31 ideas
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| Full Idea: Modal logic is not an extensional language. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.159 n8) | |
| A reaction: [I record this for investigation. Possible worlds seem to contain objects] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one. |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to? |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve. | |
| From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics. |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |
| A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
| 16664 | Everything that exists is either a substance or an accident [Albert of Saxony] |
| Full Idea: Everything that exists is either a substance or an accident. | |
| From: Albert of Saxony (On 'Physics' [1357], I.18), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.2 | |
| A reaction: This seems to be the view of those who base their ontology on first-order classical logic. The more austere reading of that makes the accidents into sets of substances, so it's just substances. All the non-substance stuff cries out for recognition. |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
| 16703 | God could make a successive thing so that previous parts cease to exist [Albert of Saxony] |
| Full Idea: Something can be conceived of as successive simpliciter, with respect to both its substance and its state. For example, if Socrates were continually made and made again by the First Cause, as the Seine flow, so nothing of what preexists remains. | |
| From: Albert of Saxony (On 'Physics' [1357], III.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.4 | |
| A reaction: This is precisely the problem that modern stage theory faces, of knowing how to connect the stages together. |
| 16699 | Successive entities just need parts to succeed one another, without their existence [Albert of Saxony] |
| Full Idea: For existence to hold of completely successive entities it is not required that their parts exist, but that one part succeed another, as a future part succeeds a past part. | |
| From: Albert of Saxony (On 'Physics' [1357], III.3 ad 2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3 | |
| A reaction: A nice move, but it doesn't quite solve it. How can non-existent things 'succeed one another'? It is worrying for metaphysics that some things have entirely different concepts of persistence from other things. |
| 14703 | Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter] |
| Full Idea: If we have a 'fixedly' operator F, then a sentence is fixedly actually true if it is true no matter which world is designated as actual (which 'he actually won in 2008' fails to be). Maybe '□' is superficial necessity, and FA is 'deep' necessity. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.2) | |
| A reaction: Gareth Evans distinguishes 'deep' from 'superficial' necessity. Humberstone and others introduced 'F'. Presumably FA is deeper because it has to pass a tougher test. |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |
| Full Idea: It seems apriori coherent that there could be a necessarily existing god, and that there could be no such god - but they can't both be true. Other examples include unprovable mathematical necessities | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.4) |
| 14704 | 2D semantics gives us apriori knowledge of our own meanings [Schroeter] |
| Full Idea: Generalized 2D semantics is meant to vindicate the traditional idea that we have apriori access to our own meanings through armchair reflection. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.1) | |
| A reaction: The idea is to split meaning in two, so that we know one part of it a priori. It is an unfashionably internalist view of meaning (which doesn't make it wrong!). |
| 14706 | Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter] |
| Full Idea: Your verdicts about whether the stuff on Twin Earth counts as water depends on whether you think of Twin Earth as a hypothesis about your actual environment or as a purely counterfactual possibility. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.2.3) | |
| A reaction: This is the 'two-dimensional semantics' approach to the Twin Earth problem, which splits meaning into two components. Whether you start from the actual world or from Twin Earth, you will rigidly designate the local wet stuff as 'water'. |
| 14711 | Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter] |
| Full Idea: In rationalist views of meaning, based on the 'golden triangle', to be competent with an expression is to be in an internal cognitive state that puts one in a position to identify its extension in any possible world based only on apriori reflection. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.1) | |
| A reaction: This looks like a proper fight-back against modern rampant externalism about meaning. All my intuitions are with internalism, which I think points to a more coherent overall philosophy. Well done, David Chalmers! Even if he is wrong. |
| 14717 | Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter] |
| Full Idea: Internalists take the notion of meaning to capture an aspect of an individual's current state of understanding, while externalists take the notion of meaning to reflect how an individual is embedded within her social and physical environment. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.4.3) | |
| A reaction: This idea also occurs in discussions of concepts (filed here under 'Thought'). |
| 14720 | Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter] |
| Full Idea: A semantic theory assigns semantic values (meanings) to particular expressions of the language. In contrast, a metasemantic theory explains why expressions have those semantic values, appealing to facts about speakers and communities. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 3.4) | |
| A reaction: Presumably some people only want the metasemantic version. I assume that the two are entangled, but I would vote for both. |
| 14695 | Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter] |
| Full Idea: Semantic theories explain how the truth or falsity of whole sentences depends on the meanings of their parts by stating rules governing the interpretation of subsentential expressions and their modes of combination. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: Somehow it looks as if the mystery of the whole business will still be missing if this project is ever successfully completed. Also one suspects that such a theory would be a fiction, rather than a description of actuality, which is too complex. |
| 14696 | Simple semantics assigns extensions to names and to predicates [Schroeter] |
