The Other Kind of Induction John P. McCaskey History · Philosophy · Case Study.
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Transcript of The Other Kind of Induction John P. McCaskey History · Philosophy · Case Study.
The Other Kind of Induction
John P. McCaskey
History · Philosophy · Case Study
The Other Kind of Induction“Socratic Induction”
Two things may be ascribed to Socrates: inductive reason-ing and universal definitions.
Which kind of argument [is] called by the learned, “Socrates Induction”
has not yet been . . . tried except only by Plato . . . in settling on definitions
[Anatomist should proceed] according to the rule of Socrates.
Socrates made extensive use of it in his discussions
Particular & universal propositions
Particular things & universal terms
Two Conceptions of Induction
?Induction is a proceeding from particulars to a universal.
Man, horse, mule are long-lived.Bileless animals are man, horse, mule.Bileless animals are long-lived.
It is true of Father, Son and Holy Ghost.Father, Son and Holy Ghost are God.It is true of God.This animal chews by moving its lower jaw.That animal chews by moving its lower jaw.The other animal chews by moving its lower jaw.All animals chew by moving the lower jaw.What is true of the observed is true of all.This is true of the observed.This is true of all.
Scholastic Induction
Particular & universal propositions
Induction takes its force from the syllogism. So it suffices to discuss the syllogism which is, as it were, principal.Induction, therefore, so far as it is an argument, may, of course, be stated syllogistically.This view takes inductions to be defective deductions—deductions that do not quite make the grade.An inductive inference can always be looked upon as an aspiring but failed deductive inference.
Scholastic Induction
Particular & universal propositions
Particulars and universals are primarily propositions
A kind of inference that gains force the more it is like a complete enumeration, an argument that can be rendered as a syllogism.
Prior Analytics B 23misunderstood
A kind of inference inferior to deduction.
Positive instances determine reliability.
Particulars and universals are primarily propositions
Scholastic Induction
Particular & universal propositions
Particular things & universal terms
Two Conceptions of InductionParticulars and universals are primarily propositions
?Induction is a proceeding from particulars to a universal.
Prosecuting a wrongdoer, even if 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 k ind of just ice. What k ind?
Socratic Induction
Two things may be ascribed to Socrates: inductive reasoning and universal definitions.
A kind of inference that gains force the more it is like a complete enumeration, an argument that can be rendered as a syllogism.
Prior Analytics B 23misunderstood
A kind of inference inferior to deduction.
Positive instances determine reliability.
Particulars and universals are primarily propositions
A compare-and-contrast process for discovering properties that characterize all members of a kind, some of which are unique to the kind, some of which even define the kind.
TopicsPosterior AnalyticsSocrates
Not an inference and not inferior to deduction.
Breadth and depth of comparisons determine reliability.
Particulars and universals are primarily things, concepts, or terms.
Scholastic Induction
Socratic Induction
Ampliation takes place at the propositional level.
Ampliation takes place at the conceptual level.
Socratic Induction
Prosecut ing a w rongdoer, even i f your own f a ther.W hat i s p i e t y?
Tha t ’s an exam ple . W hat i s p i e t y i t se l f ?Do ing what p l eases t he gods .
Bu t gods d i sagree .
And t he re a re m any k i nds o f d i sagreem ent :
D i sagreem ent over wh i ch num ber i s g rea t er.
D i sagreem ent over wh i ch t h i ng i s l a rge r.
D i sagreem ent over wh i ch t h i ng i s heav ie r.
D i sagreem ent over j us t and un jus t .
D i sagreem ent over beau t i f u l and ug l y.
D i sagreem ent over good and bad.
P ie t y i s what p l eases a l l gods.Bu t i s i t p ious because i t p l eases t he gods or does i t p lease t he gods because i t i s p ious?
W hat i s l oved vs . what l oves .
W hat i s t he d i f f e rence?
W hat i s l ed vs . wha t l eads .
W hat i s seen vs . what sees .
So . . . wha t i s adm i red vs . what adm i res .
I don ’ t know wh i ch .
Le t ’s s ta r t over. I sn ’ t every th i ng p i ous a l so j us t bu t no t v i ce ve rsa?
Yes.
T h e n p i e t y i s a k i n d o f j u s t i c e . W h a t k i n d ?
Two things may be ascribed to Socrates: inductive reasoning and universal definitions.
Socrates
Categories
On Interpretation
Prior Analytics
Posterior Analytics
Topics
BookII
Ἐπαγωγὴ μὲν οὖν ἐστι καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸςτὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι.
Induction then is—or the from-induction deduction—deducing one extreme to the middle through the other extreme.
Socrates
Of the two deductions, then, the “induction” one, that is the “from-induction deduction” is deducing that one extreme belongs to the middle through the other extreme.
Socratic Induction
Scholastic Induction
Aristotle
Socratic Induction
Categories
On Interpretation
Prior Analytics
Posterior Analytics
Topics
Aristotle
Socrates
210
27
0
13
1
• 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 . . .
BookV
Socratic Induction
Aristotle
Socrates
Cicero
GalenStoicsEpicureansQuintilian
Aristotle
Socrates
Cicero
GalenStoicsEpicureansQuintilian
Scholastic Induction
Neo-Platonists
Clement
Simplicius
Philoponus
Alexanderof Aphrodisias
Socratic Induction
The great Alexandrian synthesis:• better known by nature vs. better known to us• prior vs. posterior• knowing the fact vs. knowing the reasoned fact• deduction vs. induction• deduction as a priori vs. induction as a posteriori
Makes Prior Analytics B 23 the definitive text
First to suggest that induction gains its force by a complete enumeration of particulars.
al-Farabi AverroesAvicenna
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Scholastic Induction
6th c. → 12th c.
Study of the Organon
Isagoge
Categories
On Interpretation
Prior Analytics
Posterior Analytics
Topics
210
27
0
13
0
1
Peter ofSpain Zabarella
AlbertAquinasScotus
Ockham
al-Farabi AverroesAvicenna
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Scholastic Induction
Peter ofSpain Zabarella
AlbertAquinasScotus
Ockham
[In induction it] is required to suppose that he has listed all the things . . . . One cannot in virtue of the fact that Socrates and Plato and Cicero run, induce of necessity that every man runs.
al-Farabi AverroesAvicenna
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Scholastic Induction
Peter ofSpain Zabarella
AlbertAquinasScotus
Ockham
Devices for addressing the conflict between induction as a kind of defective syllogism and induction found elsewhere in the corpus:• Formal vs. material reduction to syllogism• Formally valid vs. materially valid• Regular induction vs. abstraction• Regular induction vs. demonstrative induction• Use of “et cetera”
6th c. → 12th c.
Study of the Organon
Isagoge
Categories
On Interpretation
Prior Analytics
Posterior Analytics
Topics
210
27
0
13
0
1
Aristotle
Socrates
Cicero
al-Farabi AverroesAvicenna
Peter ofSpain
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
GalenStoicsEpicureansQuintilian
Zabarella
RenaissanceHumanists
AlbertAquinasScotus
Ockham
VallaAgricola
Nifo
Scholastic Induction
Socratic Induction
Cicero defines induction as follows . . . . Boethius, who followed a different school, disagrees . . .
Aristotle
Socrates
CiceroBacon Whewell
GalenStoicsEpicureansQuintilian
RenaissanceHumanists
Socratic Induction
• Idols• Concepts, not propositions• Comparisons, not enumerations• The predicate, not the subject
al-Farabi AverroesAvicenna
Peter ofSpain
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Zabarella
AlbertAquinasScotus
Ockham
Scholastic Induction
Hume
Aristotle
Socrates
CiceroBacon Whewell
GalenStoicsEpicureansQuintilian
RenaissanceHumanists
Socratic Induction
al-Farabi AverroesAvicenna
Peter ofSpain
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Zabarella
AlbertAquinasScotus
Ockham
Scholastic Induction
MillWhately
MillWhately
Every Tom, Dick, Harry, etc. is an animal.[ Every man is Tom, Dick, Harry, etc. ] Therefore, every man is an animal.
[Induction is] a Syllogism in Barbara with the major* Premiss suppressed.
* Not the minor, as Aldrich represents it.
Every induction may be thrown into the form of a syllogism by supplying a major premise. . . .The uniformity of nature will
appear as the ultimate major premise of all inductions.
[ What is true of the observed is true of all. ] This is true of the observed. Therefore, this is true of all.
To the Deductive Method . . . the human mind is indebted for its most conspicuous triumphs in the investigation of nature.
The Deductive Method . . . is destined to henceforth irrevocably to predominate in the course of scientific investigation.
Aristotle
Socrates
CiceroBacon Whewell
GalenStoicsEpicureansQuintilian
RenaissanceHumanists
Socratic Induction
al-Farabi AverroesAvicenna
Peter ofSpain
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Zabarella
AlbertAquinasScotus
Ockham
Scholastic Induction
MillWhately
The Case of Cholera
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
18191829
C. accidentalisC. spontanea
C. spontaneaC. accidentalis
Epidemic C.C. Morbus=
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
1825
C. spontaneaC. accidentalis
Epidemic C.C. Morbus ≠ ?
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
1832
=
Epidemic CholeraCholera Morbus
Broad Street Pump Epidemic
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
1854
C. spontaneaC. accidentalis
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
Epidemic CholeraCholera Morbus
Asiatic CholeraBilious CholeraEuropean CholeraCholera InfantumCholera Morbus
1870
C. spontaneaC. accidentalis
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
Epidemic CholeraCholera Morbus
Asiatic CholeraBilious CholeraEuropean CholeraCholera InfantumCholera Morbus
Robert Koch Louis Pasteur
Cholera OutbreakCairo
1883
C. spontaneaC. accidentalis
True cholera(wirklich, echt)
1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s
Epidemic CholeraCholera Morbus
Asiatic CholeraBilious CholeraEuropean CholeraCholera InfantumCholera Morbus
Asiatic Cholera Cholera:Cholera InfantumCholera Morbus
1910
1894
2013
1914
2013
Cholera is a malady characterized by vomiting, diarrhea, intestinal griping, lack of urination, and spasms in the leg.
Cholera is an intestinal infection caused by Vibrio cholerae.
Nominal Definition
Definition by Formal Cause
General Statements
Universal Statements
And if I ever found one that wasn’t _____ I wouldn’t call it a ____________
Tides are regular rising and falling of sea levels that occur twice a day.
Tides are regular rising and falling of sea levels caused by gravitational forces.
Dew is moisture on the ground after nights when there was no rain.
Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening due to condensation.
Electrical resistance is a material’s opposition to the passage of electricity.
The resistance of a device is the ratio of voltage across it to current through it.
Components of a Philosophy of Socratic Induction
Ampliation takes place at the conceptual level.
1
Components of a Philosophy of Socratic Induction
General Statements
Universal Statements
All Ps are Q.All Ps are Q.
2
Cholera is a malady characterized by vomiting, diarrhea, intestinal griping, lack of urination, and spasms in the leg.
Cholera is an intestinal infection caused by Vibrio cholerae.
Synthetic a posteriori
Analytica posteriori
Tides are regular rising and falling of sea levels that occur twice a day.
Tides are regular rising and falling of sea levels caused by gravitational forces.
Dew is moisture on the ground after nights when there was no rain.
Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening due to condensation.
Electrical resistance is a material’s opposition to the passage of electricity.
The resistance of a device is the ratio of voltage across it to current through it.
Components of a Philosophy of Socratic Induction
3
Cholera is a malady characterized by vomiting, diarrhea, intestinal griping, lack of urination, and spasms in the leg.
Cholera is an intestinal infection caused by Vibrio cholerae.
Formal Cause
Tides are regular rising and falling of sea levels that occur twice a day.
Tides are regular rising and falling of sea levels caused by gravitational forces.
Dew is moisture on the ground after nights when there was no rain.
Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening due to condensation.
Electrical resistance is a material’s opposition to the passage of electricity.
The resistance of a device is the ratio of voltage across it to current through it.
Components of a Philosophy of Socratic Induction
4 Material and Efficient Causes
Components of a Philosophy of Socratic Induction
5
Boundaries can be changed.
Personal and discretionary
Good, bad, better, worse
Evolve and mature
Boundaries differ in stability.
Organic theory of concept-formation
Particular & universal propositions
Particular things & universal terms
?Induction is a proceeding from particulars to a universal.
Bacon Whewell
RenaissanceHumanists
Aristotle
Socrates
Cicero
GalenStoicsEpicureansQuintilian
Socratic Induction
al-Farabi AverroesAvicenna
Peter ofSpain
Boethius
Neo-Platonists
Clement
Alexanderof Aphrodisias
Simplicius
Philoponus
Zabarella
AlbertAquinasScotus
Ockham
Scholastic Induction
McCaskey
Popper Salmon RescherKeynesBain Jevons
Ampliation takes place at the conceptual level.
MillWhately
All Ps are Q.
Analytica posteriori
FormalCauses
1
2
3
4
5