clearly ordinary objects figure in the most useful way for us to talk. I wonder whether we have a clear ontology of 'simples' in which they vanish. |
| 14487 | The simple existence conditions for objects are established by our practices, and are met [Thomasson] |
| Full Idea: The existence conditions for ordinary objects are established by our practices, and they are quite minimal, so it is rather obvious that they are fulfilled, and so there are such things. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.3) | |
| A reaction: This is one of her main arguments. The same argument would have worked for witches or ghosts in certain cultures. |
| 21651 | It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber] |
| Full Idea: Thomasson argues that the existence of ordinary objects follows analytically from the distribution of simples, assuming that there are any simples. It is an analytic truth that if there are simples arranged chair-wise, then there is a chair. | |
| From: report of Amie L. Thomasson (Ordinary Objects [2007]) by Thomas Hofweber - Ontology and the Ambitions of Metaphysics 07.3 | |
| A reaction: But how do you distinguish when simples are arranged nearly chair-wise from the point where they click into place as actually chair-wise? What is the criterion? |
| 14486 | Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson] |
| Full Idea: The eliminativist cannot claim to have 'discovered' some real existence conditions for chairs beyond those entailed by the semantic rules associated with ordinary use of the word 'chair'. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.3) | |
| A reaction: It is difficult to understand atoms arranged 'chairwise' or 'baseballwise' if you don't already know what a chair or a baseball are. |
| 14467 | Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson] |
| Full Idea: Objections to ordinary objects are the Causal Redundancy claim (objects lack causal powers), the Anti-Colocation view (statues and lumps overlap), Sorites arguments, a more economical ontology, or a more scientific ontology. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], Intro) | |
| A reaction: [my summary of two paragraphs] The chief exponents of these views are Van Inwagen and Merricks. Before you glibly accept ordinary objects, you must focus on producing a really strict ontology. These arguments all have real force. |
| 14479 | To individuate people we need conventions, but conventions are made up by people [Thomasson] |
| Full Idea: The conventionalist faces paradox if they hold that conventions are logically prior to people (since this plurality requires conventions of individuation), and people are logically prior to conventions (if they make up the conventions). | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.3) | |
| A reaction: [Sidelle is the spokesman for conventionalism] The best defence would be to deny the second part, and say that conventions emerge from whatever is there, but only conventions can individuate the bits of what is there. |
| 14481 | Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson] |
| Full Idea: In a 'modally plenitudinous' ontology, wherever there is an object at all, there are objects with intrinsic modal properties instantiating every consistent modal profile. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.5) | |
| A reaction: [She cites K.Bennett, Hawley, Rea, Sidelle] I love this. At last a label for the view I have been espousing. I am a Modal Plenitudinist. I must get a badge made. |
| 14482 | If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson] |
| Full Idea: An objection to the idea that statues are not identical to material lumps of stuff is the proliferation of instances of properties shared by those objects. If the mass of the statue is 500kg, and the mass of the lump is 500kg, do we have 1000kg? | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 04.3) | |
| A reaction: [compressed; she cites Rea 1997 and Zimmerman 1995] To wriggle out of this we would have to understand 'object' rather differently, so that an independent mass is not intrinsic to it. I leave this as an exercise for the reader. |
| 14483 | Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson] |
| Full Idea: The 'grounding problem' is that given all that the statue and the lump have in common, what could possibly ground their different modal properties? | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 04.4) | |
| A reaction: Their modal properties are, of course, different, because only one of them could survive squashing. Thomasson suggests their difference of sort, but I'm not sure what that means, separately from what they actually are. |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| Full Idea: Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1 | |
| A reaction: This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision. |
| 14476 | Identity claims between objects are only well-formed if the categories are specified [Thomasson] |
| Full Idea: Identity claims are only well-formed and truth-evaluable if the terms flanking the statement are associated with a certain category of entity each is to refer to, which disambiguates the reference and identity-criteria. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03) | |
| A reaction: The first of her two criteria for identity. She is buying the full Wiggins package. |
| 14477 | Identical entities must be of the same category, and meet the criteria for the category [Thomasson] |
| Full Idea: Identity claims are only true if the entities referred to are of the same category, and meet the criteria of identity appropriate for things of that category. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03) | |
