Unit 3: Goodman, Zero/Sainsbury, Kant

Question 1

a formal theory of confirmation

Answer 1

• a formal theory of good inductive reasoning
• how do particular repeated observations confirm a generalization?
• the idea that relations of confirmation might be modified in style of deductive logic​

Question 2

Formal theory of confirmation…deductive to inductive

Answer 2

• example of deductive logic
  
  • all humans are mortal
  • socrates is human
  • C: socrates is mortal
    
    • notice, we only had to refer to the form and not the actual content
    • attempt to argue that inductive relations and reasoning or arguments might be given as a formal theory as well
• Goal: to formulate inductive logic like deductive logic, borrowing deductive logic whenever possible

Question 3

deductive

Answer 3

logical reasoning

Question 4

inductive

Answer 4

evidential reasoning

Question 5

the ravens problem

Answer 5

• observation: repeatedly observe black ravens
• hypothesis: all ravens are black
• logical equivalence/contrapositive:
  
  • if its a raven, then its black if and only if for all x if not black it is not a raven
  • Problem: all ravens are black, if and only if all non black things are not ravens
    
    • evidence for hypothesis that all nonblack things are not ravens
    • swan f is always white, something not black, not raven evidence must also support its logial equivalent
    • so, swan f that is white, confirms all ravens are black

Question 6

goodman problem

Answer 6

• “indoor orinthology”
  
  • instances of generalization confirm the generalization of its equivalent
  • ridiculous, because we can’t investigate the color of ravens without going outside
    
    • ie brown shoe example
  • induction should require some observation

Question 7

what the raven’s problem shows

Answer 7

• PGS reports a point made by I.J. Good: trouble because comparing one proposition (oberservation) with another (hypothesis)
  
  • a binary analysis of support relations
  • a 3 place relation can exhibit disconfirmation
    
    • “confirmation depends on other factors”
• PGS reports another point made by Good
  
  • ordinality and the possibility to confirm or disconfirm
    
    • “depends on the order in which you learn of the properties of an object”
• *Overall the problem shows
  
  • ordinality and the possibility to confirm or disconfirm

Question 8

the new riddle of induction intro

Answer 8

• formal theories of confirmation and instance confirmation
• deductive: universal instantiation
  
  • all Fs are Gs
  • A is an F
  • C: A is a G
• inductive: instance, enumerative
  
  • emerald a is green
  • emerald b is green
  • C: all emeralds are green
• model of FTC of good inductive reasoning after deductive reasoning
  
  • we learn something about the nature of support
• goodman undermines the prospects for not developing this idea
  
  • goodman is NOT arguing that confirmation is impossible or that relations of confirmation dont exist
    
    • hes attacking the idea that a purely formal theory can be successful, there can never be a formal theory of induction and confirmation
    • characterized with variables, not with content

Question 9

“grue”

Answer 9

• an object is grue IFF it was first oberserved before 2015 and was green, or 2 it was not first observed before 2015 and is blue
• argument is not good because it says emeralds we observe from now on will be blue
• but this argument has exactly the same form as the good inductive argument we saw before
• All observations of emeralds before 2015 confirm both hypotheses
  
  • 1: any yet to be seen emerald is green
  • 2: any yet to be seen emerald is blue
• Therfore, FTC does not seem to be possible

Question 10

the new riddle of induction & suggestions

Answer 10

• q: what exactly is wrong with bad inductive arguments? what makes bad induction bad?
• Suggestions to fix
  
  • restrict such words as grue because they refer to time
  • properties words should refer to should be natural kinds (but what is outside of chemical elements?)
  • dont employ complex terms, replace with simpler ones
    
    • Brings us to: the curve fitting problem
      
      • do we choose a straight line to fix the curve because its simpler? then it would be wrong!

