Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'A Realistic Theory of Categories' and 'Atomism'

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18 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.
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 / E. Categories / 3. Proposed Categories
Chisholm divides things into contingent and necessary, and then individuals, states and non-states [Chisholm, by Westerhoff]
     Full Idea: Chisholm's Ontological Categories: ENTIA - {Contingent - [Individual - (Boundaries)(Substances)] [States - (Events)]} {Necessary - [States] [Non-States - (Attributes)(Substance)]}
     From: report of Roderick Chisholm (A Realistic Theory of Categories [1996], p.3) by Jan Westerhoff - Ontological Categories §01
     A reaction: [I am attempting a textual representation of a tree diagram! The bracket-styles indicate the levels.]
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.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
The social contract sees society as constituted by and for individuals [Taylor,C]
     Full Idea: The social contract theory …has a vision of society as in some sense constituted by individuals for the fulfilment of ends which are primarily individual.
     From: Charles Taylor (Atomism [1979], p.29)
     A reaction: It seems to be initiated by individuals who are only motivated by what is in it for them. This presumes self-sufficient adults, rather than children, or parents with children, or dependent people. The epitome of liberalism, perhaps.
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C]
     Full Idea: It would be incomprehensible and incoherent to ascribe rights to human beings in respect of the specifically human capacities (such as the right to beliefs or life-style) while at the same time denying that those capacities ought to be developed.
     From: Charles Taylor (Atomism [1979], p.33)
     A reaction: Developed by whom? The agent, their family, or the state? At what point has someone got a capacity, with no further requirement to develop it? Taylor pulls rather large rabbits out of small hats.
If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C]
     Full Idea: If realising our freedom partly depends on the society and culture in which we live, then we exercise a fuller freedom if we can help determine the shape of this society and culture.
     From: Charles Taylor (Atomism [1979], p.47)
     A reaction: This is clearly in response to the critics of communitarianism who say that it is too conservative, because your values are created for you, by your community.
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
Our reliance on other people close to us does not imply any political obligations [Taylor,C]
     Full Idea: We must all be nurtures by others as children, and we only flourish as adults in relationship with friends, mates, children and so on. But this has nothing to do with any obligation to belong to political society.
     From: Charles Taylor (Atomism [1979], p.42)
     A reaction: He is defending community, but not at that minimal human level. Political obligations follows from our need for a wider society, to achieve justice, education, travel, health etc. There are no rights without a society
25. Social Practice / C. Rights / 1. Basis of Rights
A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C]
     Full Idea: Asserting a right is more than issuing an injunction. It has an essential conceptual background, in some notion of the moral worth of certain properties or capacities, without which it would not make.
     From: Charles Taylor (Atomism [1979], p.33)
     A reaction: A simple right may arise from a contract, which could be quite trivial, and of no moral importance. The winner of the egg and spoon race has a right to the prize, which is an ice cream. I think he means legal rights in a state.
For most people the primacy of rights mainly concerns freedom [Taylor,C]
     Full Idea: Most of those who want to affirm the primacy of rights are more interested in asserting the right of freedom, and in a sense which can only be attributed to humans.
     From: Charles Taylor (Atomism [1979], p.40)
     A reaction: This is probably more pronounced in North America than in Europe. It may be that without freedom a lot of the other rights are impossible.
25. Social Practice / C. Rights / 4. Property rights
Property is not essential for life, but it may be essential for independence [Taylor,C]
     Full Idea: It is standardly said that we need the right to property as an essential underpinning of life, but this is patently not true. …In reality it is actually seen as an essential part of a life of independence.
     From: Charles Taylor (Atomism [1979], p.41)
     A reaction: Hence it has a high value for liberals, for whom an independent life is the prime social aspiration. The law of trespass will define the degree of independence provided by property.
25. Social Practice / E. Policies / 3. Welfare provision
If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka]
     Full Idea: Charles Taylor says the neutral [liberal] state undermines the sense of community which is required for citizens to accept the sacrifices demanded by the welfare state.
     From: report of Charles Taylor (Atomism [1979]) by Will Kymlicka - Community 'legitimacy'
     A reaction: As someone who believes in the welfare state, I think this is correct. Extreme individualistic liberalism is incompatible with a welfare state. A liberal society needs institutions which draw free individuals into the community.