Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'A World of States of Affairs' and 'Essays on Intellectual Powers 6: Judgement'

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22 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
The existence of tensed verbs shows that not all truths are necessary truths [Reid]
     Full Idea: If all truths were necessary truths, there would be no occasion for different tenses in the verbs by which they are expressed.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5)
     A reaction: This really is like modern linguistic analysis. Of course the tensed verbs might only indicate times when the universal necessities have been noticed by speakers. …But then the noticing would be contingent!
2. Reason / F. Fallacies / 7. Ad Hominem
An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid]
     Full Idea: It is a good argument ad hominem, if it can be shewn that a first principle which a man rejects, stands upon the same footing with others which he admits, …for he must then be guilty of an inconsistency.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 4)
     A reaction: Good point. You can't divorce 'pure' reason from the reasoners, because the inconsistency of two propositions only matters when they are both asserted together. …But attacking the ideas isn't quite the same as attacking the person.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong]
     Full Idea: In Armstrong's version of the correspondence theory, the truth-making relation is not one-one, but one-many or many-one. Thus 'p or q' has two truth makers, p and q.
     From: David M. Armstrong (A World of States of Affairs [1997], p.129), quoted by Pascal Engel - Truth Ch.1
     A reaction: Interesting. Armstrong deals in universals. He also cites many swans as truth-makers for 'there is a least one black swan'. Not correspondence as we know it, Jim.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
     Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
     Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
     Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
     Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
     A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
     Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)
     A reaction: Each expansion brings a limitation, but then you can expand again.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
     Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
7. Existence / D. Theories of Reality / 7. Fictionalism
Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong]
     Full Idea: Armstrong has difficulty explaining how laws entail regularities. There is no real modality in the basic components of the world, but he wants to support counterfactuals. His official position is a kind of fictionalism.
     From: comment on David M. Armstrong (A World of States of Affairs [1997], 49-51) by Alexander Bird - Nature's Metaphysics 4.4.4
     A reaction: Armstrong seems to be up against the basic problems that laws won't explain anything if they are merely regularities (assuming they are not decrees of a supernatural force).
8. Modes of Existence / B. Properties / 1. Nature of Properties
Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis]
     Full Idea: Armstrong has a distinctive conception of (fundamental) properties as contingently existing beings with multiple locations in space and time.
     From: report of David M. Armstrong (A World of States of Affairs [1997]) by David Lewis - A world of truthmakers? p.220
     A reaction: Armstrong tries to get a naturalistically founded platonism (which he claims is Aristotelian), but the idea that one thing can be multiply located strikes me as daft (especially if the number of its locations increases or decreases).
10. Modality / C. Sources of Modality / 1. Sources of Necessity
The truth-maker for a truth must necessitate that truth [Armstrong]
     Full Idea: The truth-maker for a truth must necessitate that truth.
     From: David M. Armstrong (A World of States of Affairs [1997], p.115), quoted by Pascal Engel - Truth Ch.1
     A reaction: Armstrong's 'truth-make principle'. It seems to be a necessity which is neither natural nor analytic, making it metaphysically necessary. Or is it part of the definition of truth?
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid]
     Full Idea: If any man could be found so frantic as to deny that he thinks, while he is conscious of it, I may wonder, I may laugh, or I may pity him, but I cannot reason the matter with him.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5)
     A reaction: An example of the influence of Descartes' Cogito running through all subsequent European philosophy. There remain the usual questions about personal identity which then arise, but Reid addresses those.
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
The existence of ideas is no more obvious than the existence of external objects [Reid]
     Full Idea: If external objects be perceived immediately, we have the same reason to believe their existence as philosophers have to believe the existence of ideas.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5)
     A reaction: He doesn't pay much attention to mirages and delusions, but in difficult conditions of perception we are confident of our experiences but doubtful about the objects they represent.
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
We are only aware of other beings through our senses; without that, we are alone in the universe [Reid]
     Full Idea: We can have no communication, no correspondence or society with any created being, but by means of our senses. And, until we rely on their testimony, we must consider ourselves as being alone in the universe.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5)
     A reaction: I'm not aware of any thinker before this so directly addressing solipsism. Even the champion of direct and common sense realism has to recognise the intermediary of our senses when accepting other minds.
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
In obscure matters the few must lead the many, but the many usually lead in common sense [Reid]
     Full Idea: In matters beyond the reach of common understanding, the many are led by the few, and willingly yield to their authority. But, in matters of common sense, the few must yield to the many, when local and temporary prejudices are removed.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 4)
     A reaction: Wishful thinking in the 21st century, when the many routinely deny the authority of the expert few, and the expert few occasionally prove that the collective common sense of the many is delusional. I still sort of agree with Reid.
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
The theory of ideas, popular with philosophers, means past existence has to be proved [Reid]
     Full Idea: The theory concerning ideas, so generally received by philosophers, destroys all the authority of memory. …This theory made it necessary for them to find out arguments to prove the existence of external objects …and of things past.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5)
     A reaction: Reid was a very articulate direct realist. He seems less aware than the rest of us of the problem of delusions and false memories. Our strong sense that immediate memories are reliable is certainly inexplicable.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Consciousness is an indefinable and unique operation [Reid]
     Full Idea: Consciousness is an operation of the understanding of its own kind, and cannot be logically defined.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5)
     A reaction: It is interesting that has tried to define consciousness, rather than just assuming it. I note that he calls consciousness an 'operation', rather than an entity. Good.
18. Thought / A. Modes of Thought / 8. Human Thought
The structure of languages reveals a uniformity in basic human opinions [Reid]
     Full Idea: What is common in the structure of languages, indicates an uniformity of opinion in those things upon which that structure is grounded.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 4)
     A reaction: Reid was more interested than his contemporaries in the role of language in philosophy. The first idea sounds like Chomsky. I would add to this that the uniformity of common opinion reflects uniformities in the world they are talking about.
18. Thought / E. Abstraction / 2. Abstracta by Selection
If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid]
     Full Idea: If you perceive an object, white, round, and a foot in diameter, if you had not been able to distinguish the colour from the figure, and both from the magnitude, your senses would only give you one complex and confused notion of all these mingled together
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 1)
     A reaction: His point is that if you reject the 'abstraction' of these qualities, you still cannot deny that distinguishing them is an essential aspect of perceiving complex things. Does this mean that animals distinguish such things?
21. Aesthetics / A. Aesthetic Experience / 3. Taste
There are axioms of taste - such as a general consensus about a beautiful face [Reid]
     Full Idea: I think there are axioms, even in matters of taste. …I never heard of any man who thought it a beauty in a human face to want a nose, or an eye, or to have the mouth on one side.
     From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 6)
     A reaction: It is hard to disagree, but the human face may be a special case, since it is so deeply embedded in the minds of even the youngest infants. More recent artists seem able to discover beauty in very unlikely places.
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos]
     Full Idea: In recent writings, Armstrong makes a direct identification of necessitation with causation.
     From: report of David M. Armstrong (A World of States of Affairs [1997]) by Stathis Psillos - Causation and Explanation §6.3.3
     A reaction: Obviously logical necessity is not causal, but as a proposal for simplifying accounts of necessity in nature, this is wonderfully simple and appealing. Is his proposal an elevation of causation, or a degradation of necessity?