23 ideas
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
| A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
| Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4) | |
| A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point. |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3) | |
| A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him. |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1) | |
| A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm. |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
| A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| Full Idea: Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2) | |
| A reaction: Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads. |
| 12056 | An ancestral relation is either direct or transitively indirect [Wiggins] |
| Full Idea: x bears to y the 'ancestral' of the relation R just if either x bears R to y, or x bears R to some w that bears R to y, or x bears R to some w that bears R to some z that bears R to y, or..... | |
| From: David Wiggins (Substance [1995], 4.10.1) | |
| A reaction: A concept invented by Frege (1879). |
| 12050 | Substances contain a source of change or principle of activity [Wiggins] |
| Full Idea: Substances are things that have a source of change or principle of activity within them. | |
| From: David Wiggins (Substance [1995], 4.4.1) | |
| A reaction: A vey significant concession. I think we can talk of 'essences' and 'powers', and drop talk of 'substances'. 'Powers' is a much better word, because it immediately pushes the active ingredient to the forefront. |
| 12052 | We never single out just 'this', but always 'this something-or-other' [Wiggins] |
| Full Idea: What is singled out is never a bare this or that, but this or that something or other. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: I like, in ontological speculation, to contemplate the problem of the baffling archaeological find. 'This thing I have dug up - what the hell IS it?'. Wiggins is contemptuous of the term 'thisness', and the idea of bare particulars. |
| 12055 | Sortal predications are answers to the question 'what is x?' [Wiggins] |
| Full Idea: Predications which answer the question 'what is x?' are often called 'sortal predications' in present-day philosophy. | |
| From: David Wiggins (Substance [1995], 4.10.1) | |
| A reaction: The word 'sortal' comes from Locke. Wiggins is the guru of 'sortal essentialism'. I just can't believe that in answer to the question 'what really is David Wiggins?' that he would be happy with a sequence of categorisations. |
| 12059 | A river may change constantly, but not in respect of being a river [Wiggins] |
| Full Idea: To say that the river is changing constantly in every respect is not to say that it is changing in respect of being a river. | |
| From: David Wiggins (Substance [1995], 4.11.2) | |
| A reaction: Can't a river become a lake, or a mere stream? Wiggins's proposal does not help with the problem of a river which sometimes dries up (as my local river sometimes does). At what point do we decide it is no longer a river? |
| 12063 | Sortal classification becomes science, with cross reference clarifying individuals [Wiggins] |
| Full Idea: The sense of the sortal term under which we pick out an individual expands into the scientific account of things of that kind, where the account clarifies what is at issue in questions of sameness and difference of specimens of that kind. | |
| From: David Wiggins (Substance [1995], 4.13.1) | |
| A reaction: This is how the sortal approach is supposed to deal with individuals. So the placid tiger reveals much by falling under 'tiger', and a crucial extra bit by falling under 'placid'. See Idea 12053 for problems with this proposal. |
| 12051 | If the kinds are divided realistically, they fall into substances [Wiggins] |
| Full Idea: Substance are what the world is articulated into when the segments of kinds corresponds to the real divisions in reality. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: This is very helpful in clarifying Wiggins's very obscurely expressed views. He appears to be saying that if we divide the sheep from the goats correctly, we reveal sheep-substance and goat-substance (one substance per species). Crazy! |
| 12053 | 'Human being' is a better answer to 'what is it?' than 'poet', as the latter comes in degrees [Wiggins] |
| Full Idea: One person can be more or less of a poet than another, so 'poet' is not a conclusory answer to the question 'What is it that is singled out here?' 'Poet' rides on the back of the answer 'human being'. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: So apparently one must assign a natural kind, and not just a class. Wiggins lacks science fiction imagination. In the genetic salad of the far future, being a poet may be more definitive than being a human being. See Idea 12063. |
| 12054 | Secondary substances correctly divide primary substances by activity-principles and relations [Wiggins] |
| Full Idea: A system of secondary substances with a claim to separate reality into its genuine primary substances must arise from an understanding of a set of principles of activity on the basis of which identities can be glossed in terms of determinate relations. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: I translate this as saying that individual essences are categorised according to principles which explain behaviour and relations. I'm increasingly bewildered by the 'secondary substances' Wiggins got from 'Categories', and loves so much. |
| 12047 | We refer to persisting substances, in perception and in thought, and they aid understanding [Wiggins] |
| Full Idea: A substance is a persisting and somehow basic object of reference that is there to be discovered in perception and thought, an object whose claim to be recognized as a real entity is a claim on our aspirations to understand the world. | |
| From: David Wiggins (Substance [1995], 4.1) | |
| A reaction: A lot of components are assigned by Wiggins to the concept, and the tricky job, inititiated by Aristotle, is to fit all the pieces together nicely. Personally I am wondering if the acceptance of 'essences' implies dropping 'substances'. |
| 12057 | Matter underlies things, composes things, and brings them to be [Wiggins] |
| Full Idea: Matter ex hypothesi is what ultimately underlies (to huperkeimenon) a thing; it is that from which something comes to be and which remains as a non-coincidental component in the thing's make-up. | |
| From: David Wiggins (Substance [1995], 192a30) | |
| A reaction: This is an interesting prelude to the much more comprehensive discussion of matter in Metaphysics, where he crucially adds the notion of 'form', and gives it priority over the underlying matter. |
| 12064 | The category of substance is more important for epistemology than for ontology [Wiggins] |
| Full Idea: For us the importance of the category of substance, if it has any importance, is not so much ontological as relative to our epistemological circumstances and the conditions under which we have to undertake inquiry. | |
| From: David Wiggins (Substance [1995], 4.13.2) | |
| A reaction: This seems to be a rather significant concession. Wiggins has revived the notion of substance in recent times, but he is not quite adding it to the furniture of the world. Personally I increasingly think we can dump it, in ontology and epistemology. |
| 12049 | Naming the secondary substance provides a mass of general information [Wiggins] |
| Full Idea: Answering 'what is it?' with the secondary substance identifies an object with a class of continuants which survive certain changes, come into being in certain ways, are qualified in certain ways, behave in certain ways, and cease to be in certain ways. | |
| From: David Wiggins (Substance [1995], 4.3.3) | |
| A reaction: Thus the priority of this sort of answer is that a huge range of explanations immediately flow from it. I take the explanation to be prior, and the primary substance to be prior, since secondary substance is inductively derived from it. |
| 12065 | Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins] |
| Full Idea: It seems mandatory to an observer of soldiers to give 'the final touch of unity' to their aggregate entity (the army). ...Similar claims arise with the ontological and explanatory claims of other corporate entities. | |
| From: David Wiggins (Substance [1995], 4.13.3) | |
| A reaction: Wiggins must say (following Leibniz Essays II.xxiv,1) that we add the unity, but I take the view that an army has powers, and hence offers explanations, which are lacking in a merely group of disparate soldiers. So an army has an essence and identity. |