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All the ideas for 'Mathematical Methods in Philosophy', 'Thus Spake Zarathustra' and 'Logic for Philosophy'

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77 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
But what is the reasoning of the body, that it requires the wisdom you seek? [Nietzsche]
     Full Idea: There is more reason in your body than in your best wisdom. For who knows for what purpose your body requires precisely your best wisdom?
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.05)
     A reaction: Lovely question. For years I've paid lip-service to wisdom as the rough aim of all philosophy. Not quite knowing what wisdom is doesn't bother me, but knowing why I want wisdom certainly does, especially after this idea.
1. Philosophy / D. Nature of Philosophy / 8. Humour
Reject wisdom that lacks laughter [Nietzsche]
     Full Idea: Let that wisdom be false to us that brought no laughter with it!
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 3.12.23)
3. Truth / A. Truth Problems / 7. Falsehood
To love truth, you must know how to lie [Nietzsche]
     Full Idea: Inability to lie is far from being love of truth. ....He who cannot lie does not know what truth is.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 4.13.9)
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
'Theorems' are formulas provable from no premises at all [Sider]
     Full Idea: Formulas provable from no premises at all are often called 'theorems'.
     From: Theodore Sider (Logic for Philosophy [2010], 2.6)
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables assume truth functionality, and are just pictures of truth functions [Sider]
     Full Idea: The method of truth tables assumes truth functionality. Truth tables are just pictures of truth functions.
     From: Theodore Sider (Logic for Philosophy [2010], 6.3)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
     Full Idea: Deontic accessibility seems not to be reflexive (that it ought to be true doesn't make it true). One could argue that it is serial (that there is always a world where something is acceptable).
     From: Theodore Sider (Logic for Philosophy [2010], 6.3.1)
In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
     Full Idea: In D we add to K a new axiom saying that 'what's necessary is possible' (□φ→◊φ), ..and it can then be proved that tautologies are possible and contradictions are not necessary.
     From: Theodore Sider (Logic for Philosophy [2010], 6.4.2)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
System B introduces iterated modalities [Sider]
     Full Idea: With system B we begin to be able to say something about iterated modalities. ..S4 then takes a different stand on the iterated modalities, and neither is an extension of the other.
     From: Theodore Sider (Logic for Philosophy [2010], 6.4.4)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
     Full Idea: S5 is the strongest system, since it has the most valid formulas. That's because it has the fewest models; it's easy to be S5-valid since there are so few potentially falsifying models. K is the weakest system, for opposite reasons.
     From: Theodore Sider (Logic for Philosophy [2010], 6.3.2)
     A reaction: Interestingly, the orthodox view is that S5 is the correct logic for metaphysics, but it sounds a bit lax. Compare Idea 13707.
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider]
     Full Idea: Epistemic accessibility should be required to be reflexive (allowing Kφ→φ). S4 allows the 'KK principle', or 'positive introspection' (Kφ→KKφ), and S5 allows 'negative introspection' (¬Kφ→K¬Kφ).
     From: Theodore Sider (Logic for Philosophy [2010], 7.2)
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
We can treat modal worlds as different times [Sider]
     Full Idea: We can think of the worlds of modal logic as being times, rather than 'possible' worlds.
     From: Theodore Sider (Logic for Philosophy [2010], 7.3.3)
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
     Full Idea: The Converse Barcan Formula reads □∀αφ→∀α□φ (or an equivalent using ◊).
     From: Theodore Sider (Logic for Philosophy [2010], 9.5.2)
     A reaction: I would read that as 'if all the αs happen to be φ, then αs have to be φ'. Put like that, I would have thought that it was obviously false. Sider points out that some new object could turn up which isn't φ.
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
     Full Idea: The Barcan Formula ∀x□Fx→□∀xFx is often regarded as a defect of Simple Quantified Modal Logic, though this most clearly seen in its equivalent form ◊∃xFx→∃x◊Fx.
