modesty in claims
more modest to say
- “someone stole the car”
than
- “Sam stole the car”
What opportunities do modest claims have?
more opportunities to be true
- “Sam stole the car” - need evidence that Sam did it
- “Someone stole the car” - need evidence that Sam did it or Tom did it or Jerry did it, etc.
modest defensibility rule
if a claim is at all defensible, a more modest version will either maintain or increase its defensibility
exception to defensibility rule
neither are practically possible
- “He will win 2 trillion to nil”
- “He will win by a 2 trillion margin”
logical strength
- claim X is logically stronger than claim Y if and only if you can derive Y from X but not X from Y
- X, therefore Y holds true but Y, therefore X doesn’t hold true
how can you diminish logical strength?
- Existential introduction rule
- “John is ill, therefore someone is ill”
- Disjunction introduction rule
- “This coffee has sugar, therefore is coffee has sugar or milk”
- Conjunction elimination rule
- “The winter will be cold and dry, therefore the winter will be cold”
What does diminishing logical strength do for modesty?
- claims are more modest and therefore more defensibly
- because logically stronger claims commit themselves more than logically weaker ones
- logically stronger cliams have fewer opportunities to be true
Duhem-Quine thesis
hypotheses cannot be tested in isolation as they don’t have consequences on their own
Quien’s web of belief metaphor
all of our beliefs are nestled in an interconnected web of support
what are systems made up of?
central hypotheses and auxiliaries
- word for when system is true
- word for when system is false
- confirmed
- disconfirmed
If a consequence is false, will adding premises rectify it?
- no because classical logic is monotonic
- something must be removed or replaced
analogical reasoning
- use of such reasoning is widespread throughout the scientific and everyday domains
- e.g. Newton’s law of gravity
what decides the stength of an analogy?
how much we have had to abstract away in order to find commonalities
completely uninformative analogy
- abstract away so much that what is left behind is trivial
- e.g. Newton’s equations have lots of variables so others will too
informative analogy
only one layer is abstracted away
e.g. isomorphism = bijective mapping between objects that preserves relations
