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12801
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Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley]
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Full Idea:
Coherentists try to provide an explication of epistemic rationality in terms of a set of deductive and probabilistic relations among beliefs and properties such as simplicity, conservativeness, and explanatory power.
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From:
Richard Foley (Justified Belief as Responsible Belief [2005], p.317)
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A reaction:
I have always like the coherentist view of justification, and now I see that this has led me to the question of explanation, which in turn has led me to essentialism. It's all coming together. Watch this space. 'Explanatory' is the key to everything!
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10751
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Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
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Full Idea:
Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation.
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From:
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1)
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A reaction:
The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics.
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10753
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Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
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Full Idea:
Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence.
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From:
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2)
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A reaction:
If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation.
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10752
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Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
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Full Idea:
Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'.
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From:
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2)
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A reaction:
We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another.
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10756
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A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
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Full Idea:
A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc.
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From:
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3)
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A reaction:
The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts.
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10758
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If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
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Full Idea:
A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one.
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From:
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3)
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A reaction:
So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'.
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12800
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Externalists want to understand knowledge, Internalists want to understand justification [Foley]
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Full Idea:
Externalists are principally interested in understanding what knowledge is, ..while internalists, by contrast, are principally interested in explicating a sense of justification ..from one's own perspective.
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From:
Richard Foley (Justified Belief as Responsible Belief [2005], p.314)
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A reaction:
I find this very helpful, since I have a strong bias towards internalism (with a social dimension), and I see now that it is because I am more interested in what a (good) justification is than what some entity in reality called 'knowledge' consists of.
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12802
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We aren't directly pragmatic about belief, but pragmatic about the deliberation which precedes it [Foley]
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Full Idea:
It is rare for pragmatic considerations to influence the rationality of our beliefs in the crass, direct way that Pascal's Wager envisions. Instead, they determine the direction and shape of our investigative and deliberative projects and practices.
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From:
Richard Foley (Justified Belief as Responsible Belief [2005], p.320)
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A reaction:
[See Idea 6684 for Pascal's Wager] Foley is evidently a full-blown pragmatist (which is bad), but this is nicely put. We can't deny the importance of the amount of effort put into an enquiry. Maybe it is an epistemic duty, rather than a means to an end.
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5689
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Freud and others have shown that we don't know our own beliefs, feelings, motive and attitudes [Freud, by Shoemaker]
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Full Idea:
Freud persuaded many that beliefs, wishes and feelings are sometimes unconscious, and even sceptics about Freud acknowledge that there is self-deception about motive and attitudes.
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From:
report of Sigmund Freud (works [1900]) by Sydney Shoemaker - Introspection p.396
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A reaction:
This seems to me obviously correct. The traditional notion is that the consciousness is the mind, but now it seems obvious that consciousness is only one part of the mind, and maybe even a peripheral (epiphenomenal) part of it.
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