15 ideas
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 16641 | Whiteness does not exist, but by it something can exist-as-white [Aquinas] |
| Full Idea: Whiteness is said to exist not because it subsists in itself, but because by it something has existence-as-white. | |
| From: Thomas Aquinas (Quodlibeta [1267], IX.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.2 | |
| A reaction: It seems unavoidable to refer to the whiteness as 'it'. It might be called the 'adverbial' theory of properties, as ways of doing something. |
| 4304 | Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham] |
| Full Idea: Descartes was a dualist about substance, Spinoza was a monist, and Leibniz was a pluralist (an infinity of substances). | |
| From: John Cottingham (The Rationalists [1988], p.76) | |
| A reaction: Spinoza is appealing. We posit a substance, as the necessary basis for existence, but it is unclear how more than one substance can be differentiated. If mind is a separate substance, why isn't iron? Why aren't numbers? |
| 22170 | Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas] |
| Full Idea: Our imagination and senses grasp only the outer properties of things, not their natures. ...Understanding, however, grasps the very substance and nature of things, so that what is represented in understanding is a likeness of thing's very essence. | |
| From: Thomas Aquinas (Quodlibeta [1267], 8.2.2) | |
| A reaction: This is exactly the picture I endorse for modern science. Explanation is the path to understanding, and that must venture beyond immediate experience. |
| 22169 | Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas] |
| Full Idea: For present in us by nature are certain initial truths everyone knows, in which lie potentially known conclusions our reasons can draw out and make actually known. | |
| From: Thomas Aquinas (Quodlibeta [1267], 8.2.2) | |
| A reaction: Note that these are truths rather than concepts, but that they have to be 'drawn out' by reason. This is Descartes' view of the matter, where the 'natural light' of reason is needed to articulate what is innate, such as geometry. |
| 22168 | Minds take in a likeness of things, which activates an awaiting potential [Aquinas] |
| Full Idea: What the mind takes in is not some material element of the agent, but a likeness of the agent actualising some potential the patient already has. This, for example, is the way our seeing takes in the colour of a coloured body. | |
| From: Thomas Aquinas (Quodlibeta [1267], 8.2.1) | |
| A reaction: This is exactly right. Descartes agreed. It works for colour, but not (obviously) for cheese graters. |
| 4303 | The notion of substance lies at the heart of rationalist metaphysics [Cottingham] |
| Full Idea: The notion of substance lies at the heart of rationalist metaphysics. | |
| From: John Cottingham (The Rationalists [1988], p.75) | |
| A reaction: The idea of 'substance' has had an interesting revival in modern philosophy (though not, obviously, in physics). Maybe physics and philosophy have views of reality which are not complementary, but are rivals. |
| 4306 | For rationalists, it is necessary that effects be deducible from their causes [Cottingham] |
| Full Idea: The rationalist view of causation takes it that to make effects intelligible, it must be shown that they are in principle deducible from their causes. | |
| From: John Cottingham (The Rationalists [1988], p.92) | |
| A reaction: This has intuitive appeal, but deduction is only possible with further premises, such as the laws of physics. The effects of human behaviour look a bit tricky, even if we cause them. |