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5515
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Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit]
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Full Idea:
I believe it is worth considering imaginary cases (such as Teletransportation), as we can use them to discover, not what the truth is, but what we believe.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.293)
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A reaction:
The trouble is that we might say that IF I were suddenly turned into a pig, then I would come to believe in dualism, but that will not and cannot happen, because dualism is false. It seems essential to accept the natural possibility of the case.
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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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5516
|
Reduction can be by identity, or constitution, or elimination [Parfit, by PG]
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Full Idea:
We can distinguish Identifying Reductionism (as in 'persons are bodies'), or Constitutive Reductionism (as in 'persons are distinct, but consist of thoughts etc.'), or Eliminative Reductionism (as in 'there are no persons, only thoughts etc.').
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From:
report of Derek Parfit (The Unimportance of Identity [1995], p.295) by PG - Db (ideas)
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A reaction:
Constitutive Reductionism seems the most common one, as in 'chemistry just consists of lots of complicated physics'. He doesn't mention bridge laws, which are presumably only required in more complicated cases of constitutive reduction.
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5514
|
Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit]
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Full Idea:
When psychologists discuss identity, they are typically concerned with the kind of person someone is, or wants to be (as in an 'identity crisis'). But when philosophers discuss identity, it is numerical identity they mean.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.293)
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A reaction:
I think it is important to note that the philosophical problem breaks down into two areas: whether I have numerical identity with myself over time, and whether other people have it. It may be that two different sets of criteria will emerge.
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5521
|
If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit]
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Full Idea:
If the two halves of my brain are transplanted into different bodies just like mine, they cannot both be me, since that would make them the same person. ..But my relation to these two contains everything that matters, so identity is not what matters.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.314)
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A reaction:
I challenge his concept of what 'matters'. He has a rather solipsistic view of the problem, and I take Parfit to be a rather unsociable person, since his friends and partner will be keenly interested in the identities of the new beings.
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5519
|
It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit]
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Full Idea:
If I am largely paralysed, and my twin brother is dying of brain disease, then if the operation to graft my head onto his body is offered, I should accept the operation, and it is irrelevant whether this person would be me.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.308)
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A reaction:
Parfit notes that the brain is a particularly significant part of the process. The fact that I might cheerfully accept this offer without philosophical worries doesn't get rid of the question 'who is this person?' Who should they remain married to?
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5520
|
If two humans are merged surgically, the new identity is a purely verbal problem [Parfit]
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Full Idea:
If there is someone with my head and my brother's body, it is a merely verbal question whether that person will be me, and that is why, even if it won't be me, that doesn't matter. ..What matters is not identity, but the facts of which identity consists.
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From:
Derek Parfit (The Unimportance of Identity [1995], p.310)
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A reaction:
It strikes me that from the subjective psychological point of view identity is of little interest, but from the objective external viewpoint (e.g. the forensic one) such questions are highly significant, and rightly so.
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