Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'On Carnap's Views on Ontology' and 'Essential vs Accidental Properties'

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19 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Quine rejects Carnap's view that science and philosophy are distinct [Quine, by Boulter]
     Full Idea: Quine rejects Carnap's view that the methods of science and philosophy are distinct.
     From: report of Willard Quine (On Carnap's Views on Ontology [1951]) by Stephen Boulter - Why Medieval Philosophy Matters 5
     A reaction: I can't decide this one. Leibniz agreed with Carnap, but rated philosophy more highly. I like the view of philosophy as continuous with science, but that doesn't make it a branch of science. I incline towards science being a branch of philosophy.
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 / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Names have no ontological commitment, because we can deny that they name anything [Quine]
     Full Idea: I think there is no commitment to entities through use of alleged names of them; other things being equal, we can always deny the allegation that the words in question are names.
     From: Willard Quine (On Carnap's Views on Ontology [1951], p.205)
     A reaction: Hm. So why can't you deny that variables actually refer to existing entities? If I say 'I just saw James', it's a bit cheeky to then deny that James refers to anyone. He uses Russell's technique to paraphrase names.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
We can use quantification for commitment to unnameable things like the real numbers [Quine]
     Full Idea: Through our variables of quantification we are quite capable of committing ourselves to entities which cannot be named individually at all in the resources of our language; witness the real numbers.
     From: Willard Quine (On Carnap's Views on Ontology [1951], p.205)
     A reaction: The real numbers are uncountable, and thus cannot all be named. This is quite an impressive point. I've always had doubts about the existence of real numbers, on the grounds that they could never all be named.
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The extremes of essentialism are that all properties are essential, or only very trivial ones [Rami]
     Full Idea: It would be natural to label one extreme view 'maximal essentialism' - that all of an object's properties are essential - and the other extreme 'minimal' - that only trivial properties such as self-identity of being either F or not-F are essential.
     From: Adolph Rami (Essential vs Accidental Properties [2008])
     A reaction: Personally I don't accept the trivial ones as being in any way describable as 'properties'. The maximal view destroys any useful notion of essence. Leibniz is a minority holder of the maximal view. I would defend a middle way.
9. Objects / D. Essence of Objects / 3. Individual Essences
An 'individual essence' is possessed uniquely by a particular object [Rami]
     Full Idea: An 'individual essence' is a property that in addition to being essential is also unique to the object, in the sense that it is not possible that something distinct from that object possesses that property.
     From: Adolph Rami (Essential vs Accidental Properties [2008], §5)
     A reaction: She cites a 'haecceity' (or mere bare identity) as a trivial example of an individual essence.
9. Objects / D. Essence of Objects / 5. Essence as Kind
'Sortal essentialism' says being a particular kind is what is essential [Rami]
     Full Idea: According to 'sortal essentialism', an object could not have been of a radically different kind than it in fact is.
     From: Adolph Rami (Essential vs Accidental Properties [2008], §4)
     A reaction: This strikes me as thoroughly wrong. Things belong in kinds because of their properties. Could you remove all the contingent features of a tiger, leaving it as merely 'a tiger', despite being totally unrecognisable?
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Unlosable properties are not the same as essential properties [Rami]
     Full Idea: It is easy to confuse the notion of an essential property that a thing could not lack, with a property it could not lose. My having spent Christmas 2007 in Tennessee is a non-essential property I could not lose.
     From: Adolph Rami (Essential vs Accidental Properties [2008], §1)
     A reaction: The idea that having spent Christmas in Tennessee is a property I find quite bewildering. Is my not having spent my Christmas in Tennessee one of my properties? I suspect that real unlosable properties are essential ones.
10. Modality / A. Necessity / 3. Types of Necessity
Physical possibility is part of metaphysical possibility which is part of logical possibility [Rami]
     Full Idea: The usual view is that 'physical possibilities' are a natural subset of the 'metaphysical possibilities', which in turn are a subset of the 'logical possibilities'.
     From: Adolph Rami (Essential vs Accidental Properties [2008], §1)
     A reaction: [She cites Fine 2002 for an opposing view] I prefer 'natural' to 'physical', leaving it open where the borders of the natural lie. I take 'metaphysical' possibility to be 'in all naturally possible worlds'. So is a round square a logical possibility?
10. Modality / B. Possibility / 2. Epistemic possibility
If it is possible 'for all I know' then it is 'epistemically possible' [Rami]
     Full Idea: There is 'epistemic possibility' when it is 'for all I know'. That is, P is epistemically possible for agent A just in case P is consistent with what A knows.
     From: Adolph Rami (Essential vs Accidental Properties [2008], §1)
     A reaction: Two problems: maybe 'we' know, and A knows we know, but A doesn't know. And maybe someone knows, but we are not sure about that, which seems to introduce a modal element into the knowing. If someone knows it's impossible, it's impossible.
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.
19. Language / E. Analyticity / 3. Analytic and Synthetic
Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine]
     Full Idea: If there is no proper distinction between analytic and synthetic, then no basis at all remains for the contrast which Carnap urges between ontological statements and empirical statements of existence. Ontology then ends up on a par with natural science.
     From: Willard Quine (On Carnap's Views on Ontology [1951], p.211)
     A reaction: Carnap says ontology is relative to a linguistic framework. 'External' ontology is empty. This quotation gives Quine's main motivation for denying the analytic/synthetic distinction.