| A reaction: This may be a little too optimistic about having a set of clear-cut and reasonably objective categories to work with, but attempts at establishing metaphysical categories have not gone especially well. |
| 14478 | Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson] |
| Full Idea: Modal Conventionalism has at least three theses: 1) modal truths are either analytic truths, or combine analytic and empirical truths, 2) modal properties are not intrinsic features of the world, 3) modal propositions depend on linguistic conventions. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.2) | |
| A reaction: [She cites Alan Sidelle 1989 for this view] I disagree mainly with number 2), since I take dispositions to be key intrinsic features of nature, and I interpret dispositions as modal properties. |
| 14466 | A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson] |
| Full Idea: Showing how, reflectively, we can make sense of our unreflective common sense worldview is arguably one of the chief tasks of philosophy. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], Intro) | |
| A reaction: Maybe. The obvious problem is that when you look at weird and remote cultures like the Aztecs, what counts as 'common sense' might be a bit different. She is talking of ordinary objects, though, where her point is reasonable. |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| Full Idea: If we need such signs, we also need definitions so that we can cram this sense into the receptacle and also take it out again. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: Has anyone noticed that Frege is the originator of the idea of the mental file? Has anyone noticed the role that definition plays in his account? |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| Full Idea: We often need to use a sign with which we associate a very complex sense. Such a sign seems a receptacle for the sense, so that we can carry it with us, while being always aware that we can open this receptacle should we need what it contains. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: This exactly the concept of a mental file, which I enthusiastically endorse. Frege even talks of 'opening the receptacle'. For Frege a definition (which he has been discussing) is the assigment of a label (the 'definiendum') to the file (the 'definiens'). |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| Full Idea: No sense accrues to a sign by the mere fact that it is used in one or more sentences, the other constituents of which are known. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.213) | |
| A reaction: Music to my ears. I've never grasped how meaning could be grasped entirely through use. |
| 14475 | How can causal theories of reference handle nonexistence claims? [Thomasson] |
| Full Idea: Pure causal theories of reference have problems in handling nonexistence claims | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 02.3) | |
| A reaction: This is a very sound reason for shifting from a direct causal baptism view to one in which the baptism takes place by a social consensus. So there is a consensus about 'unicorns', but obviously no baptism. See Evans's 'Madagascar' example. |
| 14474 | Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson] |
| Full Idea: Pure causal theories of reference face the 'qua problem' - that it may be radically indeterminate what the term refers to unless there is some very basic concept of what sort of thing is being referred to. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 02.3) | |
| A reaction: She cites Dummett and Wiggins on this. There is an obvious problem that when I say 'look at that!' there are all sorts of conventions at work if my reference is to succeed. |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| Full Idea: A thought is not something subjective, is not the product of any form of mental activity; for the thought that we have in Pythagoras's theorem is the same for everybody. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: When such thoughts are treated as if the have objective (platonic) existence, I become bewildered. I take a thought (or proposition) to be entirely psychological, but that doesn't stop two people from having the same thought. |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| Full Idea: The sentence is of value to us because of the sense that we grasp in it, which is recognisably the same in a translation. I call this sense the thought. What we prove is not a sentence, but a thought. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: The 'sense' is presumably the German 'sinn', and a 'thought' in Frege is what we normally call a 'proposition'. So the sense of a sentence is a proposition, and logic proves propositions. I'm happy with that. |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| Full Idea: A sentence is generally a complex sign, so the thought expressed by it is complex too: in fact it is put together in such a way that parts of a thought correspond to parts of the sentence. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.207) | |
| A reaction: This is the compositional view of propositions, as opposed to the holistic view. |
| 14488 | Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson] |
| Full Idea: The analytic interrelations among elements of language become evident through redundancy. It is redundant to utter 'He bought a house and a building', since buying a house analytically entails that he bought a building. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.4) | |
| A reaction: This appears to concern necessary class membership. It is only linguistically redundant if the class membership is obvious. Houses are familiar, uranium samples are not. |