     From: Theodore Sider (Logic for Philosophy [2010], 9.5.2)
     A reaction: [See Idea 13719 for an explanation why it might be a defect] I translate the first one as 'if xs must be F, then they are always F', and the second one as 'for x to be possibly F, there must exist an x which is possibly F'. Modality needs existence.
System B is needed to prove the Barcan Formula [Sider]
     Full Idea: The proof of the Barcan Formula require System B.
     From: Theodore Sider (Logic for Philosophy [2010], 9.7)
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
You can employ intuitionist logic without intuitionism about mathematics [Sider]
     Full Idea: Not everyone who employs intuitionistic logic is an intuitionist about mathematics.
     From: Theodore Sider (Logic for Philosophy [2010], 7.4.1)
     A reaction: This seems worthy of note, since it may be tempting to reject the logic because of the implausibility of the philosophy of mathematics. I must take intuitionist logic more seriously.
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
     Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1)
     A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark.
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
     Full Idea: On the question of the nature of genuine logical consequence, ...the most popular answer is the semantic, or model-theoretic one.
     From: Theodore Sider (Logic for Philosophy [2010], 1.5)
     A reaction: Reading the literature, one might be tempted to think that this is the only account that anyone takes seriously. Substitutional semantics seems an interesting alternative.
Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
     Full Idea: The 'modal' account of logical consequence is that it is not possible for the premises to be true and the consequent false (under some suitable notion of possibility).
     From: Theodore Sider (Logic for Philosophy [2010], 1.5)
     A reaction: Sider gives a nice summary of five views of logical consequence, to which Shapiro adds substitutional semantics.
Maybe logical consequence is a primitive notion [Sider]
     Full Idea: There is a 'primitivist' account, according to which logical consequence is a primitive notion.
     From: Theodore Sider (Logic for Philosophy [2010], 1.5)
     A reaction: While sympathetic to substitutional views (Idea 13674), the suggestion here pushes me towards thinking that truth must be at the root of it. The trouble, though, is that a falsehood can be a good logical consequence of other falsehoods.
Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
     Full Idea: Another answer to the question about the nature of logical consequence is a proof-theoretic one, according to which it is more a matter of provability than of truth-preservation.
     From: Theodore Sider (Logic for Philosophy [2010], 1.5)
     A reaction: I don't like this, and prefer the model-theoretic or substitutional accounts. Whether you can prove that something is a logical consequence seems to me entirely separate from whether you can see that it is so. Gödel seems to agree.
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
     Full Idea: A 'theorem' is defined as the last line of a proof in which each line is either an axiom or follows from earlier lines by a rule.
     From: Theodore Sider (Logic for Philosophy [2010], 9.7)
     A reaction: In other words, theorems are the axioms and their implications.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
     Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise.
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
     Full Idea: When a variable is not combined with a quantifier (and so is 'free'), the result is, intuitively, semantically incomplete, and incapable of truth or falsity.
     From: Theodore Sider (Logic for Philosophy [2010], 4.2)
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
A 'total' function must always produce an output for a given domain [Sider]
     Full Idea: Calling a function a 'total' function 'over D' means that the function must have a well-defined output (which is a member of D) whenever it is given as inputs any n members of D.
     From: Theodore Sider (Logic for Philosophy [2010], 5.2)
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ can treat 'is cold and hungry' as a single predicate [Sider]
     Full Idea: We might prefer λx(Fx∧Gx)(a) as the symbolization of 'John is cold and hungry', since it treats 'is cold and hungry' as a single predicate.
     From: Theodore Sider (Logic for Philosophy [2010], 5.5)
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Good axioms should be indisputable logical truths [Sider]
     Full Idea: Since they are the foundations on which a proof rests, the axioms in a good axiomatic system ought to represent indisputable logical truths.
     From: Theodore Sider (Logic for Philosophy [2010], 2.6)
No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
     Full Idea: Axiomatic systems do not allow reasoning with assumptions, and therefore do not allow conditional proof or reductio ad absurdum.
