20 ideas
| 14231 | We should always apply someone's theory of meaning to their own utterances [Liggins] |
| Full Idea: We should interpret philosophers as if their own theory of the meaning of their utterances were true, whether or not we agree with that theory. | |
| From: David Liggins (Nihilism without Self-Contradiction [2008], 8) | |
| A reaction: This seems to give legitimate grounds for some sorts of ad hominem objections. It would simply be an insult to a philosopher not to believe their theories, and then apply them to what they have said. This includes semantic theories. |
| 17325 | Truth-maker theory can't cope with non-causal dependence [Liggins] |
| Full Idea: My charge is that truth-maker theory cannot be integrated into an attractive general account of non-causal dependence. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.6) | |
| A reaction: [You'll have to read Liggins to see why] |
| 17318 | Truthmakers for existence is fine; otherwise maybe restrict it to synthetic truths? [Liggins] |
| Full Idea: Many philosophers agree that true existential propositions have a truth-maker, but some go further, claiming that every true proposition has a truth-maker. More cautious theorists specify a class of truths, such as synthetic propositions. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.1) | |
| A reaction: [compressed; Armstrong is the ambitious one, and Rodriguez-Pereyra proposes the synthetic propositions] Presumably synthetic propositions can make negative assertions, which are problematic for truth-makers. |
| 14232 | We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins] |
| Full Idea: It is quite standard to interpret sentences of the form 'There are Fs' using a singular quantifier and a singular predicate, but this tradition may be mistaken. | |
| From: David Liggins (Nihilism without Self-Contradiction [2008], 8) | |
| A reaction: Liggins is clearly in support of the use of plural quantification, referring to 'there are some xs such that'. |
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
| From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
| From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
| A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 17320 | Either p is true or not-p is true, so something is true, so something exists [Liggins] |
| Full Idea: Either p or not-p. If p, then the proposition 'p' is true. If not p, then the proposition 'not p' is true. Either way, something is true. Thus something exists. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.3 n5) | |
| A reaction: Liggins offers this dodgy argument as an objection to conceptual truths having truth-makers. |
| 17326 | The dependence of {Socrates} on Socrates involves a set and a philosopher, not facts [Liggins] |
| Full Idea: The dependence of {Socrates} on Socrates appears to involve a set and a philosopher, neither of which is a fact. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.6) | |
| A reaction: He points out that defenders of facts as the basis of dependence could find a suitable factual paraphrase here. Socrates is just Socrates, but the singleton has to be understood in a particular way to generate the dependence. |
| 17327 | Non-causal dependence is at present only dimly understood [Liggins] |
| Full Idea: Non-causal dependence is at present only dimly understood. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.8) | |
| A reaction: Not very helpful, you may be thinking, but it is always helpful to know where we have got to in the enquiry. |
| 17322 | Necessities supervene on everything, but don't depend on everything [Liggins] |
| Full Idea: Necessities supervene upon everything, but they do not depend on everything. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.4) | |
| A reaction: I'm not sure if merely existing together counts as sufficiently close to be 'supervenience'. If 2+2 necessitates 4, that hardly seems to 'supervene' on the Eiffel Tower. If so, how close must things be to qualify for supervenience? |
| 14233 | Nihilists needn't deny parts - they can just say that some of the xs are among the ys [Liggins] |
| Full Idea: We can interpret '..is a part of..' as '..are among..': the xs are a part of the ys just when the xs are among the ys (though if the ys are 'one' then they would not have parts). | |
| From: David Liggins (Nihilism without Self-Contradiction [2008], 9) | |
| A reaction: The trouble is that this still leaves us with gerrymandered 'parts', in the form of xs that are scattered randomly among the ys. That's not what we mean by 'part'. No account of identity works if it leaves out coherent structure. |
| 17324 | 'Because' can signal an inference rather than an explanation [Liggins] |
| Full Idea: 'Because' can signal an inference rather than an explanation. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.5) | |
| A reaction: Aristotle starts from words like 'why?', but it can be a deceptive approach to explanation. |
| 17321 | Value, constitution and realisation are non-causal dependences that explain [Liggins] |
| Full Idea: 'It is wrong because it produces pain for fun', and 'these constitute a table because they are arranged tablewise', and 'tea is poisonous because it contains arsenic' are clearly non-causal uses of 'because', and neither are they conceptual. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.4) | |
| A reaction: The general line seems to be that any form of determination will underwrite an explanation. He talks later of the 'wrongmaker' and 'poisonmaker' relationships to add to the 'truthmaker'. The table example is the 'object-maker' dependence relation. |
| 17323 | If explanations track dependence, then 'determinative' explanations seem to exist [Liggins] |
| Full Idea: If explanation often tracks dependence, then we have a theoretical reason to expect such explanations to exist. Let us call such explanations 'determinative'. | |
| From: David Liggins (Truth-makers and dependence [2012], 10.4) | |
| A reaction: There seems to be an emerging understanding that this 'determination' relation is central to all of explanation - with causal explanations, for example, being a particular instance of it. I like it. These are real, not conventional, explanations. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |