Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Barcan Formula and Metaphysics' and 'The History of the Jews'

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26 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
     Full Idea: The Barcan Formula and its converse gives expression to the most straightforward way of combining modal operators with classical quantification.
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1)
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
     Full Idea: The Barcan Formulas are a threat to 'actualism' in modal metaphysics, which seems regrettable since the Formulas are validated by standard modal logics, but clash with the plausible and attractive actualist view (that there are no merely possible things).
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1)
     A reaction: He notes that the Barcan Formulas 'appear to require quantification over possibilia'. So are you prepared to accept the 'possible elephant in your kitchen'? Conceptually yes, but actually no, I would have thought. So possibilia are conceptual.
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
     Full Idea: In accordance with the Barcan Formula we assume that if it is possible that Wittgenstein should have had a child, then something or other is possibly Wittgentein's child.
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §5)
     A reaction: Put like this it sounds unpersuasive. What is the something or other? Someone else's child? A dustbin? A bare particular? Wittgenstein's child? If it was the last one, how could it be Wittgenstein's child while only possibly being that thing?
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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)
'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)
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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)
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Serious Actualism says there are no facts at all about something which doesn't exist [Simchen]
     Full Idea: Serious Actualism is the view that in possible circumstances in which something does not exist there are no facts about it of any kind, including its very non-existence
     From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1 n4)
     A reaction: He suggests that the Converse Barcan Formula implies this view. It sounds comparable to the view of Presentism about time, that no future or past truthmakers exist right now. If a new square table were to exist, it would have four corners.
24. Political Theory / D. Ideologies / 10. Theocracy
In Mosaic legal theory, crimes are sins and sins are crimes [Johnson,P]
     Full Idea: In Mosaic legal theory, all breaches of the law offend God. All crimes are sins, just as all sins are crimes.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: This would seem to define Josephus called a 'theocracy'. Not just rule by a priesthood, but also an attempt to make civil law coincide with the teachings of sacred texts. But doing 80 m.p.h. on a motorway at 2 a.m. hardly seems like a sin.
Because human life is what is sacred, Mosaic law has no death penalty for property violations [Johnson,P]
     Full Idea: Where other codes provided the death penalty for offences against property, in Mosaic law no property offence is capital; human life is too sacred, where the rights of property alone are violated.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: We still preserve this idea in our law, and also in our culture, where we are keen to insist that catastrophes like earthquakes or major fires are measured almost entirely by the loss of life, not the loss of property. I approve.
25. Social Practice / A. Freedoms / 1. Slavery
The Pharisees undermined slavery, by giving slaves responsibility and status in law courts [Johnson,P]
     Full Idea: It is no accident that slavery among Jews disappeared with the rise of the Pharisees, as they insisted that all were equal before God in a court. Masters were no longer responsible for actions of slaves, so a slave had status, and slavery could not work.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: As in seventeenth century England, the rise of social freedom comes from religious sources, not social sources. A slave has status in the transcendent world of souls, despite being a nobody in the physical world.
25. Social Practice / B. Equalities / 3. Legal equality
Mosaic law was the first to embody the rule of law, and equality before the law [Johnson,P]
     Full Idea: Mosaic law meant that God ruled through his laws, and since all were equally subject to the law, the system was the first to embody the double merits of the rule of law and equality before the law.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: If this is correct, it seems to be a hugely important step, combined with Idea 1659, that revenge should be the action of a the state, not of the individual. They are the few simple and essential keys to civilization.
25. Social Practice / F. Life Issues / 1. Causing Death
Man's life is sacred, because it is made in God's image [Johnson,P]
     Full Idea: In Mosaic theology, man is made in God's image, and so his life is not just valuable, it is sacred.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: The obvious question is what exactly is meant by "in God's image". Physically, spiritually, intellectually, morally? I am guessing that the original idea was intellectual, because we are the only rational animal. The others seem unlikely, or arrogant.
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The Jews sharply distinguish human and divine, but the Greeks pull them closer together [Johnson,P]
     Full Idea: The Jews drew an absolute distinction between the human and the divine; the Greeks constantly elevated the human - they were Promethean - and lowered the divine.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: An intriguing observation. The Greek idea runs right through European culture, surfacing (for example) in 'Faust', or 'Frankenstein', or the films of James Cameron. I'm with the Greeks; I want to see how far humanity can be elevated.
29. Religion / B. Monotheistic Religion / 2. Judaism
A key moment is the idea of a single moral God, who imposes his morality on humanity [Johnson,P]
     Full Idea: The discovery of monotheism, and not just of monotheism but of a sole, omnipotent God actuated by ethical principles and seeking methodically to impose them on human beings, is one of the greatest turning-points in history, perhaps the greatest of all.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: 'Discovery' begs some questions, but when put like this you realise what a remarkable event it was. It is a good candidate for the most influential idea ever, even if large chunks of humanity, especially in the orient, never took to monotheism.