Question 11

Zeno’s background and 2 radical conclusions

Answer 11

• Background
  
  • use of conceptual clarification of calculus and the development of rigorous methods for invetigating the infinite
  • challenging fundamental concepts in metaphysics
    
    • the relation of the parts of an object to the whole object, mereology
    • problems about the way objects persist through time, persistence
    • the nature of space, metaphysics
    • abstract qs about exactly how math or geometric concepts can be applied to material objects, from metaphysics to physics
• Claim 1
  
  • there is not more than one thing
• claim 2
  
  • change or motion is not possible

Question 12

spatial relations and mereology

Answer 12

• spatial relation and parts whole relations
• example: how can 1 thing, a book, be many things: pages, molecues
• answer: its not, the book is not identical to many things, the book just has many parts
• zero attempts to show that the idea that material objects have parts is absurd
  
  • so, we must reject the claim that anything has parts–it is all one thing
• example
  
  • 1: if a book has parts, infinitley many
  • 2: if a book has infinite parts, it is infinitley large
  • 3: so, if a book has parts it is infinitlyey large
  • 4: no book is inifinitley large
  • C: no book has parts

Question 13

Re premis 1: if a book has parts, infinitley many

Answer 13

• if a book has parts, then the region of space it contains has parts, and the book has a part corresponding to every part of space it fills
• so, if a region of space has parts, it has infinitley many parts

Question 14

Re premis 2: if a book has infinite parts, it is infinitley large

Answer 14

• if a region of space has infinitley many parts, it is infinitley large
  
  • this claim does a lot of work for the argument
• parthood for space requires infinite divisibility
  
  • reasonable, because finite amount of space parts is finitley large
    
    • there is something wrong with this
    • a finite region of space contains infinitley many parts
      
      • Q: how do they all fit?, thet are continually getting smaller
  • Distinction
    
    • **if, for some finite size, a whole contains infinite parts, none smaller than this size, then the whole is infinitley large
      
      • true: saying 0.5 + 0.5…=infinity (not going to be a finite size)
    • if a whole contains infinitley many parts, each of some finite size, then the whole is inifinitley large
      
      • False: they can be smaller than the other ie 0.4 + 0.3 + 0.2…does not equal infinity
  • so, there is no contradiction in the idea that space is divisible. but this does not entail that space, the actual space, actually is infinitley divisible
• premis 2 is false: zenos argument against plurality fails, fails because of of this statement **
  
  • for all we know, space might be granular
  • zeno has not given us any reason to think that space is granular

Question 15

The Racetrack, the dichotomy, sainsbury

Answer 15

• paradox: motion is impossible
  
  • traveling from a to b requires infinitley many journeys
  • it is impossible for anything to complete infinite number of journeys
  • C: impossible to get from A to B
  • C2: points are arbitrary, so all motion is impossible (False)

Question 16

re premis 1 “traveling from a to b requires infinite journeys”

Answer 16

• which is correct?

passing through all z points is sufficient for reaching z

passing through all the z points is not sufficient for reaching z

both good arguments, both cant be true

objection argument for a: benacerraf: where would the runner be after passing all the z points? nowhere because one might cease to exist after reaching every point but without reaching z ie shrinking genie

argument of a: sainsbury: “there is some discrepancy here between the abstract mathematical space like notions and our notions of physical space”

suppose we divide a line into x, y, and point b

is b in x, y, or both? cannot be in both…

say b is in x, imagine an archer asked to shoot through y without touching x: problem

the point b has to partally compose a line to which it belongs. we need a different notion: one that allowes x and y to touch without overlapping and a boundary that does not itself occupy space

Question 17

immanuel kant on the reality of space

Answer 17

• on the first ground of the distinction of regions of space
• importance 1768
• contains an ingenous argument for existence of space
• claim defending: absolute space has a reality of its own, independent of the existence of all matter and indeed as the first ground of possibility of the compositness of matter (an ontological claim)

Question 18

kants reality of space claim

Answer 18

• ontological claim: claim about what exists
  
  • that in addition to particular spatiotemporal relations between materials objects and their parts, there also exists a further thing-space itself
• why is it at all controversial whether space exists?
  
  • it has been debated since the beginning of intellectual thought through today: Gottfried Leibniz and Isaac Newton famously disagreed

Question 19

an ontological debate on space

Answer 19

• what question is being asked in whether space exists?
  
