40 ideas
| 7490 | Because of Darwin, wisdom as a definite attainable state has faded [Watson] |
| Full Idea: As well as killing the need for God, Darwin's legacy transformed the idea of wisdom, as some definite attainable state, however far off. | |
| From: Peter Watson (Ideas [2005], Ch.31) | |
| A reaction: Where does this leave philosophy, if it is still (as I like to think) the love of wisdom? The best we can hope for is wisdom as a special sort of journey - touring, rather than arriving. |
| 7461 | The three key ideas are the soul, Europe, and the experiment [Watson] |
| Full Idea: The three key ideas that I have settled on in the history of ideas are: the soul, Europe, and the experiment. | |
| From: Peter Watson (Ideas [2005], Intro) | |
| A reaction: The soul is a nice choice (rather than God). 'Europe' seems rather vast and indeterminate to count as a key idea. |
| 7464 | The big idea: imitation, the soul, experiments, God, heliocentric universe, evolution? [Watson] |
| Full Idea: Candidates for the most important idea in human history are: mimetic thinking (imitation), the soul, the experiment, the One True God, the heliocentric universe, and evolution. | |
| From: Peter Watson (Ideas [2005], Ch.03) | |
| A reaction: From this list I would choose the heliocentric universe, because it so dramatically downgraded the importance of our species (effectively we went from everything to nothing). We still haven't recovered from the shock. |
| 7465 | Babylonian thinking used analogy, rather than deduction or induction [Watson] |
| Full Idea: In Babylon thought seems to have worked mainly by analogy, rather than by the deductive or inductive processes we use in the modern world. | |
| From: Peter Watson (Ideas [2005], Ch.04) | |
| A reaction: Analogy seems to be closely related to induction, if it is comparing instances of something. Given their developments in maths and astronomy, they can't have been complete strangers to the 'modern' way of thought. |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
|
Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
|
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
| A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 7466 | Mesopotamian numbers applied to specific things, and then became abstract [Watson] |
| Full Idea: To begin with, in Mesopotamia, counting systems applied to specific commodities (so the symbol for 'three sheep' applied only to sheep, and 'three cows' applied only to cows), but later words for abstract qualities emerged. | |
| From: Peter Watson (Ideas [2005], Ch.04) | |
| A reaction: It seems from this that we actually have a record of the discovery of true numbers. Delightful. I think the best way to describe what happened is that they began to spot patterns. |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3) |
| 7477 | Modern democracy is actually elective oligarchy [Watson] |
| Full Idea: What we regard as democracy in the twenty-first century is actually elective oligarchy. | |
| From: Peter Watson (Ideas [2005], Ch.06) | |
| A reaction: Even dictatorships want to be called 'democracies'. The modern system is a bit of a concession to Plato, and he would probably have preferred it to his system, because at least the rulers tend to be more educated than the direct assembly. |
| 7478 | Greek philosophers invented the concept of 'nature' as their special subject [Watson] |
| Full Idea: Greek philosophers may have invented the concept of 'nature' to underline their superiority over poets and religious leaders. | |
| From: Peter Watson (Ideas [2005], Ch.06) | |
| A reaction: Brilliant. They certainly wrote a lot of books entitled 'Peri Physis' (Concerning Nature), and it was the target of their expertise. A highly significant development, along with their rational methods. Presumably Socrates extends nature to include ethics. |
| 5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |
| Full Idea: The four major disputes in classical cosmology were whether the cosmos is 'open' or 'closed', whether it is explained mechanistically or teleologically, whether it is alive or mere matter, and whether or not it has a beginning. | |
| From: report of T.M. Robinson (Classical Cosmology (frags) [1997]) by PG - Db (ideas) | |
| A reaction: A nice summary. The standard modern view is closed, mechanistic, inanimate and non-eternal. But philosophers can ask deeper questions than physicists, and I say we are entitled to speculate when the evidence runs out. |
| 7462 | DNA mutation suggests humans and chimpanzees diverged 6.6 million years ago [Watson] |
| Full Idea: The basic mutation rate in DNA is 0.71 percent per million years. Working back from the present difference between human and chimpanzee DNA, we arrive at 6.6 million years ago for their divergence. | |
| From: Peter Watson (Ideas [2005], Ch.01) | |
| A reaction: This database is committed to evolution (a reminder that even databases have commitments), and so facts of this kind are included, even though they are not strictly philosophical. All complaints should be inwardly digested and forgotten. |
| 7470 | During the rise of civilizations, the main gods changed from female to male [Watson] |
