23 ideas
| 12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
| Full Idea: That knowledge is worthiest which is charged with least multiplicity, which appeareth to be metaphysic | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.6) | |
| A reaction: A surprising view, coming from the father of modern science, but essentially correct. Obviously metaphysics aspires to avoid multiplicity, but it is riddled not only with complexity in its researches, but massive uncertainties. |
| 12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
| Full Idea: Knowledges are as pyramides, whereof history is the basis. So of natural philosophy, the basis is natural history, the stage next the basis is physic; the stage next the vertical point is metaphysic. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.6) | |
| A reaction: The father of modern science keeps a place for metaphysics, as the most abstract level above the physical sciences. I would say he is right. It leads to my own slogan: science is the servant of philosophy. |
| 12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
| Full Idea: Physic should contemplate that which is inherent in matter, and therefore transitory; and metaphysic that which is abstracted and fixed | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.3) | |
| A reaction: He cites the ancients for this view, with which he agrees. One could do worse than hang onto metaphysics as the study of necessities, but must then face the attacks of the Quineans - that knowledge of necessities is beyond us. |
| 12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
| Full Idea: Physic inquireth and handleth the material and efficient causes; and metaphysic handleth the formal and final causes. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.3) | |
| A reaction: Compare Idea 12119. This divides up Aristotle's famous Four Causes (or Explanations), outlined in 'Physics' II.3. The concept of 'matter', and the nature of 'cause' seem to me to fall with the purview of metaphysics. Interesting, though. |
| 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) |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 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. |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 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. |
| 12121 | We don't assume there is no land, because we can only see sea [Bacon] |
| Full Idea: They are ill discoverers that think there is no land, when they can see nothing but sea. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.5) | |
| A reaction: Just the sort of pithy remark for which Bacon is famous. It is an obvious point, but a nice corrective to anyone who wants to apply empirical principles in a rather gormless way. |
| 12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
| Full Idea: All true and fruitful natural philosophy hath a double scale or ladder, ascendent and descendent, ascending from experiments to the invention of causes, and descending from causes to the invention of new experiments. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.1) | |
| A reaction: After several hundred years, I doubt whether anyone can come up with a better account of scientific method than Bacon's. |
| 12127 | Many different theories will fit the observed facts [Bacon] |
| Full Idea: The ordinary face and view of experience is many times satisfied by several theories and philosophies. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VIII.5) | |
| A reaction: He gives as his example that the Copernican system and the Ptolemaic system both seem to satisfy all the facts. He wrote in 1605, just before Galileo's telescope. His point is regularly made in modern discussions. In this case, he was wrong! |
| 12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
| Full Idea: It is the nature of the mind of man (to the extreme prejudice of knowledge) to delight in the spacious liberty of generalities, as in a champaign region, and not in the inclosures of particularity. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VIII.1) | |
| A reaction: I have to plead guilty to this myself. He may have pinpointed the key motivation behind philosophy. We all want to know things, as Aristotle said, but some of us want the broad brush, and others want the fine detail. |
| 12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
| Full Idea: To say 'leaves are for protecting of fruit', or that 'clouds are for watering the earth', is well inquired and collected in metaphysic, but in physic they are impertinent. They are hindrances, and the search of the physical causes hath been neglected. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.7) | |
| A reaction: This is the standard rebellion against Aristotle which gave rise to the birth of modern science. The story has been complicated by natural selection, which bestows a sort of purpose on living things. Nowadays we pursue both paths. |
| 12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |
| Full Idea: I assign to summary philosophy the operation of essences (as quantity, similitude, diversity, possibility), with this distinction - that they be handled as they have efficacy in nature, and not logically. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.3) | |
| A reaction: I take this to be a splendid motto for scientific essentialism, in a climate where modal logicians appear to have taken over the driving seat in our understanding of essences. |