31 ideas
| 23770 | Reductive analysis makes a concept clearer, by giving an alternative simpler set [Williams,NE] |
| Full Idea: A reductive analysis is one that provides an alternative set of concepts by which some target concept can be understood. It must be non-circular, and given in terms of concepts that are themselves better understood. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 01.2) | |
| A reaction: There seem to be two aims of analysis: this one emphasises understanding, but the other one concerns ontology - by demonstrating that some concept or thing can be understood fully by what happens at a lower level. |
| 23769 | Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE] |
| Full Idea: The form of argument which sells an ontology on the basis a metaphysic is known as an 'argument-by-display'. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 01.2) | |
| A reaction: [Attributed to John Bigelow 1999] New to me, but I'm quite a fan of this. For example, my rejection of platonism is not based on specific arguments, but on looking at the whole platonic picture of reality. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 23783 | Change exists, it is causal, and it needs an explanation [Williams,NE] |
| Full Idea: There is a phenomenon of change. I am starting with the assumptions that it is a causal phenomenon, and that it requires explanation. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 06.1) | |
| A reaction: That is, I take it, that we need a theory which explains change, rather than just describing it. Well said. Williams says, roughly, that each stage causes the next stage. |
| 23784 | Processes don't begin or end; they just change direction unexpectedly [Williams,NE] |
| Full Idea: No process every really starts or ends. …A process we see as derailed is really just an expected sequence that continues in an unexpected direction. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 06.3) | |
| A reaction: Obviously if you cannot individuate processes, then the concept of a process is not much use in ontology. Williams rejects processes, and I think he is probably right. He breaks processes down into smaller units. |
| 23790 | Processes are either strings of short unchanging states, or continuous and unreducible events [Williams,NE] |
| Full Idea: Processes can be modelled in two ways. They are drawn out events encompassing many changes, but dissectible into short-lived states, none including change. Or they are continuous and impenetrable, and to split them is impossible. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 09.3) | |
| A reaction: Obviously a process has temporal moments in it, so the unsplittability is conceptual. I find the concept of changeless parts baffling. But if processes are drawn out, they can't be basic to ontology. |
| 23768 | A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE] |
| Full Idea: A metaphysic is what you get when you embed a fundamental ontology within a larger metaphysical framework by repeatedly appealing to elements of that ontology in explaining metaphysical phenomena. …Only then do you see what the ontology is worth. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 01.1) | |
| A reaction: Confirming my mantra that metaphysics is an explanatory activity. I think it is important that the ontology includes relations (such as 'determinations'), and is not just an inventory of types of entity. |
| 23773 | Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE] |
| Full Idea: The main components of neo-Humean metaphysics are that properties are inherently non-modal and passive, that what is possible is restricted only by imagination and coherence, that laws are non-governing descriptions, and causation is weak and extrinsic. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 02.1) | |
| A reaction: This is Williams identifying the enemy, prior to offering the much more active and restictive powers ontology. I'm with Williams. |
| 23779 | We shouldn't posit the existence of anything we have a word for [Williams,NE] |
| Full Idea: There seems to be a mysterious desire to posit entities simply because certain terms pop up in our vocabulary. But we should not be so indiscriminate about our posits, even if our talk is properly vetted. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 04.1) | |
| A reaction: This should hardly need saying, and the familiar example is 'for the sake of' entailing sakes, but it seems to be a vice that is still found in metaphysical philosophy. The word 'nothingness' comes to mind. |
| 23786 | The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE] |
| Full Idea: The status quo is part of what exists, and thus it is a proper topic of concern for the metaphysician, and so it warrants explanation. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 07.2) | |
| A reaction: His point is that ontology as a mere inventory of things gives no account of why they remain unchanged, as well as their processes and connections. |
| 23775 | Powers are 'multi-track' if they can produce a variety of manifestations [Williams,NE] |
| Full Idea: Powers are 'multi-track', meaning that they are capable of producing a variety of different manifestations when me with diverse stimuli. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 03.1) | |
| A reaction: He later mentions magnetism. Not convinced of this. Powers probably never exist in isolation, so a different manifestation could be because a different power becomes involved. (Bird is a single-tracker). |
| 23780 | Every possible state of affairs is written into its originating powers [Williams,NE] |
| Full Idea: On the model of powers I prefer, every possible state of affairs that can arise is written into the powers that would constitute them. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 04.3) | |
| A reaction: I can't make any sense of 'written into', any more than I could when Leibniz proposed roughly the same thing about monads. I presume he means that any state of affairs which ever arises is the expression of the intrinsic nature of powers. |
| 23789 | Naming powers is unwise, because that it usually done by a single manifestation [Williams,NE] |
| Full Idea: Naming powers is unwise; the main reason is that there is a long tradition of naming powers according to the manifestations they can produce, and that does not square well with multi-track powers. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 08.4) | |
| A reaction: On the other hand there must be some attempt to individuate powers (by scientists, if not by philosophers), and that can only rely on the manifestations. Describe them, rather than name them? Just assign them a number! |
| 23771 | Fundamental physics describes everything in terms of powers [Williams,NE] |
| Full Idea: Physics describes fundamental entities exclusively in terms of what sound like powers. 'Charge' names the power to produce electromagnetic fields; 'spin' the power to contribute to the angular momentum of of system; 'mass' to produce gravitational force. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 01.4) | |
| A reaction: These are the three basic properties of an electron, which is fundamental in the standard model. You can say that their field is more fundamental than the particles, but the field is also only known as a set of powers. Powers rule! |
| 23776 | Rather than pure powers or pure categoricals, I favour basics which are both at once [Williams,NE] |
| Full Idea: Power Monism: all properties are powers. Categoricalism: all fundamentals are categorical. Dualism allows both types. I defend Mixed Monism - that there is a single class of fundamental properties that are at once powerful and categorical. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 03.3) | |
| A reaction: This is the main dilemma for the powers ontology - of how powers can be basic, if there needs to be some entity which possesses the power. But what possesses the powers of an electron? I like Williams's idea, without being clear about it. |
| 23777 | Powers are more complicated than properties which are always on display [Williams,NE] |
| Full Idea: The mode in which a power presents itself is more complicated than those properties that have (strictly) nothing more to them than that which is always on display. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 03.3) | |
| A reaction: This is the key idea that nature is dynamic, and so must consist of potentials as well as actuals. Interesting distinction. A basic division between those properties 'always on display', and those that are not? |
| 23774 | There are basic powers, which underlie dispositions, potentialities, capacities etc [Williams,NE] |
| Full Idea: It is no surprise that talk of dispositions, capacities, abilities, tendencies, powers, and potentialities are part of our everyday interactions. …I have in mind a basic set of powers, the sort which underlie all of these. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 03.1) | |
| A reaction: This strikes me as the correct picture. It is misleading say that a ball has a 'power' to roll smoothly. The powers are inside the ball. |
| 23791 | Dispositions are just useful descriptions, which are explained by underlying powers [Williams,NE] |
| Full Idea: Powers are the properties at the core of the powers ontology, and dispositions are more like useful talk. …Dispositions are the phenomena to be explained by the power metaphysic. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 10.2) | |
| A reaction: The picture I subscribe to. The first step is to see nature as dynamic (as Aristotle does with his 'potentialities'), and the next step to understand what must ground these dynamic dispositional properties. He calls dispositions 'process initiators'. |
| 23772 | If objects are property bundles, the properties need combining powers [Williams,NE] |
| Full Idea: If objects are bundles of properties …they must be robust enough to enter into building relations with one another such that they can form objects. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 01.5) | |
| A reaction: A very nice point. The Humean bundle view of objects just seems to take properties to be 'impressions' or verbal predicates, but they must have causal powers to be a grounding for ontology. |
| 23788 | Four-Dimensional is Perdurantism (temporal parts), plus Eternalism [Williams,NE] |
| Full Idea: 'Perdurantism' is the view that objects persist by being composed of temporal parts. When it is commonly combined with the eternalist account of the ontology of time, the result is known as 'four-dimensionalism'. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 08.1) | |
| A reaction: At last, a clear account of the distinction between these two! They're both wrong. He says the result is the spatiotemporal 'worm' view (i.e. one temporal extended thing, rather than a collection of parts). |
| 23782 | Causation is the exercise of powers [Williams,NE] |
| Full Idea: Causation is the exercising of powers. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 06.1) | |
| A reaction: Job done. Get over it. This is the view I prefer. |
| 23785 | Causation needs to explain stasis, as well as change [Williams,NE] |
| Full Idea: I believe that it is also the job of a theory of causation to explain non-change | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 07.2) | |
| A reaction: Good point. Most attempts to pin down causation refer only to changes and differences. Two playing cards propping one another up is his example. |
| 23787 | If causes and effects overlap, that makes changes impossible [Williams,NE] |
| Full Idea: It would be shocking if an account of causation ruled out the possibility of change. But if a cause perfectly overlaps its effect in time, then the rejection of change is precisely what follows. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 07.6) | |
| A reaction: He cites Kant, Martin, Heil and Mumford/Anjum for this view. The latter seem to see causation as a 'process' (allowing change), which Williams as ruled out. The Williams point must be correct. |
| 23778 | Powers contain lawlike features, pointing to possible future states [Williams,NE] |
| Full Idea: Powers carry their lawlike features within them: it is part of their essence, qua power. Their pointing at future states just is their internal law-like nature; it is what gets expressed in such and such conditions. | |
| From: Neil E. Williams (The Powers Metaphysics [2019], 03.3) | |
| A reaction: Modern writers on powers seem unaware that Leibniz got there first. This seems to me the correct account of the ontology of laws. The formulation of laws is probably the best descriptive system for nature's patterns (over time as well as space). |
| 9287 | Bruno said that ancient Egyptian magic was the true religion [Bruno, by Yates] |
| Full Idea: Giordano Bruno maintained that the magical Egyptian religion of the world was not only the most ancient but also the only true religion, which both Judaism and Christianity had obscured and corrupted. | |
| From: report of Giordano Bruno (works [1590]) by Frances A. Yates - Giordano Bruno and Hermetic Tradition Ch.1 | |
| A reaction: His beliefs were based on the Hermetic writings. No wonder he was burned at the stake. Atheists now lay flowers at his memorial in Rome. The sixteenth century was when the hunt for alternatives to established religion began. |