Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Interview with Baggini and Stangroom' and 'Our Knowledge of Mathematical Objects'

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22 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
Humour is practically enacted philosophy [Critchley]
     Full Idea: Humour, for me, is practically enacted philosophy.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.198)
     A reaction: This may be overstating it, as the funniest jokes may be the least philosophical, and remarks may be faintly amusing but very profound. Lear and his Fool make up a single worldview together.
Humour can give a phenomenological account of existence, and point to change [Critchley]
     Full Idea: Humour provides an oblique phenomenology of ordinary life; it is a way of describing the situation of our existence, and, at its best, it indicates how we might change that situation.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.198)
     A reaction: The trouble is that this leads us to relentlessly political standup comedians who aren't very funny. Critichley may have a problem with remarks which are very funny precisely because they are so politically incorrect. I sympathise, though.
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Scientism is the view that everything can be explained causally through scientific method [Critchley]
     Full Idea: Scientism is the belief that all phenomena can be explained through the methodology of the natural sciences, and the belief that, therefore, all phenomena are capable of a causal explanation.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.196)
     A reaction: He links two ideas together, but I tend to subscribe fully to the second idea, but less fully to the first. Scientific method, if there is such a thing (Idea 6804), may not be the best way to lay bare the causal network of reality.
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
German idealism aimed to find a unifying principle for Kant's various dualisms [Critchley]
     Full Idea: In his Third Critique Kant established a series of dualisms (pure/practical reason, nature/freedom, epistemology/ethics) but failed to provide a unifying principle; German idealism can be seen as an attempt to provide this principle.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.187)
     A reaction: He cites 'subject', 'spirit', 'art', 'will to power', 'praxis' and 'being' as candidates. This is a helpful overview for someone struggling to get to grips with that tradition.
Continental philosophy fights the threatened nihilism in the critique of reason [Critchley]
     Full Idea: If reason must criticise itself (in Kant) how does one avoid total scepticism? In my view, the problem that has animated the continental tradition since Jacobi (early 19th cent) is the threat of nihilism.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.188)
     A reaction: As an outsider to 'continental' philosophy, this is the most illuminating remark I have read about it. It is not only a plausible account of the movement, but also a very worth aim, which should be taken seriously by analytical philosophers.
Since Hegel, continental philosophy has been linked with social and historical enquiry. [Critchley]
     Full Idea: In continental philosophy from Hegel onwards, systematic philosophical questions have to be linked to socio-historical enquiry, and the distinctions between philosophy, history and society begin to fall apart.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.188)
     A reaction: I have a strong sales resistance to this view of philosophy, just as I would if it was said about mathematics. It seems to imply a bogus view that history exhibits direction and purpose (the 'Whig' view). There are pure reasons among the prejudices.
Continental philosophy is based on critique, praxis and emancipation [Critchley]
     Full Idea: The basic map of the continental tradition can be summarised in three terms: critique, praxis and emancipation.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.189)
     A reaction: I wince at 'emancipation', which seems to take freedom as of unquestionably high value, instead of being one of the principles up for question in social philosophy. There are more presuppositions in Marxist than in analytical philosophy.
Continental philosophy has a bad tendency to offer 'one big thing' to explain everything [Critchley]
     Full Idea: In continental philosophy there is a pernicious tendency to explain everything in terms of 'one big thing', such as the 'death drive' (Freud), 'being' (Heidegger), 'the real' (Lacan), 'power' (Foucault), 'the other' (Levinas), or 'différance' (Derrida).
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.197)
     A reaction: From a fan of this type of philosophy, this is a refreshing remark, because if pinpoints a very off-putting feature. Each of these 'big things' should be up for question, not offered as axiomatic assumptions that explain everything else.
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology is a technique of redescription which clarifies our social world [Critchley]
     Full Idea: Phenomenology (as in the later Husserl) is for me a way of assembling reminders which clarify the social world in which we exist; it is a technique of redescription.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.198)
     A reaction: I'm not sure if I can identify with this as a target for philosophy, but it is interesting and sound worthy of effort. Critchley offers this as the best strand in 'continental' philosophy, rather than the big explanatory ideas.
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 / 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 / J. Model Theory in Logic / 1. Logical Models
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.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
     Full Idea: My Proceduralism offers axiom-free foundations for mathematics. Axioms give way to the stipulation of procedures. We obtain a form of logicism, but with a procedural twist, and with a logic which is ontologically neutral, and no assumption of objects.
     From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
     A reaction: [See Ideas 9222 and 9223 for his Proceduralism] Sounds like philosophical heaven. We get to take charge of mathematics, without the embarrassment of declaring ourselves to be platonists. Someone, not me, should evaluate this.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
     Full Idea: I call my new approach to mathematics 'proceduralism'. It agrees with Hilbert and Poincaré that the objects and truths are postulations, but takes them to be imperatival rather than indicative in form; not propositions, but procedures for construction.
     From: Kit Fine (Our Knowledge of Mathematical Objects [2005], Intro)
     A reaction: I'm not sure how an object or a truth can be a procedure, any more than a house can be a procedure. If a procedure doesn't have a product then it is an idle way to pass the time. The view seems to be related to fictionalism.
My Proceduralism has one simple rule, and four complex rules [Fine,K]
     Full Idea: My Proceduralism has one simple rule (introduce an object), and four complex rules: Composition (combining two procedures), Conditionality (if A, do B), Universality (do a procedure for every x), and Iteration (rule to keep doing B).
     From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
     A reaction: It sounds like a highly artificial and private game which Fine has invented, but he claims that this is the sort of thing that practising mathematicians have always done.
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.
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.
23. Ethics / F. Existentialism / 2. Nihilism
Perceiving meaninglessness is an achievement, which can transform daily life [Critchley]
     Full Idea: If nihilism is the threat of the collapse of meaning, then my position is that one has to accept meaninglessness as an achievement, as an accomplishment that permits a transformed relation to everyday life.
     From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.193)
     A reaction: This sounds cheerfully upbeat and life-enhancing, but I don't quite see how it works. One could easily end up laughing at the most appalling tragedies, and that seems to me to be an inappropriate (Aristotelian word) way to respond to tragedy.