     From: Theodore Sider (Logic for Philosophy [2010], 2.6)
     A reaction: Since these are two of the most basic techniques of proof which I have learned (in Lemmon), I shall avoid axiomatic proof systems at all costs, despites their foundational and Ockhamist appeal.
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
     Full Idea: A proof by induction starts with a 'base case', usually that an atomic formula has some property. It then assumes an 'inductive hypothesis', that the property is true up to a certain case. The 'inductive step' then says it will be true for the next case.
     From: Theodore Sider (Logic for Philosophy [2010], 2.7)
     A reaction: [compressed]
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
     Full Idea: The style of proof called 'induction on formula construction' (or 'on the number of connectives', or 'on the length of the formula') rest on the fact that all formulas are built up from atomic formulas according to strict rules.
     From: Theodore Sider (Logic for Philosophy [2010], 2.7)
     A reaction: Hence the proof deconstructs the formula, and takes it back to a set of atomic formulas have already been established.
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction helpfully allows reasoning with assumptions [Sider]
     Full Idea: The method of natural deduction is popular in introductory textbooks since it allows reasoning with assumptions.
     From: Theodore Sider (Logic for Philosophy [2010], 2.5)
     A reaction: Reasoning with assumptions is generally easier, rather than being narrowly confined to a few tricky axioms, You gradually show that an inference holds whatever the assumption was, and so end up with the same result.
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
We can build proofs just from conclusions, rather than from plain formulae [Sider]
     Full Idea: We can construct proofs not out of well-formed formulae ('wffs'), but out of sequents, which are some premises followed by their logical consequence. We explicitly keep track of the assumptions upon which the conclusion depends.
     From: Theodore Sider (Logic for Philosophy [2010], 2.5.1)
     A reaction: He says the method of sequents was invented by Gerhard Gentzen (the great nazi logician) in 1935. The typical starting sequents are the introduction and elimination rules. E.J. Lemmon's book, used in this database, is an example.
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
     Full Idea: A valuation function in predicate logic will assign truth values to formulas relative to variable assignments.
     From: Theodore Sider (Logic for Philosophy [2010], 4.2)
     A reaction: Sider observes that this is a 'double' relativisation (due to Tarski), since propositional logic truth was already relative to an interpretation. Now we are relative to variable assignments as well.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
     Full Idea: The semantical notion of a logical truth is that of a valid formula, which is true in all interpretations. In propositional logic they are 'tautologies'.
     From: Theodore Sider (Logic for Philosophy [2010], 2.3)
     A reaction: This implies that there is a proof-theoretic account of logical truth as well. Intuitively a logical truth is a sequent which holds no matter which subject matter it refers to, so the semantic view sounds OK.
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
     Full Idea: It isn't clear which formulas of modal propositional logic are logical truths, ...especially for sentences that contain iterations of modal operators. Is □P→□□P a logical truth? It's hard to say.
     From: Theodore Sider (Logic for Philosophy [2010], 6.3)
     A reaction: The result, of course, is that there are numerous 'systems' for modal logic, so that you can choose the one that gives you the logical truths you want. His example is valid in S4 and S5, but not in the others.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
     Full Idea: In model theory one normally defines some notion of truth in a model, and then uses it to define validity as truth in all models, and semantic consequence as the preservation of truth in models.
     From: Theodore Sider (Logic for Philosophy [2010], 10.1)
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
     Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea.
5. Theory of Logic / K. Features of Logics / 4. Completeness
In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
     Full Idea: You can establish facts of the form Γ|-φ while avoiding the agonies of axiomatic proofs by reasoning directly about models to conclusions about semantic consequence, and then citing completeness.
     From: Theodore Sider (Logic for Philosophy [2010], 4.5)
     A reaction: You cite completeness by saying that anything which you have shown to be a semantic consequence must therefore be provable (in some way).
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
     Full Idea: Compactness is intuitively surprising, ..because one might have thought there could be some contradiction latent within some infinite set, preventing it from being satisfiable, only discovered when you consider the whole set. But this can't happen.
     From: Theodore Sider (Logic for Philosophy [2010], 4.5)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]
     Full Idea: A single second-order sentence has second-order semantic consequences which are all and only the truths of arithmetic, but this is cold comfort because of incompleteness; no axiomatic system draws out the consequences of this axiom.
     From: Theodore Sider (Logic for Philosophy [2010], 5.4.3)
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
     Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting.
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider]
     Full Idea: For a 'precisification' we take a trivalent interpretation and preserve the T and F values, and then assign all the third values in some way to either T or F.
     From: Theodore Sider (Logic for Philosophy [2010], 3.4.5)
     A reaction: [my informal summary of Sider's formal definition]
A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider]
     Full Idea: In a 'supervaluation' we take a trivalent interpretation, and assign to each wff T (or F) if it is T (or F) in every precisification, leaving the third truth-value in any other cases. The wffs are then 'supertrue' or 'superfalse' in the interpretation.
     From: Theodore Sider (Logic for Philosophy [2010], 3.4.5)
     A reaction: [my non-symbolic summary] Sider says the Ts and Fs in the precisifications are assigned 'in any way you like', so supervaluation is a purely formal idea, not a technique for eliminating vagueness.
Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider]
     Full Idea: Supervaluation preserves classical logic (even though supervaluations are three-valued), except when we add the Δ operator (meaning 'definitely' or 'determinately').
     From: Theodore Sider (Logic for Philosophy [2010], 3.4.5)
We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider]
     Full Idea: We can introduce 'sharpenings', to make vague terms precise without disturbing their semantics. Then truth (or falsity) becomes true(false)-in-all-sharpenings. You are only 'rich' if you are rich-on-all-sharpenings of the word.
     From: Theodore Sider (Logic for Philosophy [2010], 3.4.5)
     A reaction: Not very helpful. Lots of people might be considered rich in many contexts, but very few people would be considered rich in all contexts. You are still left with some vague middle ground.
8. Modes of Existence / A. Relations / 1. Nature of Relations
A relation is a feature of multiple objects taken together [Sider]
     Full Idea: A relation is just a feature of multiple objects taken together.
     From: Theodore Sider (Logic for Philosophy [2010], 1.8)
     A reaction: Appealingly simple, especially for a logician, who can then just list the relevant objects as members of a set, and the job is done. But if everyone to the left of me is also taller than me, this won't quite do.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider]
     Full Idea: The identity of indiscernibles (∀x∀y(∀X(Xx↔Xy)→x=y) is necessarily true, provided that we construe 'property' very broadly, so that 'being a member of such-and-such set' counts as a property.
     From: Theodore Sider (Logic for Philosophy [2010], 5.4.3)
     A reaction: Sider's example is that if the two objects are the same they must both have the property of being a member of the same singleton set, which they couldn't have if they were different.
10. Modality / A. Necessity / 3. Types of Necessity
'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider]
     Full Idea: 'Strong necessity' requires the truth of 'necessarily φ' is all possible worlds. 'Weak necessity' merely requires that 'necessarily φ' be true in all worlds in which objects referred to within φ exist.
     From: Theodore Sider (Logic for Philosophy [2010], 9.6.3)
     A reaction: This seems to be a highly desirably distinction, given the problem of Idea 13719. It is weakly necessary that humans can't fly unaided, assuming we are referring the current feeble wingless species. That hardly seems to be strongly necessary.
10. Modality / A. Necessity / 5. Metaphysical Necessity
Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider]
     Full Idea: Some argue that metaphysical accessibility is intransitive. The individuals involved mustn't be too different from the actual world. A world in which I am a frog isn't metaphysically possible. Perhaps the logic is modal system B or T.
     From: Theodore Sider (Logic for Philosophy [2010], 6.3.1)
     A reaction: This sounds rather plausible and attractive to me. We don't want to say that I am necessarily the way I actually am, though, so we need criteria. Essence!
10. Modality / A. Necessity / 6. Logical Necessity
Logical truths must be necessary if anything is [Sider]
     Full Idea: On any sense of necessity, surely logical truths must be necessary.
     From: Theodore Sider (Logic for Philosophy [2010], 6.4)
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider]
     Full Idea: To show the semantic difference between counterfactuals and indicative conditionals, 'If Booth hadn't shot Lincoln someone else would have' is false, but 'If Booth didn't shoot Lincoln then someone else did' is true.
     From: Theodore Sider (Logic for Philosophy [2010], 8)
     A reaction: He notes that indicative conditionals also differ in semantics from material and strict conditionals. The first example allows a world where Lincoln was not shot, but the second assumes our own world, where he was. Contextual domains?
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
     Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory.
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
     Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
     Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular).
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
     Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds.
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
     Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5)
     A reaction: They accept lots of successes in modelling necessity and time.
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider]
     Full Idea: There is no problem of transworld identification with de dicto modal sentence, for their evaluation does not require taking an individual from one possible world and reidentifying it in another.
     From: Theodore Sider (Logic for Philosophy [2010], 9.2)
     A reaction: If 'de dicto' is about the sentence and 'de re' is about the object (Idea 5732), how do you evaluate the sentence without at least some notion of the object to which it refers. Nec the Prime Minister chairs the cabinet. Could a poached egg do the job?
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider]
     Full Idea: A problem with the Barcan Formula is it might be possible for there to exist a ghost, even though there in fact exists nothing that could be a ghost. There could have existed some 'extra' thing which could be a ghost.
     From: Theodore Sider (Logic for Philosophy [2010], 9.5.2)
     A reaction: Thus when we make modal claims, do they only refer to what actually exists, or is specified in our initial domain? Can a claim enlarge the domain? Are domains 'variable'? Simple claims about what might have existed seem to be a problem.
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
The powerful self behind your thoughts and feelings is your body [Nietzsche]
     Full Idea: Behind your thoughts and feelings stands a powerful commander, an unknown wise man - he is called a self. He lives in your body; he is your body.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], I.4), quoted by Kevin Aho - Existentialism: an introduction 5 'Creature'
     A reaction: I find Nietzsche's view of the self very congenial, though I tend to see the self as certain central functions of the brain. The brain is enmeshed in the body (as in the location of pains).
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
Forget the word 'I'; 'I' is performed by the intelligence of your body [Nietzsche]
     Full Idea: You say 'I' and you are proud of this word. But greater than this - although you will not believe in it - is your body and its great intelligence, which does not say 'I' but performs 'I'.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.05)
     A reaction: I'm not sure if I understand this, but I offer it as a candidate for the most profound idea ever articulated about personal identity.
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
The will is constantly frustrated by the past [Nietzsche]
     Full Idea: Powerless against that which has been done, the will is an angry spectator of all things past. The will cannot will backwards; that it cannot break time and time's desire - that is the will's most lonely affliction.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 2.20)
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
We created meanings, to maintain ourselves [Nietzsche]
     Full Idea: Man first implanted values into things to maintain himself - he first created the meaning of things, a human meaning!
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.16)
     A reaction: It is certainly hard to see anything resembling values or meaning in the cosmos, if you remove the human beings. We should expect an evolutionary grounding in their explanation.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
The noble man wants new virtues; the good man preserves what is old [Nietzsche]
     Full Idea: The noble man wants to create new things and a new virtue. The good man wants the old things and that the old things shall be preserved.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.09)
     A reaction: There is a limit to how many plausible virtues the noble men can come up with. We may already have run out. Are we going to have to re-run the Iliad?
22. Metaethics / B. Value / 2. Values / g. Love
We only really love children and work [Nietzsche]
     Full Idea: One loves from the very heart only one's child and one's work.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 3.03)
     A reaction: Very Nietzchean (and masculine?) to cite one's work. Rachmaninov said he was 85% musician and 15% human being, so I guess he loved music from the very heart.
