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Lost In Translation

Lost In Translation. x[RelaxingTime(x)SuntoryTime(x)]. Problems in Converting English Into Logic Gregory Lopez, MA, PharmD Skepticamp NYC 2010. Outline. Why? Some reasons why you may want to be able to translate English arguments into formal logic How? Some tips on translation WTF?

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Lost In Translation

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  1. Lost In Translation x[RelaxingTime(x)SuntoryTime(x)] Problems in Converting English Into Logic Gregory Lopez, MA, PharmD Skepticamp NYC 2010

  2. Outline • Why? • Some reasons why you may want to be able to translate English arguments into formal logic • How? • Some tips on translation • WTF? • What translation can and can’t do for you can depend on the logic you choose • Where? • Some resources for further study

  3. Outline • Why? • Some reasons why you may want to be able to translate English arguments into formal logic • How? • Some tips on translation • WTF? • What translation can and can’t do for you can depend on the logic you choose • Where? • Some resources for further study

  4. One Reason • To generously and charitably interpret others’ arguments… • …while also helps bring to the fore hidden premises whose truth can be attacked

  5. Being “Generous” • E.g: “It would be immoral and selfish not to use animals in research today, given the harm that could accrue to future generations if such research were halted.” • If animals were not used in research, then future generations could be harmed by halting animal research. • (IF a THEN b) 2) If future generations could be harmed by halting animal research, then not using animals in research is immoral and selfish. • (IF b THEN c) C) If animals were not used in research, then not using animals in research is immoral and selfish. • (IF a THEN c) Science, medicine, and animals (Washington, DC: National Academy of Sciences, Institute of Medicine, 1991), p.27

  6. A Second Reason • To ground solidly your own arguments • let a = "an given agent can do x at time t" let FW = "an given agent has freewill" let Kx = "God knows x"  P1) FW ↔ (◊a ∧ ◊~a) T1) FW → (◊a ∧ ◊~a) (biconditional elimination) T2) ~FW ∨ (◊a ∧ ◊~a) (property of material conditional) P2) Ka P3) Ka → ☐a T3) ☐a (modus ponens) T4) ~◊~a (definition of necessity) T5) ~◊~a ∨ ~◊a (disjunctive addition) T6) ~(◊~a ∧ ◊a) (DeMorgan's law) T7) ~(◊a ∧ ◊~a) (commutivity of conjunction) T8) ~FW (disjunctive syllogism of T2 and T7) QED

  7. Why Use Formal Logic To Argue? • Formal logic is a normative discipline that guarantees true conclusions given true premises Logic Arguments

  8. Outline • Why? • Some reasons why you may want to be able to translate English arguments into formal logic • How? • Some tips on translation • WTF? • What translation can and can’t do for you can depend on the logic you choose • Where? • Some resources for further study

  9. Some Translation Protips • Only assign sentence-letters to the exact same sentences • If animals were not used in research, then future generations could be harmed by halting animal research. • (IF a THEN b) 2) If future generations could be harmed by halting animal research, then not using animals in research is immoral and selfish. • (IF b THEN c)

  10. Protips (cont.) • Make sure your translations are adequate • The English and translation “say the same thing” • They have the same truth conditions using the “intended interpretation” • “…given the harm that could accrue to future generations if such research were halted” • Vs. • If animals were not used in research, then future generations could be harmed by halting animal research. Sainsbury M. (2001) Logical Forms, 2nd ed. Blackwell, Oxford. pp 63-4

  11. Outline • Why? • Some reasons why you may want to be able to translate English arguments into formal logic • How? • Some tips on translation • WTF? • What translation can and can’t do for you can depend on the logic you choose • Where? • Some resources for further study

  12. A Final Translation Protip • Translate as much as you need to until you get validity • Formal validity = English validity • Formal invalidity ≠ English invalidity Sainsbury M. (2001) Logical Forms, 2nd ed. Blackwell, Oxford.

  13. Which Logic? • All men are mortal; Socrates is a man; Therefore, Socrates is mortal • a, b ; c • INVALID • x(IF man(x) THEN mortal(x)), man(Socrates) ; mortal(Socrates) • VALID

  14. Outline • Why? • Some reasons why you may want to be able to translate English arguments into formal logic • How? • Some tips on translation • WTF? • What translation can and can’t do for you can depend on the logic you choose • Where? • Some resources for further study

  15. Resources • Copi IM, Cohen C. (1994) Introduction to Logic, 9th Ed. Macmillan, New York. • Overview of logic with plenty of opportunities to analyze arguments as well as learn the basics of logic • The Daily Translation: http://www.unco.edu/philosophy/trans.html • A daily challenge to translate part of a news article into predicate logic • Sainsbury M. (2001) Logical Forms, 2nd ed. Blackwell, Oxford. • The best source for all issues related to translating English into philosophical logic, but presumes you know some basic logic

  16. Take-Home Message • Being logical is hard work and not always worth it, but it’s important if you really want to: • Dig into someone else’s argument • Build up your own argument

  17. Questions?

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