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19125
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If we define truth, we can eliminate it [Halbach/Leigh]
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Full Idea:
If truth can be explicitly defined, it can be eliminated.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
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A reaction:
That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination.
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19127
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The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
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Full Idea:
Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2)
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A reaction:
They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth.
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19124
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A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
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Full Idea:
If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2)
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A reaction:
This seems like a big attraction of axiomatic theories of truth for students of metamathematics.
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19126
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If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
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Full Idea:
If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
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A reaction:
So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values?
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19129
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The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
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Full Idea:
It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), …
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3)
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A reaction:
It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels.
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19130
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KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
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Full Idea:
KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4)
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A reaction:
[summary, which I hope is correct! Stanford is not wholly clear]
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19121
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We can reduce properties to true formulas [Halbach/Leigh]
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Full Idea:
One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1)
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A reaction:
[compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids.
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23266
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The spirit in the soul wants freedom, power and honour [Galen]
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Full Idea:
The spirited part of the soul is desiderative of freedom, victory, power, authority, reputation, and honour.
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From:
Galen (The soul's dependence on the body [c.170], Kiv.2.772)
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A reaction:
This is the concept of 'thumos' [spirit], taken straight from Plato's tripartite account of the soul, in 'Republic'. Note that it includes a desire for freedom (in an age of slavery).
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23220
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The brain contains memory and reason, and is the source of sensation and decision [Galen]
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Full Idea:
The brain is the principal organ of the psychical members. For within the brain is seated memory, reason and intellect, and from the brain is distributed the power, sensation and voluntary motion.
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From:
Galen (The soul's dependence on the body [c.170]), quoted by Matthew Cobb - The Idea of the Brain 1
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A reaction:
[not sure of ref] Interesting that he assigns the whole of mind to the brain, and not just some aspect of it. He had done experiments. Understanding the role of the brain was amazingly slow. Impeded by religion, I guess.
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23265
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The rational part of the soul is the desire for truth, understanding and recollection [Galen]
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Full Idea:
That part of the soul which we call rational is desiderative: …it desires truth, knowledge, learning, understanding, and recollection - in short, all the good things.
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From:
Galen (The soul's dependence on the body [c.170], Kiv.2.772)
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A reaction:
Truth is no surprise, but recollection is. Note the separation of knowledge from understanding. This is a very good characterisation of rationality. For the Greeks it has a moral dimension, of wanting what is good.
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7453
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Galen's medicine followed the mean; each illness was balanced by opposite treatment [Galen, by Hacking]
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Full Idea:
Galen ran medicine on the principle of the mean; afflictions must be treated by contraries; hot diseases deserve cold medicine and moist illnesses want drying agents. (Paracelsus rebelled, treating through similarity).
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From:
report of Galen (On Medical Experience [c.169]) by Ian Hacking - The Emergence of Probability Ch.5
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A reaction:
This must be inherited from Aristotle, with the aim of virtue for the body, as Aristotle wanted virtue for the psuché. In some areas Galen is probably right, that natural balance is the aim, as in bodily temperature control.
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6030
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Each part of the soul has its virtue - pleasure for appetite, success for competition, and rectitude for reason [Galen]
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Full Idea:
We have by nature these three appropriate relationships, corresponding to each form of the soul's parts - to pleasure because of the appetitive part, to success because of the competitive part, and to rectitude because of the rational part.
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From:
Galen (On Hippocrates and Plato [c.170], 5.5.8)
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A reaction:
This is a nice combination of Plato's tripartite theory of soul (in 'Republic') and Aristotle's derivation of virtues from functions. Presumably, though, reason should master the other two, and there is nothing in Galen's idea to explain this.
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23268
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We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen]
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Full Idea:
We kill the irredeemably wicked, for three reasons: that they may no longer harm us; as a deterrent to others like them; and because it is actually better from their own point of view to die, when their souls are so damaged they cannot be improved.
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From:
Galen (The soul's dependence on the body [c.170], Kiv.11.816)
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A reaction:
The third one sounds like a dubious rationalisation, given that the prisoner probably disagrees. Nowadays we are not so quick to judge someone as irredeemable. The first one works when they run wild, but not after their capture.
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