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?
– 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
One Reason
• To generously and charitably interpret
others’ arguments…
• …while also helps bring to the fore hidden
premises whose truth can be attacked
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 sentences
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)
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”
“…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, 2
Blackwell, Oxford. pp 63-4
nd
ed.
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?