When and how is it (ir)rational to...Hempel & Jeffrey, 2000; Davey, 2014). In such a case, scientific rationality would be in imminent danger (Vickers, 2013). Deny contradictions,

María del Rosario Martínez-Ordaz1

1 Institute for Philosophical Research-UNAMWith support of UNAM-PAPIIT projects

IA401117 “Aspectos filosóficos de las lógicas contraclásicas” and IA401717 “Pluralismo y Normatividad en Lógica y Matematicas”

[email protected]

October 23, 2018Normativity across Disciplines, UNAM.

When and how is it (ir)rational to go paraconsistent in science?When and how

is it (ir)rational to go para-consistent in scienceMaría del Rosario Martínez-Ordaz

Preliminaries

Risk & Rational Choice

Contradictions in science

Paraconsistency& Triviality

Risk Analysis

Final remarks

Special thanks to:

When and how is it (ir)rational to go para-consistent in scienceMaría del Rosario Martínez-Ordaz

Preliminaries




Risk Analysis

Final remarks2


Preliminaries




Risk Analysis

Final remarks

(Pre-)preliminaries

Contradictions

Empirical sciences

Paraconsistency

Formal sciences3


Preliminaries




Risk Analysis

Final remarks

(Pre-)preliminaries

Contradictions

Empirical sciences

Paraconsistency

Formal sciences4

The intuition


Preliminaries




Risk Analysis

Final remarks

If our best scientific theories were to be inconsistent,after having identified a contradiction in any of ourtheories, the risk of arriving at arbitrary conclusions(triviality) would be extremely high (Popper, 1959;

Hempel & Jeffrey, 2000; Davey, 2014).In such a case, scientific rationality would be in

imminent danger (Vickers, 2013).

Deny contradictions, go classical Accept contradictions, go paraconsistent

But such a common intuition is methodologicallyunsound -at least, for the case of empirical sciences.

5

The intuition


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Risk Analysis

Final remarks






6

The intuition


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Risk Analysis

Final remarks






7


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Risk Analysis

Final remarks

Plan

Preliminaries


Contradictions in Science

Paraconsistency and Triviality

Risk Analysis

Final Remarks

8


Preliminaries




Risk Analysis

Final remarks

Assumptions

Contradiction + belief

Domain

Empirical sciences ≠ Formal sciences

The study of contradictory beliefs, and the different ways in which wemanage (and resolve) such contradictions, play a fundamental role inelucidating the foundations of rationality (Rovane, 2004).

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Risk Analysis

Final remarks

Assumptions

Science

Problem solving enterprise

Scientific Rationality

Science as a great exemplar of human rationality

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Preliminaries




Risk Analysis

Final remarks

Assumptions (Sc. Rationality)

Context sensitivity

While something can be regarded as adequate in one domain, it might not happen the same for all possible scientific domains

Epistemic justificationBoth scientists having certain epistemic attitudes under specific

circumstances as well scientists explaining why such epistemicstances are likely to be correct in certain contexts (or useful forcertain purposes) are often perceived as indicators of specificstyles of reasoning and thus, of scientific rationality.

Maximization of utilityEmpirical theories to provide as much accurate information aboutthe world as possible (Hempel & Jeffrey 2000), and the leastamount of false information (failed predictions) as possible.

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Preliminaries




Risk Analysis

Final remarks

Preliminaries

Sensible reasoning

Epistemic agents are -at least- still able to distinguish betweenthe (inferential) products of their reasoning that are sensiblegiven a particular context from those that are not (Carnielli &Coniglio, 2016; Friend & Martinez-Ordaz, forthcoming).

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Preliminaries




Risk Analysis

Final remarks

Preliminaries

Contradiction

A pair of propositions, where one is the negation of the other.

Principle of ExplosionOne of the most characteristic principles of any explosive logic(including, of course, classical logic).Any theory, if closed under an explosive logical consequencerelation, will trivialize when containing a contradiction.

Triviality

A theory is trivial if any proposition is a theorem.

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Preliminaries




Risk Analysis

Final remarks

Preliminaries

Contradictions

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Contradictions entail everything & contradictions cannot bebelieved rationally.

ParaconsistencyA logical consequence relation is said to be paraconsistent if it isnot explosive. Thus, if a consequence relation is paraconsistent,then even in circumstances where the available information isinconsistent, the consequence relation does not explode intotriviality.


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Risk Analysis

Final remarks

Preliminaries

History of science

Aristotle’s Theory of Motion.

Bohr’s theory of the Atom. Classical Electrodynamics. Classical Mechanics (T-O). Early Calculus.

Kirchhoff’s Theory of Diffraction.

Newtonian Cosmology. Nineteenth century

physics/geology. Nuclear models.

Inconsistency toleration

A phenomenon which takes place once agents identify a contradiction in a relevant part of their reasoning and are still able to distinguish between the (inferential) products of their reasoning that are sensible given a particular context from those that are not (Meheus 2002, Carnielli and Coniglio 2016, Friend and Martínez-Ordaz forthcoming).

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Preliminaries




Risk Analysis

Final remarks

Triviality

History of science

Aristotle’s Theory of Motion.

Bohr’s theory of the Atom. Classical Electrodynamics. Classical Mechanics (T-O). Early Calculus.

Kirchhoff’s Theory of Diffraction.

Newtonian Cosmology. Nineteenth century

physics/geology. Nuclear models.

Principle of ExplosionOne of the most characteristic principles of any explosive logic(including, of course, classical logic).Any theory, if closed under an explosive logical consequencerelation, will trivialize when containing a contradiction.

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Preliminaries




Risk Analysis

Final remarks

Triviality




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Preliminaries




Risk Analysis

Final remarks

Risky science (1)

(1815) ’Prout’s hypotesis’:

William Prout proposed that atomic

weights of all chemical elements

(identified at the time) were

multiples of that of the atomic

number of hydrogen. From this, he

claimed that hydrogen was some

sort of "prime matter" from which

other elements were composed

(Laudan 1977).

• Since the very beginning, the

evidence in favor of such a

hypothesis was almost null,

Prout’s hypothesis was very

likely to be false.

• In addition because it was a

very new proposal and

because it was not causally

related to any other important

theory at the moment, the

harm that it could have

caused by being false was

very low.18


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Risk Analysis

Final remarks

Risky science (1)

(1815) ’Prout’s hypotesis’:

William Prout proposed that atomic

weights of all chemical elements

(identified at the time) were

multiples of that of the atomic

number of hydrogen. From this, he

claimed that hydrogen was some

sort of "prime matter" from which

other elements were composed

(Laudan 1977).

• Since the very beginning, the

evidence in favor of such a

hypothesis was almost null,

Prout’s hypothesis was very

likely to be false.

• In addition because it was a

very new proposal and

because it was not causally

related to any other important

theory at the moment, the

harm that it could have

caused by being false was

very low.19


Preliminaries




Risk Analysis

Final remarks

Risky science (2)

(1859) Le Verrier:

Kepler’s laws + Newton’s

gravitational theory (including

Newtonian mechanics):

• Before 1859, astronomers believed

that the risk of Newtonian dynamics

being mistaken was extremely low.

• Immediately after Le Verrier

presented the anomalous rate of

precession of the perihelion of

Mercury’s orbit as a problem in

Newtonian celestial mechanics,

astronomers still thought that the

risk of Newton’s theory of being

mistaken was still low.

• Nonetheless, after several

unsuccessful solutions to the

problem, they started to realize that

the chances of the theory being

mistaken were higher that they

expected.20


Preliminaries




Risk Analysis

Final remarks

Risky science (2)

(1859) Le Verrier:

Kepler’s laws + Newton’s

gravitational theory (including

Newtonian mechanics):

• Before 1859, astronomers believed

that the risk of Newtonian dynamics

being mistaken was extremely low.

• Immediately after Le Verrier

presented the anomalous rate of

precession of the perihelion of

Mercury’s orbit as a problem in

Newtonian celestial mechanics,

astronomers still thought that the

risk of Newton’s theory of being

mistaken was still low.

• Nonetheless, after several

unsuccessful solutions to the

problem, they started to realize that

the chances of the theory being

mistaken were higher that they

expected.21


Preliminaries




Risk Analysis

Final remarks

Risky science (C)

The study of the negative impact that contradictions can have on

scientific rationality, requires an analysis of not only the frequency

of contradictions in science but also the possible harm that

contradictions could cause to rationality.

Risk={A,C,P}

[W]here A represents the events (initiating events,

scenarios), C the consequences of A, and P the associated

probabilities. Examples of events A are: gas leakage

occurring in a process plant, and the occurrence of a

terrorist attack. Examples of C are the number of

causalities due to leakages, terrorist attacks, etc.

(Avent 2010: 623)

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Preliminaries




Risk Analysis

Final remarks

What does it mean to be in danger?

Risk={A,C,P}

[W]here A represents the events (initiating events,

scenarios), C the consequences of A, and P the associated

probabilities. Examples of events A are: gas leakage

occurring in a process plant, and the occurrence of a

terrorist attack. Examples of C are the number of

causalities due to leakages, terrorist attacks, etc.

(Avent 2010: 623)

The study of the negative impact that contradictions can have on

scientific rationality, requires an analysis of not only the frequency

of contradictions in science but also the possible harm that

contradictions could cause to rationality.

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Preliminaries




Risk Analysis

Final remarks

Risk

Frequency Risk vs. Severity Risk

Low Severity High Severity

High Frequency

Low Frequency

Maximizing utilities, reducing (expected) loss

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Preliminaries




Risk Analysis

Final remarks

Risk

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Preliminaries




Risk Analysis

Final remarks

Risk management

26

The precaution-based (also called safety-preserving)

strategies are the ways in which it is possible to avoid or

minimize the severity of the consequences of a particular

event before knowing the probability of such an event.

On the other hand, the risk-based approaches invest efforts

on mitigating the consequences of an event if the event were

already obtained.

Risk-management mechanisms are the different ways in which it is

possible to avoid or minimize the severity of the consequences of a

particular event once the probability of such an event is known.


Preliminaries




Risk Analysis

Final remarks

Risk management

27







already obtained.

Risk-management mechanisms are the different ways in which it

is possible to avoid or minimize the severity of the

consequences of a particular event once the probability of such

an event is known.


Preliminaries




Risk Analysis

Final remarks

Decision under risk

The study of risky decision making has addressed twobroad questions. How should individuals behavewhen faced with a risky choice like the ones above?How do individuals behave when faced with a riskychoice? The first question is normative; the second,descriptive.(Wu, Zang & Gonzalez, 2004: 1)

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Preliminaries




Risk Analysis

Final remarks


29


Decision under risk


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Risk Analysis

Final remarks


30


Decision under risk


Preliminaries




Risk Analysis

Final remarks

Risk & science

31







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Risk Analysis

Final remarks

Sc. Contradictions

32

(Re)presentation IdentificationGroups of propositionsFamilies of models…LanguageLogical consequence(s)

Cf. Vickers 2013, Azzouni 2014

Theory itselfTheory-ObservationTheory-Theory

Cf. Priest 2002, Davey 2014

ContradictionEmpirical Scientific Theories

Inconsistency toleration

Logical EpistemicConsistency preservationInconsistency toleration(handling inconsistency mech.,Dialetheism)

Cf. Bueno 2017

UseBelieveEvidenceTruth*

Cf. Vickers 2013,


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Risk Analysis

Final remarks

Assumptions (Sc. Rationality)

Context sensitivity

While something can be regarded as adequate in one domain, it might not happen the same for all possible scientific domains

Epistemic justificationBoth scientists having certain epistemic attitudes under specific

circumstances as well scientists explaining why such epistemicstances are likely to be correct in certain contexts (or useful forcertain purposes) are often perceived as indicators of specificstyles of reasoning and thus, of scientific rationality.

Maximization of utilityEmpirical theories to provide as much accurate information aboutthe world as possible (Hempel & Jeffrey 2000), and the leastamount of false information (failed predictions) as possible.

33


Preliminaries




Risk Analysis

Final remarks

What are the dangers?

34

• Basic scientific irrationality — the scientist• False theories — theory• Medium scientific irrationality— the scientist• Evidential impasse — theory• Evidential impasse — the scientist• Triviality — theory• Scientific rationality —the scientist


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Risk Analysis

Final remarks

Basic Scientific irrationality|the scientist

35

(1.1) It is common wisdom that contradictions are logically false,

hence never true, and this is taken to be known by any scientist.

(1.2) To provide epistemic justification for our own beliefs is a

constraint of scientific rationality.

It is commonly thought that anyone knowingly believing a falsity can

justifiable believe it.

(1.3) From this, it seems to follow that a scientist believing an

inconsistent fails at satisfying the demand for epistemic justification

that constraints scientific rationality .

(Therefore) A scientist believing a contradiction must be

irrational (Davey, 2014).

Distinctive object of harm: Epistemic justification for scientific rationality.


Preliminaries




Risk Analysis

Final remarks

False theories|theory

"It is impossible for all the elements of a logically inconsistent set of sentences to be true, (…) a logically inconsistent theory is false”

Davey 2014; 3010

“inconsistency has typicallybeen regarded as the kiss of death for a theory.”

Davey2014: 3009

Distinctive object of harm: Maximization of utility (the theory contains

falsities).


Preliminaries




Risk Analysis

Final remarks

Medium scientific irrationality| scientist

37

(3.1) Preservation of justified belief through conjunction is

valid, that is, the validity of the following is granted:

JBSC(A), JBSC(¬A) ⊢ JBSC(A^ ¬A)

(3.2) Rational belief is closed under entailment, and thus,

justified belief is closed under entailment.

(Therefore) The scientist renders triviality for rational

belief.

Distinctive object of harm: Epistemic justification.


Preliminaries




Risk Analysis

Final remarks

Evidential impasse | theory

38

If a theory provides evidence in favor of A but also provides

evidence in favor of ¬A, that theory fails at solving problems

in its discipline.

Distinctive object of harm: Maximization of utility (the theory does not allow

for efficient problem solving)


Preliminaries




Risk Analysis

Final remarks

Evidential impasse|scientist

39

A scientists believes to have conclusive evidence of A

constituting a solution for Γ, but she also believes to haveconclusive evidence of ¬ A constituting a solution for Γ, she

will never be able to rationally choose between the two

alternative solutions.

Distinctive object of harm: Maximization of utility and Epistemic

justification (the scientist is never justified to take any of the

mutually contradictory alternatives as a solution of the problem).


Preliminaries




Risk Analysis

Final remarks

Triviality | theory

40

–Distinctive object of harm: Scientific rationality —as the disjunctionof (i) epistemic justification, (ii) context sensitivity and (iii)maximization of utility.

“an inconsistent theory implies any conceivableobservational prediction as well as it is negation and thustells us nothing about the world”

Hempel 2000: 79

“an auto contradictory system is uninformative, becauseany conclusion we please can be derived from it”

Popper 1959


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Risk Analysis

Final remarks

Triviality |scientist

41

Distinctive object of harm:Scientific rationality —as the conjunction of (i) epistemic justification, (ii)context sensitivity and (iii) maximization of utility; (meta) context sensitivity.

“Given some purpose, the trivialist can have no reason for behaving inone way rather than another to bring it about. But the situation is worse.The trivialist—at least whilst they remember that they are a trivialist—can have no purpose at all.” (Priest, 2005: 69).

“if rational belief is closed under entailment, because of the explosionprinciple, no sensible reasoning could take place once an agent hasaccepted a contradiction.” (Priest, 1998: 410)


Going paraconsistent?

