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Whence the Uniformity PrincipleJohn P. McCaskey · Stanford University
Richard Whately
AncientScholastic
Humanist
Whatelian
Prosecuting a wrongdoer, even if it’s your own father.
What is piety?
That’s an example. What is piety itself? Doing what pleases the
gods.But gods disagree.
And there are many kinds of disagreement:Disagreement over which number is greater.Disagreement over which thing is larger.Disagreement over which thing is heavier.Disagreement over just and unjust.
Disagreement over beautiful and ugly.
Disagreement over good and bad.Piety is what pleases all gods.But is it pious because it
pleases the gods or does it please the gods because it is pious?
What is loved vs. what loves.
What is the difference?
What is led vs. what leads.
What is seen vs. what sees.So . . . what is admired vs. what admires.
I don’t know which.Let’s start over. Isn’t everything pious also just but not vice versa?
Yes.
Then piety is a kind of justice. What kind?
Ancient“
”Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.
Ancient
• Ensure property applies in individual cases.
• Test kinds broader and narrower.• Identify linked contraries.• Ensure the predicate can be applied
broadly.• Use terms that are unambiguous.• Identify temporal qualifications.• Identify dependencies.• Use language that makes clear in what
way exceptions are allowed.• Check relationship of whole to parts.• Be clear whether relationship is absolute
or relative.• . . .
Use observations and comparisons to . . .
“”
Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.
Ancient
“This procedure, which arrives at its aim from several instances, may be named inductio, which in Greek is called epagoge; Socrates made extensive use of it in his discussions.”
— Topica
“”
Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.
“[used] chiefly by Socrates and his disciples,”
— De InventionePhoto posted on Flickr by John Sellars (aka
photobiblon)
Scholastic
BoethiusPeter
AlbertAquinas
ScotusOckham
Zabarella
al-FarabiAvicenna
AverroesAncient
ClementAlexander
Sextus EmpiricusThemistius
Ammonius HermiaeSimplicius
Philoponus
Father, Son and Holy Spirit are eternal.[God is Father, Son and Holy Spirit.]
Therefore, God is eternal.
An induction has no necessity unless turned into a syllogism.
Everything that is this man, or that man, et cetera, is an animal.[Every man is this man, or that man, et cetera.]
Therefore, every man is an animal.
An induction is a syllogism in Barbara
with the minor premise
suppressed.
AncientScholastic
Socratic
Higginsian
Ancient
Humanist
Scholastic
Thomas
Wilson
1551
1552
Ancient
Humanist
Sunlight
Sunlight through magnifier
Flame
Heated or boiling liquidsWet, compressed plantsFibrous fabricsQuicklime with waterAnimals
Horse dung
LightningMeteors
Volcanoes
Solids on fireNatural hot baths
Distilled spirits?
PresenceRelated Absence
MoonlightStarlight…magnifier turned around?Moonlt through magnifier?
Liquids in natural state“further inquiry is needed”“let an experiment be made”Quicklime with oil?Insects
Sheet lightningComets, aurora borealis
Rotting wood?“not enough investigations”
X
X
Degrees
Fish
Different parts of animals
Dung as fertilizer
Kinds of animals
Corpse right after death
SeasonsAltitude
Lightning hotter than fireMany kindsSmaller solids heat up faster
Three Tables
1• Light? No: Dark things can be hot.• Something celestial? No: Heat can emerge from
underground.• Something terrestrial? No: Heat can come from the
heavens.• Expansion? No: Water does, but iron doesn’t expand when
heated.• Rarity? No: Fire and hot air are rare, but dense things can
be hot.• Motion? Not motion generally; some things move without
getting hot, but everything hot involves motion.
Candidates&
Exclusions
2
Heat is a kind of motion.3 Genus
• Expansive motion—most apparent in flame, but also apparent in boiling liquids, combustible materials, metals melting, rocks softening when heated. Also consistent with opposite behavior in cold. For example, glass expands when heated then contracts and cracks when cooled.
• Motion is of the parts (maybe too small to see) not of the whole as a unit . . .
4 Differentia
Definition5 Heat is an expansive motion which is checked
and restrained, and acting through particles, expanding in all directions, . . .
. . . a true induction
Scholastic
Socratic
Scholastic
Exploding French gunpowder is hot.Exploding German gunpowder is hot.Exploding English gunpowder is hot.
All exploding gunpowder is hot.
Heat is such-and-such motion.
All gunpowder has heat.
By induction
By the nature of definition
Hot things exhibit such-and-such motion.
Such-and-such motion is heat.All gunpowder has such-and-such motion.
Humanist
Socratic
Ancient
Ancient
2Identify Genus : the (Fundamental) Idea
1Identify Facts
“Induction is a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception.”The “Inductive Step” is the “Invention of the Conception.” “In every inference by Induction, there is some Conception superinduced upon the Facts.”
Scholastic
3Form Conception4Form Definition
Humanist
Socratic William Whewe
ll
AncientScholastic
“Inductive Principle”
Things will continue as they have.
The very foundation of induction.
But the principle is not true.
?
Humanist
Socratic
Thomas Reid
(But induction is valid.)
AncientScholastic
Whatelian
Socratic
Higginsian
Humanist
Ancient
Humanist
This, that and the other magnet attract iron.[All magnets are this, that and the other.]
Therefore, all magnets attract iron.
An induction is a syllogism in Barbara
with the minor premise
suppressed.
1823
* Not the minor, as Aldrich represents it.
1826
Scholastic
* “Not the minor, as Aldrich represents it.”
“[Induction is] a Syllogism in Barbara
with the major* Premiss suppressed.”
Henry Aldrich
Richard Whately
Not the minor, as Aldrich represents it. The instance he gives will sufficiently prove this: . . . “All magnets are this, that and the other”. . . is manifestly false.
Therefore all magnets attract iron.
Observed tyrannies are short-lived.
Therefore Socrates is mortal.
Therefore all tyrannies are short-lived.
Therefore attracting iron is a property of all magnets.
Therefore being short-lived is a property of all tyrannies.
Being short-lived is a property of observed tyrannies.
[A property of observed tyranniesis a property of all tyrannies.]
“[Induction is] a Syllogism in Barbara
with the major* Premiss suppressed.”
Minor Major
Minor
Conc.
Major
Observed tyrannies are short-lived.
Therefore all tyrannies are short-lived.
Therefore being short-lived is a property of all tyrannies.
Being short-lived is a property of observed tyrannies.
[A property of observed tyranniesis a property of all tyrannies.]
Minor
Conc.
Major
“[Induction is] a Syllogism in Barbara
with the major* Premiss suppressed.”
“original”“extremely important”
“[This] one remark would have sufficed to correct the erroneous notion the ancients had of induction, and to which Lord Bacon . . . [was responding]. They in fact mistook altogether the inductive syllogism, completing it by the addition of a minor, instead of a major.”
1828
“palpably suicidal”
“As Archbishop Whately remarks, every induction is a syllogism with the major premise suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism by supplying a major premise. If this be actually done, the principle we are now considering, that of the uniformity of the course of nature, will appear as the ultimate major premise of all inductions.”
“[Induction is] a Syllogism in Barbara
with the major* Premiss suppressed.”
Socratic
Higginsian
Propositional
Inference
Concept-Formation
Prior AnComment’
rsTopicsCicero
Early Humanist
s
? ?
Bacon Purge thisFind formal causeü
û
Better sense: Syllogism with supp’d major
Original and strict
sense
üWhately ’23
Mill ’43Syllogism
w. uniformity principle
Mere descriptionû ü
Ancients What is piety?
ScholasticsSyllogism
by complete
enumeration
Whewell
Each induction
ends with a new
conception
De Morgan ’47Original and logical sense
The sense nowadays
CorrectIncorrectû ü Bain ’70
Find probability
that the major is true
Jevons ’70
• Induction is about universal propositions, not universal concepts.
• It’s a risky kind of inference to be understood with reference to the better kind, deduction.• Uniformity principle is
a presumed major premise.• Logicians and mathe-
maticians have displaced philosophers of mind.
• It’s about propositional inference not abstraction.
“In an Induction, there are three essentials:—(1) the result must be a proposition as opposed to a notion. . . . Sometimes we are liable to confound the two. Definitions, or general notions, are limited to one indivisible fact or attribute; they are contrasted with inductions, which always join at least two facts or attributes . . . . The generalized notions of . . . resistance, whiteness, heat could not be confounded with inductions.” Logic, Book III, “Induction”
Socratic
Propositional
Inference
Concept-Formation
Better sense: Syllogism with supp’d major
Original and strict
sense
üWhately ’23
Mill ’43Syllogism
w. uniformity principle
Mere descriptionû ü
De Morgan ’47Original and logical sense
The sense nowadays
CorrectIncorrectû ü
Bain ’70Find
probability that the major is true
Jevons ’70
“ Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, . . . go such a very little way towards establishing an universal proposition? Whoever can answer this question . . . has solved the problem of Induction. ”
“ Note 2.—Since the time of Hume, the nature of our conception of Cause has formed one of the principal topics of philosophical controversy. . . . (a controversy, however, which possesses a historical rather than a practical or scientific interest). ”
Fowler ’70Presumptions in any inference: · Sense perception · Memory · Uniformity of natureVarious defenses: · Mill’s · Reid’s · Hume’s · Venn’s own
Venn ’89
“ The very concept of an experimental inference involves a great petitio principii. Induction owes all its force to the premise that the future will be like the past, which is just what the induction itself seeks to infer. ” “— as Hume relentlessly insisted —”
Cassirer ’05
Keynes ’21
“ Hume’s sceptical criticisms
are usually associated with
causality; but argument by
induction . . .
was the real object of his
attack. . . . Hume’s statement
of the case against induction
has never been improved
upon. ”
HigginsianHumean
AncientScholastic
Socratic
Higginsian
Humanist
Whatelian
“[Logic] is the grammar of reasoning by means of words.”
“[Logic] is the art of employing language properly.”
“In introducing the mention of language . . . to the definition of Logic, I have departed from established practice, in order that it may be clearly understood, that Logic is entirely conversant about language.”
Whence the Uniformity PrincipleJohn P. McCaskey · Stanford University