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All the ideas for 'Philosophy of Mathematics', 'A World of Dispositions' and 'Quaestiones Disputatae de Malo'

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25 ideas

2. Reason / A. Nature of Reason / 1. On Reason
We are coerced into assent to a truth by reason's violence [Aquinas]
     Full Idea: We are coerced into assent to a truth by reason's violence.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.10)
2. Reason / A. Nature of Reason / 4. Aims of Reason
The mind is compelled by necessary truths, but not by contingent truths [Aquinas]
     Full Idea: Mind is compelled by necessary truths that can't be regarded as false, but not by contingent ones that might be false.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 12)
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
3. Truth / A. Truth Problems / 3. Value of Truth
For the mind Good is one truth among many, and Truth is one good among many [Aquinas]
     Full Idea: Good itself as taken in by mind is one truth among others, and truth itself as goal of mind's activity is one good among others.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
     Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world.
     From: J.H. Fetzer (A World of Dispositions [1977], Intro)
     A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'.
9. Objects / C. Structure of Objects / 1. Structure of an Object
All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
     Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind.
     From: J.H. Fetzer (A World of Dispositions [1977], 5)
     A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics.
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas]
     Full Idea: All our knowledge comes through our senses, but that doesn't mean that everything we know is sensed.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 18)
16. Persons / F. Free Will / 3. Constraints on the will
If we saw something as totally and utterly good, we would be compelled to will it [Aquinas]
     Full Idea: Something apprehended to be good and appropriate in any and every circumstance that could be thought of would compel us to will it.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply)
16. Persons / F. Free Will / 4. For Free Will
Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas]
     Full Idea: Nothing can be willed except good, but many and various things are good, and you can't conclude from this that wills are compelled to choose this or that one.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 05)
However habituated you are, given time to ponder you can go against a habit [Aquinas]
     Full Idea: However habituated you are, given time to ponder you can go against a habit.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 24)
Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas]
     Full Idea: Reasoning powers can entertain opposite objects. Now will is a reasoning power, so will can entertain opposites and is not compelled to embrace one of them.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.x2)
The will is not compelled to move, even if pleasant things are set before it [Aquinas]
     Full Idea: The will is not compelled to move, for it doesn't have to want the pleasant things set before it.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 21)
Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas]
     Full Idea: Because will moves itself by deliberation - a kind of investigation which doesn't prove some one way correct but examines the alternatives - will doesn't compel itself to will.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply)
16. Persons / F. Free Will / 5. Against Free Will
We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas]
     Full Idea: We are forced to admit that, in any will that is not always willing, the very first movement to will must come from outside, stimulating the will to start willing.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply)
     A reaction: cf Nietzsche
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
The will must aim at happiness, but can choose the means [Aquinas]
     Full Idea: The will is compelled by its ultimate goal (to achieve happiness), but not by the means to achieve it.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.07)
We don't have to will even perfect good, because we can choose not to think of it [Aquinas]
     Full Idea: The will can avoid actually willing something by avoiding thinking of it, since mental activity is subject to will. In this respect we aren't compelled to will even total happiness, which is the only perfect good.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 07)
The will can only want what it thinks is good [Aquinas]
     Full Idea: Will's object is what is good, and so it cannot will anything but what is good.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.06)
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas]
     Full Idea: If we are not free to will in any way, but are compelled, everything that makes up ethics vanishes: pondering action, exhorting, commanding, punishing, praising, condemning.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply)
     A reaction: If doesn't require some magical 'free will' to avoid compulsions. All that is needed is freedom to enact your own willing, rather than someone else's.
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Good applies to goals, just as truth applies to ideas in the mind [Aquinas]
     Full Idea: Good applies to all goals, just as truth applies to all forms mind takes in.
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply)
     A reaction: In danger of being tautological, if good is understood as no more than the goal of actions. It seems perfectly possibly to pursue a wicked end, and perhaps feel guilty about it.
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Kinds are arrangements of dispositions [Fetzer]
     Full Idea: Kinds of things are specific arrangements of dispositions.
     From: J.H. Fetzer (A World of Dispositions [1977], 2)
     A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything.
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas]
     Full Idea: Even a sufficient cause doesn't always compel its effect, since it can sometimes be interfered with so that its effect doesn't happen
     From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 15)
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]
     Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations.
     From: J.H. Fetzer (A World of Dispositions [1977], 3)
     A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything.