It’s a surprise! Ron Chrisley COGS Department of Informatics University of Sussex QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. E-Intentionality, PAICS Research Group, Department of Informatics University of Sussex, June 1st 2006 Surprise! • Why is the title of this talk "It's a surprise!"? • It's a surprise! But first… …some logic (groan) Logic: What is it good for? • One application: To make explicit the logical structure of an inference • Then it becomes a mechanical/syntactic matter to determine, e.g. validity Arguments • Ron says: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." • Michael says: "Every man is mortal. Socrates is a man. Thus, Socrates is mortal." • Blay says: "All men are mortal. Schwarzenegger is a man. Therefore, Schwarzenegger is mortal." • Different words, but same logical form… Logical form Ax[M(x)->D(x)] M(S) ----- D(S) • So if one of the arguments is valid, the others are. • This logical form is valid. My claim • Either logical form does not determine validity (a contradicition, or damn near it), …Or… • Standard means of translating arguments into their logical form are incorrect. Problem case • Consider: "Ron has drawn 10 conclusions today. 10 is less than 11. Therefore, Ron has drawn fewer than 11 conclusions today." C(R,t) = 10 10 < 11 ----- C(R,t) < 11 • Is this valid? Validity • Perhaps for you, but not for me! • The problem is that carrying out the inference interacts with the truth of the premises of the inference • So either we need to say that validity does not supervene on logical form, or the foregoing is not the logical form Embodied logical form • But what is the logical form, then? • Needs to include the person who is carrying out the inference? • What else? Timing? Order? Connection to paradoxes • Moore’s paradox: – “Ron cannot know this sentence to be true” • Gödelian argument • Newcomb’s problem • Liar paradox • Rationality paradox/prisoner’s dilemma SURPRISE!
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