Lost In Translation

Problems in Converting English Into Logic

Gregory Lopez, MA, PharmDSkepticamp NYC 2010

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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

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

• To generously and charitably interpret others’ arguments…

• …while also helps bring to the fore hidden premises whose truth can be attacked

One Reason

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.”1) 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

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

Why Use Formal Logic To Argue?

• Formal logic is a normative discipline that guarantees true conclusions given true premises

Logic

Arguments

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

Some Translation Protips• Only assign sentence-letters to the

exact same sentences1) 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)

Protips (cont.)

• Make sure your translations are adequate

1. The English and translation “say the same thing”

2. They have the same truth conditions using the “intended interpretation”

Sainsbury M. (2001) Logical Forms, 2nd ed. Blackwell, Oxford. pp 63-4

“…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.

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

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.

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

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

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

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

Questions?