Logic and the Methodology of Science Formal Logic

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Logic and the Methodology of ScienceFormal Logic

• Juraj Simko
• juraj.simko_at_ucd.ie

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(Course on) Formal Logic
Logic is the study of good reasoning, and in
particular, of what makes good reasoning good.

• (Apart from other things) a useful TOOL for
  mathematics, computing, linguistics, law, , and
  philosophy
• Language of formal logic sentence, proposition,
  connective, belief, argument, form, truth,
  deduction, predicate, quantifier, model

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(Course on) Formal Logic

• 0?X (a)(a?X ? a?X ) (a)(Lim(a)(ß)(ßlt0a ?
  ? ß?X)) ? a?X) ? OnltX
• No effect can cause itself, but requires another
  cause, so if there were no first cause, there
  would be an infinite sequence of preceding
  causes, thus because there cannot be an infinite
  sequence of causes, there is a first cause, and
  this is God.
• , v, , ? - useful symbols, for modelling good
  reasoning

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(Course on) Formal Logic

• History? (Aristotle, Aquinas, Ockham, Leibniz,
  Frege, Russell, Wittgenstein, Gödel, Church,
  Quine, Tarski)
• Foundations? (Logic and Philosophy, Logic and
  Maths, Logic and Science, Where does the Logic
  come from?, Does God have to obey the rules of
  Logic?...)
• Aim Understanding of fundamental concepts and
  techniques of Logic

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Course Outline

• Propositional logic
• Propositions and arguments
• Connectives and argument forms
• Truth tables
• Trees
• ?Natural deduction
• Predicate logic
• Predicates, names and quantifiers
• Models for predicate logic

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Reference

• Greg Restall Logic, An Introduction, Routledge,
  2006
• Richard C. Jeffrey Formal Logic Its Scope and
  Limits, McGraw-Hill, 1967
• Wilfrid Hodges Logic, an Introduction to
  Elementary Logic, Penguin, 1997, 2001
• http//people.hofstra.edu/faculty/Stefan_Waner/Re
  alWorld/logic/logicintro.html