19 ideas
| 1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
| Full Idea: Twelfth mode: all reasoning leads on to further reasoning, and this process goes on forever. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
| Full Idea: Fifteenth mode: proofs often presuppose the thing to be proved. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
| Full Idea: Fourteenth mode: reasoning requires arbitrary faith in preliminary hypotheses. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
| Full Idea: Eleventh mode: all topics of discussion are full of uncertainty and contradiction. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 10911 | Part-whole is the key relation among truth-makers [Mulligan/Simons/Smith] |
| Full Idea: The most important (ontological) relations holding among truth-makers are the part and whole relations. | |
| From: Mulligan/Simons/Smith (Truth-makers [1984], §6) | |
| A reaction: Hence Peter Simons goes off and writes the best known book on mereology. Looks very promising to me. |
| 10909 | Truth-makers cannot be the designata of the sentences they make true [Mulligan/Simons/Smith] |
| Full Idea: Truth-makers cannot be the designata of the sentences they make true, because sentences with more than one truth-maker would then be ambiguous, and 'a' and 'a exists' would have the same designatum. | |
| From: Mulligan/Simons/Smith (Truth-makers [1984], §3) |
| 10906 | Moments (objects which cannot exist alone) may serve as truth-makers [Mulligan/Simons/Smith] |
| Full Idea: A 'moment' is an existentially dependent or non-self-sufficient object, that is, an object which is of such a nature that it cannot exist alone, ....... and we suggest that moments could serve as truth-makers. | |
| From: Mulligan/Simons/Smith (Truth-makers [1984], §2) | |
| A reaction: [These three writers invented the term 'truth-maker'] |
| 10907 | The truth-maker for a sentence may not be unique, or may be a combination, or several separate items [Mulligan/Simons/Smith] |
| Full Idea: A proposition may have a minimal truth-maker which is not unique, or a sentence may be made true by no single truth-maker but only by several jointly, or again only by several separately. | |
| From: Mulligan/Simons/Smith (Truth-makers [1984], §3) |
| 10912 | Despite negative propositions, truthmakers are not logical complexes, but ordinary experiences [Mulligan/Simons/Smith] |
| Full Idea: Because of negative propositions, investigators of truth-makers have said that they are special non-objectual entities with a logical complexity, but we think a theory is possible in which the truth relation is tied to ordinary and scientific experience. | |
| From: Mulligan/Simons/Smith (Truth-makers [1984], §6) |
| 10908 | Correspondence has to invoke facts or states of affairs, just to serve as truth-makers [Mulligan/Simons/Smith] |
| Full Idea: The correspondence theory of truth invokes a special category of non-objectual entities - facts, states of affairs, or whatever - simply to serve as truth-makers. | |
| From: Mulligan/Simons/Smith (Truth-makers [1984], §3) |
| 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) |
| 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. |
| 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. |
| 8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
| Full Idea: Agrippa's Trilemma offers three possible outcomes for a regress of justification: the chain goes on for ever (infinite); or the chain stops at an unjustified proposition (arbitrary); or the chain eventually includes the original proposition (circular). | |
| From: report of Agrippa (fragments/reports [c.60], §2) by Michael Williams - Without Immediate Justification §2 | |
| A reaction: This summarises Ideas 1911, 1913 and 1914. Agrippa's Trilemma is now a standard starting point for modern discussions of foundations. Personally I reject 2, and am torn between 1 (+ social consensus) and 3 (with a benign, coherent circle). |
| 1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |
| Full Idea: Thirteenth mode: everything is always perceived in relation to something else. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |