19 ideas
| 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. |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| Full Idea: Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1) | |
| A reaction: This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results. |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| Full Idea: Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9) | |
| A reaction: As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful. |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| Full Idea: In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1) | |
| A reaction: This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns. |
| 6303 | Sets are positions in patterns [Resnik] |
| Full Idea: On my view, sets are positions in certain patterns. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5) | |
| A reaction: I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties. |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| Full Idea: If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology. |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| Full Idea: I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject. |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| Full Idea: Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3) | |
| A reaction: This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component? |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| Full Idea: An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4) | |
| A reaction: This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns. |
| 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? |
| 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. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |