Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'New System and Explanation of New System' and 'Existentialism: an introduction'

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18 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenologists say all experience is about something and is directed [Aho]
     Full Idea: Phenomenologists agree that all experience has an intentional structure, that is, my experience is always about or of something; it is always directed towards an object.
     From: Kevin Aho (Existentialism: an introduction [2014], 2 'Phenomenology')
     A reaction: I am just beginning to grasp that the analytic debates about perception are a re-enactment of the Kantian debates about the thing-in-itself. This is the sort of idea you find in McDowell. Presumably the idea denies the Given, and raw sense-data.
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)
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Reality must be made of basic unities, which will be animated, substantial points [Leibniz]
     Full Idea: A multiplicity can only be made up of true unities, ..so I had recourse to the idea of a real and animated point, or an atom of substance which must embrace some element of form or of activity in order to make a complete being.
     From: Gottfried Leibniz (New System and Explanation of New System [1696], p.116)
     A reaction: This seems to be a combination of logical atomism and panpsychism. It has a certain charm, but looks like another example of these rationalist speculators overreaching themselves.
14. Science / B. Scientific Theories / 2. Aim of Science
Science has to abstract out the subjective attributes of things, focusing on what is objective [Aho]
     Full Idea: Crucial to the scientific method is the ability to abstract out the subjective qualities that we give to things - such as beauty, meaning, purpose, and value - and focus only on the objective qualities of things, which can be measured and quantified.
     From: Kevin Aho (Existentialism: an introduction [2014], 1 'Emergence')
     A reaction: This seems to me exactly right. People who deny the primary/secondary distinction, like Hume, are usually correspondingly pessimistic about science. And Hume was wrong about that.
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
No machine or mere organised matter could have a unified self [Leibniz]
     Full Idea: By means of the soul or form, there is a true unity which is called the 'I' in us; a thing which could not occur in artificial machines, nor in the simple mass of matter, however organised it may be.
     From: Gottfried Leibniz (New System and Explanation of New System [1696], p.120)
     A reaction: I think the unity of consciousness and the unified Self are different phenomena. A wonderful remark about artificial intelligence for 1696! Note the idea of functionalism contained in 'organised'. Personally I see the brain as a 'mass of matter'.
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
The soul does know bodies, although they do not influence one another [Leibniz]
     Full Idea: I do not admit that the soul does not know bodies, although this knowledge arises without their influencing one another.
     From: Gottfried Leibniz (New System and Explanation of New System [1696], Reply 11)
     A reaction: He couldn't very well admit this without moving into pure idealism. Presumably it is like "I know her - she'll be in Harrods this morning". I wonder if Satan could steal my body, but my mind continue to believe it was still there?
23. Ethics / F. Existentialism / 3. Angst
Anxiety, nausea, guilt and absurdity shake us up, revealing our freedom and limits [Aho]
     Full Idea: Some moods, such as 'anxiety' (Heidegger), 'nausea' (Sartre), 'guilt' (Kierkegaard), and 'absurdity' (Camus) are important because they have the capacity to shake us out of complacency and self-deception, disclosing our freedom and finitude.
     From: Kevin Aho (Existentialism: an introduction [2014], Pref 'What?)
     A reaction: [bit compressed] Problem: if I fail to feel such things, and deliberately induce them in myself, am I being inauthentic? Making a huge and unnatural effort to be an existentialist seems all wrong. And who wants the permanent grip of such feelings?
23. Ethics / F. Existentialism / 5. Existence-Essence
Our 'existence' is how we create ourselves, unconstrained by any prior 'essence' [Aho]
     Full Idea: 'Existence precedes essence' means there is no pre-given 'essence' that determines who and what we are. We are self-making beings.
     From: Kevin Aho (Existentialism: an introduction [2014], Pref 'What?)
     A reaction: This not a yes/no dilemma. Personally I believe (with Aristotle, and Steven Pinker) that there is a fairly comprehensive 'human nature' which we all share, and is the basis of ethics. On top of that, though, a fair bit of 'self-making' can go on.
23. Ethics / F. Existentialism / 6. Authentic Self
The self is constituted by its choices made within a social context [Aho]
     Full Idea: The [existential] self is constituted by the continuous, open-ended process of choosing and pulling together the social interpretations that we care about and that are made available by the situation we grow into.
     From: Kevin Aho (Existentialism: an introduction [2014], 4 'Self')
     A reaction: These kind of explanations always seem wrong. That the self is influenced and moulded strongly by the choices it makes sounds right. But that the choices 'constitute' the chooser sounds like a bit of a muddle.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Social contracts and markets have made society seem disconnected and artificial [Aho]
     Full Idea: Modern society has come to be viewed as something artificial, an aggregate of disconnected individuals that is held together by instrumental social contracts and monetary exchanges.
     From: Kevin Aho (Existentialism: an introduction [2014], 1 'Emergence')
     A reaction: This is all long of you, Thomas Hobbes! Aho is explaining the rebellion of existentialists against this - though existentialism strikes me as another variant of liberal individualism.
27. Natural Reality / G. Biology / 2. Life
To regard animals as mere machines may be possible, but seems improbable [Leibniz]
     Full Idea: It seems to me that the opinion of those who transform or degrade the lower animals into mere machines, although it seems possible, is improbable, and even against the order of things.
     From: Gottfried Leibniz (New System and Explanation of New System [1696], p.116)
     A reaction: His target is Descartes. 'Against the order of things' seems to beg the question. What IS the order of things? Only a thorough-going dualist would worry about this question, and that isn't me.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Protestantism brought the modern emphasis on inner states of the soul [Aho]
     Full Idea: An important development in the formation of the modern worldview was the emergence of Protestantism, that reconfigured the self by privileging the inner states of the soul. Salvation concerns inner feelings, thoughts and desires, which can be genuine.
     From: Kevin Aho (Existentialism: an introduction [2014], 1 'Emergence')
     A reaction: [bit compressed] He is preparing the historical background for the existentialist concept of authenticity. We can link this Protestant idea with Descartes's Cogito, which grounds knowledge in the inner self.
29. Religion / C. Spiritual Disciplines / 3. Buddhism
Four Noble Truths: life is suffering, caused by attachment, it is avoidable, there is a path [Aho]
     Full Idea: The teachings of the Buddha are summarised in 'four noble truths': 1) life means suffering, 2) the origin of suffering is attachment, 3) the end of suffering is attainable, and 4) the path to the end of suffering.
     From: Kevin Aho (Existentialism: an introduction [2014], 9 'dukkha')
     A reaction: 1) and 2) summarise everything I dislike about most eastern philosophy. In the modern world life does not have to be suffering. To break off attachments in order to avoid suffering is a hideous injunction.