Deduction and Induction

Question 1

Deduction - Aristotle

Answer 1

• Regarded as one of the most long lasting and influential contributions made to civilisation.
• Other systems include Stoicism
• Kant thought that Aristotle had discovered all there was to know about logic.
• The term ‘Traditional Logic’ is used to describe the offspring of Aristotelian logic.
• The ‘book’ that contains Aristotle’s extant writings on logic is known as the Organon. This is in fact a set of 5 or 6 writings on the topic.
• Aristotle while acknowledging Induction has much less to say about it than Deduction.

Question 2

Syllogistic reasoning or logic

Answer 2

• Comes from greek for deduction
• Aristotle outlined the basic structure consisting of accepting things that are certain from the known facts.
• The structure of deductive statement is thus in two parts
  
  • The premises (2) and
  • The conclusion
• Syllogisms are thus heavily reliant on two elements;
  
  • The ‘known-ness’ of the facts
  • The linguistic understandings of the reasoners
• Two types of syllogisms in Aristotle’s system:
  
  • Linear
  • Categorical
• Linear less important for our current purpose but have a form of a linear argument. These are somewhat superfluous and add little to what is immediately obvious.
• E.g.
  
  • You are taller than John;
  • John is taller than Bill;
  • Thus you are taller than Bill
• Categorical syllogistic reasoning
  
  • Consists of two premises and a conclusion that automatically follows
  • There are four types which form a 2x2 matrix. Based on two aspects: membership and coverage
  • The terms for membership are “affirmation” and “negation”
  • For coverage “universal” and “particular”
  • Syllogisms have specific words which indicate the type of argument being put forward;
    
    • Affirmative universal is “ALL”
    • Affirmative particular “SOME”
    • Negative universal “NO”
    • Negative particular “SOME…NOT”

Question 3

Conditional reasoning

Answer 3

• A conditional reasoning proposition consists of an antecedent and a consequent
• They are of the form If p, then q where p is the antecedent and q is the consequent
• What follows from the proposition is a re-statement of the implications of the conditional proposition
• Two prominent
• Modus ponens or affirmation of the antecedent
  
  • If p then q
  • Given q
  • Deduce p
• Modus tollens
  
  • If p then q
  • Not q
  • Not p
• There are a number of other statement types which have been studied and found to be problematic from the pov of human performance.
• One of the most famous is the Wason selection test.
  
  • Takes the form of a set of cards with an associated proposition, rule or question. E K 4 7.
  • The responses of participants are invariably poor by standards of deductive logic on average between 4-10%
  • To test the truth of the claim or rule logic requires that participants examine the assertion or p and the negation of the consequent i.e not q
  • The performance is seen to improve dramatically when relevant content or context is introduced. For example the drinking rule.
  • This raises the issue of to what extent is human reasoning context dependent and so abstract tasks are of minimal use. The latter form is called deontic reasoning.
• Theories put forward to account for deductive reasoning
  
  • Rips Mental Rules
    
    • Asserts that people solve deductive problems by constructing mental proofs
    • These proofs consist of a set of sentences in working memory
    • These sentences link premises to conclusions by inference rules
    • Not following the rules occurs as a result of cognitive limitations such as working memory capacity.
  • Johnson Laird’s Mental Models
    
    • People construct mental models based on the premises of the arguments
    • These models relate to real life knowledge
    • People then attempt to solve the problems by attempting to construct alternatives. If none can be created then the initial model is accepted
    • Mental models research is generally considered the more comprehensive and robust.

Question 4

Why study reason deductively?

Answer 4

• Evans asserted in 1982 that deduction was capable of being stripped of its association which were generated by experience, training and human adaptability
• Deductive problems in a sense allow as pure a form of experimentation s possible
• This however again raises the question of normative or descriptive focus. It is appropriate to study human reasoning by placing it outside of its ecological niche?
• The findings of Deontic experiments make the point that human reasoning can follow the rules of Deductive logic to a great extent provided the context is included.

Question 5

Summary - deductive reasoning

Answer 5

• There are many forms of deductive reasoning. The most commonly studied are
  
  • Syllogistic reasoning
  • Conditional reasoning
• One of the great strengths of deductive reasoning is that if the arguments are said to be true then the conclusion is guaranteed
• Deduction does not take us beyond the assertions or premises. This is the great weakness, one cannot learn anything new.
• Syllogistic reasoning involves premises followed by a conclusion
• Conditional reasoning involves if-then statements with the form of antecedent followed by consequent

Question 6

Induction - general

Answer 6

• Induction is said to be “an activity of the mind that takes us from the observed to the unobserved”
• Induction involves “a continuous adjustment to and updating of ones confidence in a belief”
• Inductive reasoning is the most common form of everyday and scientific reasoning
• Induction is the method of human thinking can generate assertions beyond the data or premises that are used in the process of inductive reasoning.
• It is by induction that we move from ‘sample’ to ‘population’
• Induction is associated with hypothesis generation and testing
• Induction involves the continuous adjustment of one’s beliefs
• One of the pitfalls is that in going from the particular to the general a cast number of hypotheses can be generated.
• There are two types of inductive assertion:
  
  • Strong: this is where there is good reason to accept the assertion under consideration
  • Weak: here there is poor or weak support [if there is no support than we should not accept the assertion]
• Induction is one of the main topics that Hume’s critique of causation applies to.

Question 7

Induction - causal inference

Answer 7

• One of the main assertions made by Hume was that the concept of causality was the product of co-occurrence in the experience and therefore mind of the observer i.e. us
• Causation is “mental habit formed by past regularities”
• Induction is the main method of deriving causal relations. We observe “many” instances and so the events become paired. A causes B. Flame causes heat.
• Such a method is said to be a critical capability in pre-scientific method cultures and hence for early humans.
• By pairing regularly occurring events we gradually develop a model of the world and what is safe and not and what is neutral.
• Our degree of association is a result of the likelihood of events co-occurring. In other words the probability of events co-occurring is critical to rational belief.

Question 8

Induction - confirmation bias

Answer 8

• The use of induction as a method for assessing the implications of events in the world take an interesting turn. Humans are prone to belief persistence or resist belief change.
• This has shown itself in several experimental findings around the topic of confirmation bias.
• Example
  
  • Numbers challenge task from 1^st workshop.
• Many results support these findings. People are much more likely and it seems to come “naturally” to ask confirmatory questions and not disconfirmatory ones.
• These studies have been criticised on several grounds including influence of social norms, source credibility and participants may have been affirming the hypothesis.

Question 9

Abduction

Answer 9

• Concept used in philosophy to indicate the process of hypothesis generations
• More exactly it means that selection of the best explanatory hypothesis for a known set of facts
• Is almost the reverse of induction in that the conclusion is accepted and the process involves the selection of the best explanatory set of premises.
• It is applied in such areas as fault diagnosis in automated systems, belief revision which is a hallmark of scientific reasoning.
• Abduction may be seen as incorporating new information at the level of ordering of the preference of the possible worlds.