34 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. |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
| A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
| A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
| 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. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 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. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 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'. |
| 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. |
| 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. |
| 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. |