  • what did leibniz and newton agree on? spatial relations exists
  • disagree: what spatial relations are, fundamentally speaking, relations between (ie the nature of spatial relations or of space itself)

Question 20

newtons absolutism

Answer 20

• newton held that spatial relations between point in space, points of space exist independent of any material objects that occupy the points
• an absolutism about space, or defense of absolute space
• now called substantialism
• Overall: material objects, spatial relations, absolute spatial points (coordinate position)

Question 21

leibniz relationism

Answer 21

• L held that spatial relations are fundamentally relations between actual or possible material objects
• called relationism
• Overall: material objects, spatial relations
• Kant weighing in on debate: defending newt geometers assume it exists too

Question 22

absolute space

Answer 22

points on a diagram/plane

Question 23

relational space

Answer 23

im 5 meters from jack

leibniz and newton agree this exists

Question 24

the general strategy

Answer 24

• claim: absolute space has a reality of its own, independent of the existence of all matter and indeed as the first ground of the possibility of the compositeness of matter

Question 25

kants argument for the general strategy

Answer 25

• rejects the standard and traditional ways in which others have attempted to settle this issue by pure metaphysics
• armchair philosophy: established metaphysical (truth about nature of the universe) truths by purely speculating
• mentions Leonhard Eulers attempt: attempts to provide evident proof of the sort we find in geometry, by investigating what he calls the intuitive judgements of extension
  
  • kant thinks that a proof, by way of the methods in, geometry, is available
  • and it is proof of the actual existence of the sort of space presupposed in geometry
  • prepatory obeservations contain: spatial orientation, inner ground, set up his argument that centers on incongruent parts

Question 26

spatial orientation

Answer 26

• our conception of regions of space arise from a first person perspective
• something above/below, in front of/behind, to left or tright
• everything is fixed with respect to you so far
  
  • need cardinal directions

Question 27

spatial relations, positions, distance, and magnitude

Answer 27

• the substantialist and relationsist agree that spatial relations exist
• agree one way in which we can specific position in terms of where one thing is in relation to others
• we can characterize distance in terms of relations of positions
• magnitude in terms of position and distance
  
  • here is where issues become contentious, according to kant
• “absolute space has a reality of its own, independent of the existence of all matter, and indeed as the first ground of the possibility of the compositness of matter
  
  • the possibility of extended, material objects depends on absolute space

Question 28

spatial orientation: magnitude

Answer 28

• characterize magnitude: extension of a material object
• begin with simple geometrey
• we can talk about the postion and distance of the parts of an object as remaining the same in spatial manipulations
• can manipulate the spatial position by translation
• any part will maintain its relation and position and distance with any other part
• can specify position in relation to other objects
• why go on to posit the existence of absolute space? that space itself exists independently of the existence of material objects?
  
  • if no objects at all existed, there would still exist a universe of just space
  • absolute space has a reality of its own, independent of the existence of matter
  • while we may be able to depict magnitude as well as spatial relational positions, actual material objects in some way requires the existence of absolute space
  • why? i think kants discussion of an inner ground in nature is highly important

Question 29

inner ground orientation

Answer 29

• a very noteable characteristic of natural organisms
• a definite direction in which the arrangement of the parts is turned
• this feature distinguishes creatures that are otherwise similar in size, proportion, and the relative position of their parts
• why think that things in nature have an inner ground to an orientation?
  
  • idea: there are naturally occuring incongruent counterparts that have distinct orientation
  • similar = , incongruent: cant overlap
  • hand example: would make a L or R hand with the same instructions

Question 30

the existence of absolute space: reconstruction of Kants argument

Answer 30

• the relations holding among the parts of any given hand are the same as those of the incongruent counterpart
• if the relations holding among the parts of any given hand are the same as those of the incongruent counterpart then a hand is not L or R solely in virtue of such relations holding among its parts
• C: so a hand is not L or R in virtue of its relations holding between its parts
• a hand if L or R either a: soley in virtue of the reltions among the parts of the hand or b: partly in virtue of the exteral relations of the hand to something outside of it
• so a hand is L or R at least partly in virute of the external relation of the hand to something outside of it
• if a hand is L or R with part virtue of external relations either L or R a: partly in virtue of its relation to other material object or b: partly in virture of its relations to absolute space
• C:either a hand is L or R with part virtue of external relations either L or R a: partly in virtue of its relation to other material object or b: partly in virture of its relations to absolute space
• if a hand is L or R at least partly in virtue of its relation to other material objects, then it is not the case that a hand alone in the universe would be left or R
• a hand alone in the universe would have to be either left or right
• its not the case that a handis L or R at least partly in virtue of relation to other material objects
• a hand is :L or R at least partly in virtue of its relations to absolute space