| Full Idea: The simplest semantic frameworks assign extensions as semantic values of particular expressions. The extension of a name is the thing, of 'cool' is the set of cool things, and sets of ordered pairs for 2-place predicates. The sentence has T or F. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: The immediate well-known problem is different predicates with the same extensions, such as 'renate' and 'cordate'. Possible worlds semantics is supposed to be an improvement to cover this, and to give a semantics for modal talk as well. Sounds good. |
| 14697 | 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter] |
| Full Idea: A simple extensional semantics will assign the same semantic value to 'Roger Federer' and 'world's best tennis player', but they clearly differ in meaning, and if events had unfolded differently they would pick out different people. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: You would think that this would be too obvious to need pointing out, but it is clearly a view that had a lot of popularity before the arrival of possible worlds. |
| 14698 | Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter] |
| Full Idea: In standard possible worlds semantics, the semantic value of an expression is an 'intension', a function that assigns an extension to the expression 'at' every possible world. ...It keeps track of the 'modal profiles' of objects, kinds and properties. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: Personally I just don't buy a semantics which is entirely based on extensions, even if this has sorted out some more obvious problems of extensionality. When I say someone is 'my hero', I don't just mean to pick out a particular person. |
| 14699 | Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter] |
| Full Idea: In standard possible worlds semantics the semantic value of Hllary Clinton's utterance of 'I' will be the same as her utterance of 'Hillary Clinton'. But clearly the English word 'I' is not synonymous with the name 'Hillary Clinton'. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: This problem was spotted by Kaplan, and it has been a chief motivator for the creation of two-dimensional semantics, which some people have then extended into a complete semantic theory. No purely extensional semantics can be right. |
| 14709 | Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter] |
| Full Idea: In standard possible world semantics an expression's intension reflects the modal profile of an object, kind or property, which would establish an important constitutive connection between meanings and modal claims. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.1) | |
| A reaction: The central question becomes 'do you need to know a thing's modal profile in order to have a decent understanding of it?', but if you express it that way (my way), then what counts as 'decent' will be relative to all sorts of things. |
| 14719 | In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter] |
| Full Idea: A problem for a standard possible worlds analysis is that all necessary truths have precisely the same content (the function mapping every world to the True). Hesperus=Phosphorus has the same content as Hesperus=Hesperus-and-2+2=4. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 3.3) | |
| A reaction: If this is supposed to be a theory of meaning then it has gone very badly wrong indeed. Has modern semantics taken a wrong turning somewhere? Two-dimensionalism is meant to address some of these problems. |
| 14701 | Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter] |
| Full Idea: In a two-dimensional matrix we array possible circumstances of evaluation (worlds) along the horizontal axis, and possible contexts of utterance (world, person, time) along the vertical axis. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.2) | |
| A reaction: This is due to Stalnaker 1978, and is clearest in operation when applied to an indexical such as 'I' in 'I am President'. 'I' is a rigid designator, but depends on context. The grid is filled in with T or F for each utterance in each world. |
| 14702 | If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter] |
| Full Idea: At first glance necessity and possibility can be fully expressed by quantifying over all possible worlds, but this cannot capture 'Possibly everything actually red is also shiny'. This needs a double-indexed framework, with worlds playing two roles. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.1) | |
| A reaction: She points out that this also applies to tense logic, for the notion of 'now'. The point is that we not only need a set of possible worlds, but we also need a procedure (the 'Actuality' operator A or @) for picking out one of the worlds as special. |
| 14705 | Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter] |
| Full Idea: Perhaps our best way of understanding names and natural kind terms is that we have apriori access to currently associated reference-fixing criterion, but only a posteriori access to the associated modal profile. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.1) | |
| A reaction: This is the 'generalized' view of 2D semantics (covering everything, not just modals and indexicals). I know apriori what something is, but only study will reveal its possibilities. The actual world is easy to talk about, but possible worlds are harder. |
| 14715 | 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter] |
| Full Idea: Supporters of generalized two-dimensional semantics agree to defend apriori conceptual analysis in metaphysics, and that 2D captures meaning and not just belief-patterns, and it gives a broadly internalist approach to reference determination. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.4) | |
| A reaction: I'm not sure I can evaluate this, but I sort of like conceptual analysis, and the concept of meaning, and fairly internalist views of reference, so I am ripe for the picking. |
| 14716 | 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter] |
| Full Idea: It is objected to 2D semantics that it cannot explain Kripke's cases of contingent apriori truths, for there is no single proposition (construed as a set of possible worlds) that is both apriori and contingent. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.4.2) | |
| A reaction: This sounds like a rather large objection to the whole 2D plan, if it implies that when we say something there is no single proposition that is being expressed. |
| 16570 | Elements are found last in dismantling bodies, and first in generating them [Albert of Saxony] |
| Full Idea: On one possible description, an element is what is found last when bodies are taken apart, and what is found first when bodies are generated. | |
| From: Albert of Saxony (On 'Generation and Corruption' [1356], II.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 2.1 |