Sampson illustrates the idea that religious heroes often begin as outlaws and semi-criminals [Johnson,P]
     Full Idea: Sampson is the outstanding example of the point which the Book of Judges makes again and again, that the Lord and society are often served by semi-criminal types, outlaws and misfits, who become folk-heroes and then religious heroes.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: This illustrates nicely Nietzsche's claim, that the jews were responsible for his 'inversion of values', in which aristocratic virtues are downgraded, and the virtues of a good slave are elevated (though Sampson may not show that point so well!).
Isaiah moved Israelite religion away from the local, onto a more universal plane [Johnson,P]
     Full Idea: The works of Isaiah (740-700 BCE) mark the point at which the Israelite religion began to spiritualize itself, to move from a specific location in space and time on to the universalist plane.
     From: Paul Johnson (The History of the Jews [1987], Pt I)
     A reaction: This is necessary if any religion is going to make converts outside the local culture. The crucial step would be to disembody God, so that He cannot be represented by a statue. The difficulty is for him to be universal, but retain a 'chosen people'.
The Torah pre-existed creation, and was its blueprint [Johnson,P]
     Full Idea: The Torah was not just a book about God. It pre-existed creation, in the same way as God did. In fact, it was the blueprint of creation.
     From: Paul Johnson (The History of the Jews [1987], Pt III)
     A reaction: You can only become a 'people of the book' (which Moslems resented in Judaism, and then emulated) if you give this stupendously high status to your book. Hence Christian fundamentalism makes sense, with its emphasis on the divinity of the Bible.
Judaism involves circumcision, Sabbath, Passover, Pentecost, Tabernacles, New Year, and Atonement [Johnson,P]
     Full Idea: The practices of Judaism developed during their Exile: circumcision, the Sabbath, the Passover (founding of the nation), Pentecost (giving of the laws), the Tabernacles, the New Year, and the Day of Atonement.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: These were the elements of ritual created to replace the existence of a physically located state. An astonishing achievement, not even remotely achieved by any other state that was driven off its lands. A culture is an idea, not a country.
In exile the Jews became a nomocracy [Johnson,P]
     Full Idea: In exile the Jews, deprived of a state, became a nomocracy - voluntarily submitting to rule by a Law which could only be enforced by consent. Nothing like this had occurred before in history.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: It is the most remarkable case in history of a people united and strengthened by adversity, and it became an important experiment in the building of human cultures. But what is the point of preserving a culture, with no land? Why not just integrate?
29. Religion / B. Monotheistic Religion / 3. Zoroastrianism
Zoroastrians believed in one eternal beneficent being, Creator through the holy spirit [Johnson,P]
     Full Idea: Cyrus the Great was a Zoroastrian, believing in one, eternal, beneficent being, 'Creator of all things through the holy spirit'.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: Is this the actual origin of monotheism, or did they absorb this idea from the Jews? The interesting bit is the fact that the supreme being (called Marduk) is 'beneficent', which one doesn't associate with these remote and supposed pagans.
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Immortality based on judgement of merit was developed by the Egyptians (not the Jews) [Johnson,P]
     Full Idea: The idea of judgement at death and immortality on the basis of merit were developed in Egypt before 1000 BCE. It is not Jewish because it was not in the Torah, and the Sadducees, who stuck to their texts, seemed to have denied the afterlife completely.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: This is the idea considered crucial to religion by Immanuel Kant (Idea 1455), who should be declared an honorary Egyptian. To me the idea that only the good go to heaven sounds like sadly wishful thinking - a fictional consolation for an unhappy life.
The main doctrine of the Pharisees was belief in resurrection and the afterlife [Johnson,P]
     Full Idea: Belief in resurrection and the afterlife was the main distinguishing mark of Pharisaism, and thus fundamental of rabbinic Judaism.
     From: Paul Johnson (The History of the Jews [1987], Pt II)
     A reaction: Belief in an afterlife seems to go back to the Egyptians, but this development in Judaism was obviously very influential, even among early Christians, who initially seem to have only believed in resurrection of the body.
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
Pious Jews saw heaven as a vast library [Johnson,P]
     Full Idea: Pious Jews saw heaven as a vast library, with the Archangel Metatron as the librarian: the books in the shelves there pressed themselves together to make room for a newcomer.
     From: Paul Johnson (The History of the Jews [1987], Pt III)
     A reaction: I'm tempted to convert to Judaism.