42






Preliminaries




Risk Analysis

Final remarks


Preliminaries




Risk Analysis

Final remarks

Paraconsistency

43



Risk management

44







already obtained.

Risk-management mechanisms are the different ways in which it

is possible to avoid or minimize the severity of the

consequences of a particular event once the probability of such

an event is known.

Preliminaries




Risk Analysis

Final remarks


Preliminaries




Risk Analysis

Final remarks

Paraconsistency

45


Are these risk managementresources?


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Risk Analysis

Final remarks

Paraconsistency

46

ParaconsistencyA logical consequence relation is said to be paraconsistent if it isnot explosive. Thus, if a consequence relation is paraconsistent,then even in circumstances where the available information isinconsistent, the consequence relation does not explode into

triviality.

Are these appropriate risk managementresources?


Risk

Preliminaries




Risk Analysis

Final remarks47

Where isTRIVIALITY?


Preliminaries




Risk Analysis

Final remarks

Risk analysis

48

A list of individual risks

A rating of each risk (based on likelihood and impact)

An assessment of current controls (safety preserving mechanisms)

A plan of action (risk management selection)


Preliminaries




Risk Analysis

Final remarks

Inconsistent science & Risk

49


Preliminaries




Risk Analysis

Final remarks

Risk & contradiction

50

The Trivialist

Rational belief closed under entailment

False theories Evidential impasse (sc)

Trivial theory

Believing the false

Evidential impasse (th)

ScRealist’smethodologies

Empirical constraintsScientific practice constraints

Fragmentation Cognitive limitations

Explosion

The intuition







51

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Risk Analysis

Final remarks


Preliminaries




Risk Analysis

Final remarks

Final remarks

52


The intuition


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Risk Analysis

Final remarks






53



54


Decision under risk

Do we need paraconsistency for doing this?

Preliminaries




Risk Analysis

Final remarks


Preliminaries




Risk Analysis

Final remarks

Final remarks

55

But such a common intuitionseems weak -at least, for the caseof empirical sciences.



56

NOT SO OFTEN

Decision under risk

When is it rational to go paraconsistent?

Preliminaries




Risk Analysis

Final remarks


Thank you!

57

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Risk Analysis

Final remarks

María del Rosario Martínez-Ordaz1

1 Institute for Philosophical Research-UNAMWith support of UNAM-PAPIIT projects

IA401117 “Aspectos filosóficos de las lógicas contraclásicas” and IA401717 “Pluralismo y Normatividad en Lógica y Matematicas”

[email protected]

October 23, 2018UNAM

When and how is it (ir)rational to go paraconsistent in science?When and how

is it (ir)rational to go para-consistent in scienceMaría del Rosario Martínez-Ordaz

Preliminaries




Risk Analysis

Final remarks58


Preliminaries




Risk Analysis

Final remarks

Despite:“Narrowly logical approaches” I

Harman (1984, 1986) human rationality is not necessarily reducible to/ fully guided by/ described by the rules of our preferred formal logic.

Can they help us to deal with contradiction?

Motiva-question

Heuristics


Preliminaries




Risk Analysis

Final remarks

“We take it for granted that human activity, including science, is purposive.”(Wimsatt 2006)

Science: problem-solving enterprise

Empirical

Conceptual

Anomalies

Logical contradictions

…

Logical contradictions

…

Cf. Laudan 1977


“Narrowly logical approaches” I

Harman (1984, 1986) human rationality is not necessarily reducible to/ fully guided by/ described by the rules of our preferred formal logic.

Can they help us to deal with contradiction in Sc Practice?


Preliminaries




Risk Analysis

Final remarks

Heuristics


Preliminaries




Risk Analysis

Final remarks

Can they help us to deal with contradiction in Sc Practice?

Heuristics

Documents

When and how is it (ir)rational to...Hempel & Jeffrey, 2000; Davey, 2014). In such a case, scientific rationality would be in imminent danger (Vickers, 2013). Deny contradictions,