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
I want my work, not happiness! [Nietzsche]
     Full Idea: Do I aspire after happiness? I aspire after my work!
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 4.20)
     A reaction: I empathise with aspiring to do something, rather than be something. But what do we wish for our children? Happiness first, then achievement?
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Virtues can destroy one another, through jealousy [Nietzsche]
     Full Idea: Every virtue is jealous of the others, and jealousy is a terrible thing. Even virtues can be destroyed through jealousy.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.07)
     A reaction: How much more subtle and plausible than the picture of accumulating virtues, like medals! Zarathustra says it is best to have just one virtue.
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
People now find both wealth and poverty too much of a burden [Nietzsche]
     Full Idea: Nobody grows rich or poor any more: both are too much of a burden.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.01)
     A reaction: True. Most people I know are just puzzled by people who actually seem to want to be extremely wealthy.
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
If you want friends, you must be a fighter [Nietzsche]
     Full Idea: If you want a friend, you must be willing to wage war for him: and to wage war, you must be capable of being an enemy.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.15)
23. Ethics / F. Existentialism / 2. Nihilism
The greatest experience possible is contempt for your own happiness, reason and virtue [Nietzsche]
     Full Idea: What is the greatest thing you can experience? It is the hour of the great contempt. The hour in which even your happiness grows loathsome to you, and your reason and your virtue also.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.01)
     A reaction: This would be a transient state for Nietzsche, in which you realise the hollowness of those traditional ideas, and begin to seek something else.
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
An enduring people needs its own individual values [Nietzsche]
     Full Idea: No people could live without evaluating; but if it wishes to maintain itself it must not evaluate as its neighbour evaluates.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.16)
     A reaction: Political philosophers say plenty about a 'people', but little about what unifies them, or about what keeps one people distinct from another. Most people's are proud of their local values.
24. Political Theory / B. Nature of a State / 3. Constitutions
The state coldly claims that it is the people, but that is a lie [Nietzsche]
     Full Idea: The state is the coldest of all cold monsters. Coldly it lies, too; and this lie creeps from its mouth: 'I, the state, am the people'. It is a lie!
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.12)
     A reaction: This strikes me as just as true even after everyone gets the vote. Rulers can't help gradually forgetting about the people.
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Saints want to live as they desire, or not to live at all [Nietzsche]
     Full Idea: 'To live as I desire to live or not to live at all': that is what I want, that is what the most saintly man wants.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 4.09)
     A reaction: [spoken by Zarathustra]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Whenever we have seen suffering, we have wanted the revenge of punishment [Nietzsche]
     Full Idea: The spirit of revenge: my friends, that, up to now, has been mankind's chief concern; and where there was suffering, there was always supposed to be punishment.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 2.20)
25. Social Practice / F. Life Issues / 5. Sexual Morality
Man and woman are deeply strange to one another! [Nietzsche]
     Full Idea: Who has fully conceived how strange man and woman are to one another!
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 3.10.2)
28. God / A. Divine Nature / 2. Divine Nature
I can only believe in a God who can dance [Nietzsche]
     Full Idea: I should believe only in a God who understood how to dance.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.08)
28. God / C. Attitudes to God / 5. Atheism
There can't be gods, because that leaves us nothing to create! [Nietzsche]
     Full Idea: If there were gods, how could I endure not to be a god! Therefore there are no gods. ...For what would there be to create if gods - existed!
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 2.02)
     A reaction: [Zarathustra says this, not Nietzsche!]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
We don't want heaven; now that we are men, we want the kingdom of earth [Nietzsche]
     Full Idea: We certainly do not want to enter into the kingdom of heaven: we have become men, so we want the kingdom of earth.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 4.18.2)
Heaven was invented by the sick and the dying [Nietzsche]
     Full Idea: It was the sick and dying who despised the body and the earth and invented the things of heaven and the redeeming drops of blood.
     From: Friedrich Nietzsche (Thus Spake Zarathustra [1884], 1.04)