16 ideas
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
From: Melvin Fitting (Intensional Logic [2007], 3) | |
A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
From: Melvin Fitting (Intensional Logic [2007], 3.3) |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
A reaction: [He cites Fagin and Halpern 1988 for this] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
Full Idea: Quine charges that the axiom of Reducibility both undoes the effect of the ramification, and commits the theory to a platonist view of propositional functions (which is a theory of sets, once use/mention confusions are cleared up). | |
From: report of Willard Quine (Set Theory and its Logic [1963], p.249-58) by Bernard Linsky - Russell's Metaphysical Logic 6.1 |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
From: Melvin Fitting (Intensional Logic [2007], §1) |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
12756 | Substance is a force for acting and being acted upon [Leibniz] |
Full Idea: The very substance in things consists of a force for acting and being acted upon. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §08) | |
A reaction: Garber places this text just before the spiritual notion of monads took a grip on Leibniz. He seems to have thought that only some non-physical entity, with appetite and perception, could generate force. Wrong. |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
12755 | Final causes can help with explanations in physics [Leibniz] |
Full Idea: Final causes not only advance virtue and piety in ethics and natural theology, but also help us to find and lay bare hidden truths in physics itself. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §04) | |
A reaction: This rearguard action against the attack on teleology is certainly aimed at Spinoza. The notion of purpose still seems to have a role to play in evolutionary biology, but probably not in physics. |
12760 | Something rather like souls (though not intelligent) could be found everywhere [Leibniz] |
Full Idea: Nor is there any reason why souls or things analogous to souls should not be everywhere, even if dominant and consequently intelligent souls, like human souls, cannot be everywhere. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12) | |
A reaction: He is always flirting with panpsychism, though he doesn't seem to offer any account of how these little baby souls can be built up to create one intelligent soul, the latter being indivisible. 'Souls' are very different from things 'analous to souls'! |
12759 | There are atoms of substance, but no atoms of bulk or extension [Leibniz] |
Full Idea: Although there are atoms of substance, namely monads, which lack parts, there are no atoms of bulk [moles], that is, atoms of the least possible extension, nor are there any ultimate elements, since a continuum cannot be composed out of points. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §11) | |
A reaction: Leibniz has a constant battle for the rest of his career to explain what these 'atoms of substance' are, since they have location but no extension, they are self-sufficient yet generate force, and are non-physical but interact with matter. |
12718 | Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz] |
Full Idea: I understand matter as either secondary or primary. Secondary matter is, indeed, a complete substance, but it is not merely passive; primary matter is merely passive, but it is not a complete substance. So we must add a soul or form... | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |
A reaction: It sounds as if primary matter is redundant, but Garber suggests that secondary matter is just the combination of primary matter with form. |
11854 | If there is some trace of God in things, that would explain their natural force [Leibniz] |
Full Idea: If the law of God does indeed leave some vestige of him expressed in things...then it must be granted that there is a certain efficacy residing in things, a form or force such as we usually designate by the name of nature, from which the phenomena follow. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §06) | |
A reaction: I wouldn't rate this as a very promising theory of powers, but it seems to me important that Leibniz recognises the innate power in things as needing explanation. If you remove divine power, you are left with unexplained intrinsic powers. |
12758 | It is plausible to think substances contain the same immanent force seen in our free will [Leibniz] |
Full Idea: If we attribute an inherent force to our mind, a force acting immanently, then nothing forbids us to suppose that the same force would be found in other souls or forms, or, if you prefer, in the nature of substances. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §10) | |
A reaction: This is the kind of bizarre idea that you are driven to, once you start thinking that God must have a will outside nature, and then that we have the same thing. Why shouldn't such a thing pop up all over the place? Only Leibniz spots the slippery slope. |
19408 | To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz] |
Full Idea: To say that nature itself or the substance of all things is God is a pernicious doctrine, recently introduced into the world or renewed by a subtle or profane author. | |
From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], 8) | |
A reaction: The dastardly profane author is, of course, Spinoza, whom Leibniz had met in 1676. The doctrine may be pernicious to religious orthodoxy, but to me it is rather baffling, since in my understanding nature and God have almost nothing in common. |