29 ideas
| 18335 | There are five problems which the truth-maker theory might solve [Rami] |
| Full Idea: It is claimed that truth-makers explain universals, or ontological commitment, or commitment to realism, or to the correspondence theory of truth, or to falsify behaviourism or phenomenalism. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 04) | |
| A reaction: [compressed] This expands the view that truth-making is based on its explanatory power, rather than on its intuitive correctness. I take the theory to presuppose realism. I don't believe in universals. It marginalises correspondence. Commitment is good! |
| 18334 | The truth-maker idea is usually justified by its explanatory power, or intuitive appeal [Rami] |
| Full Idea: The two strategies for justifying the truth-maker principle are that it has an explanatory role (for certain philosophical problems and theses), or that it captures the best philosophical intuition of the situation. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 04) | |
| A reaction: I would go for 'intuitive', but not in the sense of a pure intuition, but with 'intuitive' as a shorthand for overall coherence. To me the appeal of truth-maker is its place in a naturalistic view of reality. I love explanation, but not here. |
| 18339 | The truth-making relation can be one-to-one, or many-to-many [Rami] |
| Full Idea: The truth-making relation can be one-to-one, or many-many. In the latter case, different truths may have the same truth-maker, and one truth may have different truth-makers. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 05) | |
| A reaction: 'There is at least one cat' obviously has many possible truth-makers. Many statements will be made true by the mere existence of a particular cat (such as 'there is an animal in the room' and 'there is a cat in the room'). Many-many wins? |
| 18333 | Central idea: truths need truthmakers; and possibly all truths have them, and makers entail truths [Rami] |
| Full Idea: The main full-blooded truth-maker principle is that x is true iff there is a y that is its truth-maker. This implies the principles that if x is true x has a truth-maker, and the principle that if x has a truth-maker then x is true. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 03) | |
| A reaction: [compressed] Rami calls the second principle 'maximalism' and the third principle 'purism'. To reject maximalism is to hold a more restricted version of truth-makers. That is, the claim is that lots of truths have truth-makers. |
| 18342 | Most theorists say that truth-makers necessitate their truths [Rami] |
| Full Idea: Most truth-maker theorists regard the necessitation of a truth by a truth-maker as a necessary condition of truth-making. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 07) | |
| A reaction: It seems to me that reality is crammed full of potential truth-makers, but not crammed full of truths. If there is no thinking in the universe, then there are no truths. If that is false, then what sort of weird beast is a 'truth'? |
| 18340 | It seems best to assume different kinds of truth-maker, such as objects, facts, tropes, or events [Rami] |
| Full Idea: Truthmaker anti-monism holds the view that there are truth-makers of different kinds. For example, objects, facts, tropes or events can all be regarded as truthmakers. Objects seem right for existential truths but not others, so anti-monism seems best. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 05) | |
| A reaction: Presumably we need to identify the different types of truth (analytic, synthetic, general, particular...), and only then ask what truth-makers there are for the different types. To presuppose one type of truthmaker would be crazy. |
| 18341 | Truth-makers seem to be states of affairs (plus optional individuals), or individuals and properties [Rami] |
| Full Idea: As truth-makers, some theorists only accept states of affairs, some only accept individuals and states of affairs, and some only accept individuals and particular properties. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 06) | |
| A reaction: It seems to me rash to opt for one of these. Truths come in wide-ranging and subtly different types, and the truth-makers probably have a similar range. Any one of these theories will almost certainly quickly succumb to a counterexample. |
| 18346 | 'Truth supervenes on being' only gives necessary (not sufficient) conditions for contingent truths [Rami] |
| Full Idea: The thesis that 'truth supervenes on being' (with or without possible worlds) offers only a necessary condition for the truth of contingent propositions, whereas the standard truth-maker theory offers necessary and sufficient conditions. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 09) | |
| A reaction: The point, I suppose, is that the change in being might be irrelevant to the proposition in question, so any old change in being will not ensure a change in the truth of the proposition. Again we ask - but what is this truth about? |
| 18345 | 'Truth supervenes on being' avoids entities as truth-makers for negative truths [Rami] |
| Full Idea: The important advantage of 'truth supervenes on being' is that it can be applied to positive and negative contingent truths, without postulating any entities that are responsible for the truth of negative truths. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 09) | |
| A reaction: [For this reason, Lewis favours a possible worlds version of the theory] I fear that it solves that problem by making the truth-maker theory so broad-brush that it not longer says very much, apart from committing it to naturalism. |
| 18343 | Maybe a truth-maker also works for the entailments of the given truth [Rami] |
| Full Idea: The 'entailment principle' for truth-makers says that if x is a truth-maker for y, and y entails z, then x is a truth-maker for z. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 08) | |
| A reaction: I think the correct locution is that 'x is a potential truth-maker for z' (should anyone every formulate z, which in most cases they never will, since the entailments of y are probably infinite). Merricks would ask 'but are y and z about the same thing?'. |
| 18338 | Truth-making is usually internalist, but the correspondence theory is externalist [Rami] |
| Full Idea: Most truth-maker theorists are internalists about the truth-maker relation. ...But the correspondence theory makes truth an external relation to some portion of reality. So a truth-maker internalist should not claim to be a narrow correspondence theorist. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 05) | |
| A reaction: [wording rearranged] Like many of Rami's distinctions in this article, this feels simplistic. Sharp distinctions can only be made using sharp vocabulary, and there isn't much of that around in philosophy! |
| 18337 | Correspondence theories assume that truth is a representation relation [Rami] |
| Full Idea: One guiding intuition concerning a correspondence theory of truth says that the relation that accounts for the truth of a truth-bearer is some kind of representation relation. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 05) | |
| A reaction: I unfashionably cling on to some sort of correspondence theory. The paradigm case is of a non-linguistic animal which forms correct or incorrect views about its environment. Truth is a relation, not a property. I see the truth in a bad representation. |
| 18347 | Deflationist truth is an infinitely disjunctive property [Rami] |
| Full Idea: According to the moderate deflationist truth is an infinitely disjunctive property. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 10) | |
| A reaction: [He cites Horwich 1998] That is, I presume, that truth is embodied in an infinity of propositions of the form '"p" is true iff p'. |
| 18350 | Truth-maker theorists should probably reject the converse Barcan formula [Rami] |
| Full Idea: There are good reasons for the truth-maker theorist to reject the converse Barcan formula. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], note 16) | |
| A reaction: In the text (p.15) Rami cites the inference from 'necessarily everything exists' to 'everything exists necessarily'. [See Williamson 1999] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer. |
| 18336 | Internal relations depend either on the existence of the relata, or on their properties [Rami] |
| Full Idea: An internal relation is 'existential' if x and y relate in that way whenever they both exist. An internal relation is 'qualitative' if x and y relate in that way whenever they have certain intrinsic properties. | |
| From: Adolph Rami (Introduction: Truth and Truth-Making [2009], 05) | |
| A reaction: [compressed - Rami likes to write these things in fashionable quasi-algebra, but I have a strong prejudice in this database for expressing ideas in English; call me old-fashioned] The distinction strikes me as simplistic. I would involve dispositions. |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6 | |
| A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea. |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example). | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology. |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power. |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives. |