| Full Idea: Around the time of the rise of the first great civilizations, the main gods changed sex, as the Great Goddess, or a raft of smaller goddesses, were demoted and male gods took their place. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: Why? War, perhaps? |
| 7474 | Hinduism has no founder, or prophet, or creed, or ecclesiastical structure [Watson] |
| Full Idea: Traditional Hinduism has been described as more a way of living than a way of thought; it has no founder, no prophet, no creed and no ecclesiastical structure. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: This contrast strikingly with all later religions, which felt they had to follow the Jews in becoming a 'religion of the book', with a sacred text, and hence a special status for the author(s) of that text. |
| 7479 | Modern Judaism became stabilised in 200 CE [Watson] |
| Full Idea: The Judaism we know today didn't become stabilized until roughly 200 CE. | |
| From: Peter Watson (Ideas [2005], Ch.07) | |
| A reaction: By that stage it would have been subject to the influences of Christianity, ancient Greek philosophy, and neo-Platonism. |
| 7481 | The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson] |
| Full Idea: Archaeology offers datable figures that seem to support the idea that the Israelites of the 'second exile' period converted Yahweh into a special, single God to justify their claims to the land. | |
| From: Peter Watson (Ideas [2005], Ch.07) | |
| A reaction: The implications for middle eastern politics of this wicked observation are beyond the remit of a philosophy database. |
| 7480 | Monotheism was a uniquely Israelite creation within the Middle East [Watson] |
| Full Idea: No one questions the fact that monotheism was a uniquely Israelite creation within the Middle East. | |
| From: Peter Watson (Ideas [2005], Ch.07) | |
| A reaction: I take the Middle East to exclude Greece, where they were developing similar ideas. Who knows? |
| 7471 | The Gathas (hymns) of Zoroastrianism date from about 1000 BCE [Watson] |
| Full Idea: The Gathas, the liturgical hymns that make up the 'Avesta', the Zoroastrian canon, are very similar in language to the oldest Sanskrit of Hinduism, so they are not much younger than 1200 BCE. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: This implies a big expansion of religion before the well-known expansion of the sixth century BCE. |
| 7473 | Zoroaster conceived the afterlife, judgement, heaven and hell, and the devil [Watson] |
| Full Idea: Life after death, resurrection, judgement, heaven and paradise, were all Zoroastrian firsts, as were hell and the devil. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: He appears to be the first 'prophet'. |
| 7483 | Paul's early writings mention few striking episodes from Jesus' life [Watson] |
| Full Idea: Paul's writings - letters mainly - predate the gospels and yet make no mention of many of the more striking episodes that make up Jesus' life. | |
| From: Peter Watson (Ideas [2005], Ch.07) | |
| A reaction: This is not proof of anything, but it seems very significant if we are trying to get at the facts about Jesus. |
| 7484 | Jesus never intended to start a new religion [Watson] |
| Full Idea: Jesus never intended to start a new religion. | |
| From: Peter Watson (Ideas [2005], Ch.08) | |
| A reaction: An intriguing fact, which makes you wonder whether any of the prophets ever had such an intention. |
| 7475 | Confucius revered the spiritual world, but not the supernatural, or a personal god, or the afterlife [Watson] |
| Full Idea: Confucius was deeply religious in a traditional sense, showing reverence towards heaven and an omnipresent spiritual world, but he was cool towards the supernatural, and does not seem to have believed in either a personal god or an afterlife. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: The implication is that the spiritual world was very remote from us, and beyond communication. Sounds like deism. |
| 7476 | Taoism aims at freedom from the world, the body, the mind, and nature [Watson] |
| Full Idea: Underlying Taoism is a search for freedom - from the world, from the body, from the mind, from nature. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: Of all the world's religions, I think Taoism is the most ridiculouly misconceived. |
| 7463 | The three basic ingredients of religion are: the soul, seers or priests, and ritual [Watson] |
| Full Idea: Anthropologist distinguish three requirements for religion: a non-physical soul which can survive death; individuals who can receive supernatural inspiration; and rituals which can cause changes in the present world. | |
| From: Peter Watson (Ideas [2005], Ch.01) | |
| A reaction: The latter two, of course, also imply belief in supernatural powers. |
| 7468 | In ancient Athens the souls of the dead are received by the 'upper air' [Watson] |
| Full Idea: An official Athenian war monument of 432 BCE says the souls of the dead will be received by the aither (the 'upper air'), though their bodies remain on earth. | |
| From: Peter Watson (Ideas [2005], Ch.05) | |
| A reaction: Intriguing. Did they think anything happened when they got there? There are also ideas about Hades, and the Isles of the Blessed floating around. |