Proof and certainty Lecture 10

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Proof and certaintyLecture 10

• Ben Bayer
• Philosophy 102 Logic and Reasoning

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Overview

• Third requirement all the relevant evidence
• Background knowledge and standards of proof
• Degrees of certainty
• Possibility of full certainty?

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All the relevant evidence

• We identified two requirements of a good
  argument
• The premises must be well-evidenced.
• The premises must be relevant to the conclusion
• Being a good argument means at best no obvious
  fallacies might still not be good enough for
  proof!
• Need a third requirement
• The premises must contain all of the relevant
  evidence
• But how do we know how much is relevant?

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Background knowledge and standards of proof

• Proof is an argument that establishes that its
  conclusion must be true
• Or a proof shows there is one and only one
  possible conclusion given the evidence
• Example the identity of a murderer

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Background knowledge and standards of proof
Mr. X was in possessionof a weapon.
Mr. X was missing at thetime of the murder.
Mr. X stood to gain fromvictims death.
Murder requires tools fordisrupting living
systems.
Murder requires physicalcontact/presence.
People take drastic actiononly for high stakes.
Possibly Mr. X had the murderweapon.
Possibly Mr. X was in the rightplace for the
murder.
Possibly Mr. X wanted tocommit the murder.
Mr. X is the murderer.
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Background knowledge and standards of proof
Possibly Mr. X had the murderweapon.
Possibly Mr. X wanted tocommit the murder.
Possibly Mr. X was in the rightplace for the
murder.
Its not possible that anyoneelse fulfilled
requirements.
Mr. X is the murderer.
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Background knowledge and standards of proof

• Proof is an argument that establishes that its
  conclusion must be true
• Or a proof shows there is one and only one
  possible conclusion given the evidence
• Example the identity of a murderer
• Background knowledge helps determine what
  evidence is relevant, and how much is all of it
• Example it tells us means, motive, opportunity
  are requirements of being a murderer

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Background knowledge and standards of proof
Mr. X was in possessionof a weapon.
Mr. X was missing at thetime of the murder.
Mr. X stood to gain fromvictims death.
Murder requires tools fordisrupting living
systems.
(Biology)
Murder requires physicalcontact/presence.
People take drastic actiononly for high stakes.
(Physics)
(Psychology)
Possibly Mr. X had the murderweapon.
Possibly Mr. X was in the rightplace for the
murder.
Possibly Mr. X wanted tocommit the murder.
Mr. X is the murderer.
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Background knowledge and standards of proof

• Proof is an argument that establishes that its
  conclusion must be true
• Or a proof shows there is one and only one
  possible conclusion given the evidence
• Example the identity of a murderer
• Background knowledge helps determine what
  evidence is relevant, and how much is all of it
• Example it tells us means, motive, opportunity
  are requirements of being a murderer
• Example it defines a domain for where to look
  for possible murder suspects

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Background knowledge and standards of proof

• (Anyone else is anyone who
• was within reasonable proximity of the victim
• who could have obtained access to a weapon
• who had dealings with the victim)

Possibly Mr. X had the murderweapon.
Possibly Mr. X wanted tocommit the murder.
Possibly Mr. X was in the rightplace for the
murder.
Its not possible that anyoneelse fulfilled
requirements.
Mr. X is the murderer.
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Background knowledge and standards of proof

• Proof is an argument that establishes that its
  conclusion must be true
• Or a proof shows there is one and only one
  possible conclusion given the evidence
• Example the identity of a murderer
• Background knowledge helps determine what
  evidence is relevant, and how much is all of it
• Example it tells us means, motive, opportunity
  are requirements of being a murderer
• Example it defines a domain for where to look
  for possible murder suspects
• These define the standard of proof for
  identifying a murderer.

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Background knowledge and standards of proof

• A standard of proof is a formulation identifying
  the types of facts needed to establish a
  conclusion on a given subject matter.
• Standards of proof will vary by subject matter
• Example Proving the shape of the earth requires
  finding signs of that shape locally and globally
  (because shapes appear differently from different
  angles)

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Background knowledge and standards of proof
Ships disappear overthe horizon.
Circular shadow of the earth in eclipse
Star patterns shift as move north/south.
Only constant curvatureexplains disappearance.
(Local sign of sphericality)
Only spherical objects roundunder every 2d
projection.
Only constant curvatureexplains disappearance
(Global sign of sphericality)
(Both local and global)
The earth is spherical.
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Background knowledge and standards of proof
Star patterns shift as move north/south.
Only constant curvatureexplains disappearance
(Both local and global)
The earth is spherical.
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Background knowledge and standards of proof

• A standard of proof is a formulation identifying
  the types of facts needed to establish a
  conclusion on a given subject matter.
• Standards of proof will vary by subject matter
• Example Proving the shape of the earth requires
  finding signs of that shape locally and globally
  (because shapes appear differently from different
  angles)
• Example Proving the dynamics of the earths
  continents requires finding a mechanism of
  motion, consistent with the earths not getting
  bigger (because it isnt)

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Background knowledge and standards of proof
The African coastline fits with the South American
Discovery of mid-Atlantictrench
Flat thin abyssal crust on bottom of ocean
Rock and fossil between distant continents
The contintents can movethrough a medium
Varying ages of ocean floor sediment
Discovery of Pacific subduction zones
Something pushes thecontinents
Continents could not have always been in same
place.
The continents have somewhere to go.
The continents have drifted apart.
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Degrees of certainty

• Standards of proof may be respected to different
  degrees
• May not need full proof when stakes are not high
• In law, reasonable suspicion needed to
  investigate
• Probable cause needed to search
• Balance of probabilities needed to win civil
  case
• Will need most proof when stakes highest
• Beyond a reasonable doubt needed for criminal
  conviction
• Degree to which full standard of proof approached
  is the degree of certainty

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Degrees of certainty

• Degree of certainty varies with amount of
  evidence
• Possibility only some of the evidence points to
  one conclusion
• Suppose we establish only a motive for Mr. X, not
  means or opportunity. (Possibly Mr. X did it.)
• Or suppose we establish motive and opportunity
  for both Mr. X and Mr. Y. (Possibly Mr. X or
  possibly Mr. Y did it.)
• Probability most of the evidence points to one
  conclusion
• Suppose you have means and opportunity for Mr. X,
  but not motive (Probably Mr. X did it)
• Or suppose we establish means, motive and
  opportunity for Mr. X, but havent yet ruled out
  Mr. Y (Probably Mr. X did it, but possibly Mr. Y
  did it.)

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Possibility of full certainty?

• To show a conclusion must be true means ruling
  out all other possible conclusions
• Two sources of uncertainty make this challenging
• Conclusions resting on generalizations
• Example All human action is motivated
• Conclusions resting on eliminations
• Example Mr. X is the only possible killer
• Generalizations themselves require eliminating
  possibilities
• Example All human action is motivated no other
  causes explain it

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Possibility of full certainty?

• Whether we can prove claims with full certainty
  depends on the basis of possibility claims
• If anything we can imagine is a possibility, it
  may be impossible to rule out every possibility,
  and impossible to prove anything with certainty
• If, however, possibilities require some evidence,
  proof will be possible