goes from the specific to the general. Deductive reasoning
goes from the general to the specific. Let me elaborate.
Deductive reasoning starts with a general rule, a premise, which we know to be true, or we accept it to be true for the circumstances. Then from that rule, we make a conclusion about something specific. Example:
All turtles have shells
The animal I have captured is a turtle
I conclude that the animal in my bag has a shell
A conclusion reached with deductive reasoning is logically sound, and airtight, assuming the premise is true. Deductive reasoning is fully convincing when it is based on a definition. If *by definition* a penny is a flat disc, copper in color and has a profile of Honest Abe on it, then I can be sure the penny in my pocket has those qualities.
The obvious strength of deductive reasoning is that conclusions derived with it are fully certain. The weakness, which was illustrated in the most recent example, is that no new information is added. The fact that the penny in my pocket is a copper disc with Lincoln on it was clear from the initial data, so the conclusion hasn't added any new information.
Inductive reasoning is making a conclusion based on a set of empirical data. If I observe that something is true many times, concluding that it will be true in all instances, is a use of inductive reasoning. Example:
All sheep that I've seen are white
All sheep must be white
This example makes inductive reasoning seem useless, but it is in fact very powerful. Most scientific discoveries are made with use of inductive reasoning. A majority of mathematical discoveries come about from conclusions made with inductive reasoning, or observation. But the key word is "discovery." With induction something can be discovered but not proven.
The general flow of events is like this: a)make observations b)form conclusions from empirical data c)prove conclusions with deductive reasoning. So if I notice that all triangles I come across have 180 degrees, through inductive reasoning I may form a hypothesis that *all* triangles have 180 degrees. But now that inductive reasoning has pointed me in the right direction, deductive reasoning allows me to prove my hypothesis as fact. There is just too much data out there to gather, to just go around blindly using deductive reasoning. Induction allows us to mine the data, and points out significant bits of information. From there we can prove things and form hard facts.
A number of e2ers have pointed out to me that my definition, particularly the definition of deduction, does not seem right. And just one week ago, I would've thought it was wrong too. In fact what triggered me to look into this was that my economics professor gave a half assed definition of deduction, which turned out to be completely wrong. So most people, including myself, have, or had, an intuitive definition of deduction which is just plain wrong.
The following text is from http://ibs.derby.ac.uk/~kpat/R&l/inductive.htm
Generalisations from experience
• Involves inferring general rules, theories or categories from the observation of specific instances.
Scientific reasoning: Generating and testing hypotheses
• Scientific reasoning is largely inductive.
• A theory, however, is just a set of inductive generalisations; it is not a set of facts.
• A theory is just a possible explanation, but not necessarily the true or only explanation.
• The non-logical nature of inductive inference has caused much debate in the philosophy of science, since scientific inferences appear to be non-logical.
• A great deal of research has attempted to model scientific reasoning in the laboratory.
• Participants are required to discover rules governing an artificial universe or situation of the experimenter’s creation.
• Participants attempt to discover these rules by using the scientific method – that is, formulating a hypothesis, and conducting experiments to test the hypothesis.
• The major interest in this work concerns the soundness of the strategies used to formulate, test, and eliminate alternative hypotheses.
Generating and testing hypotheses in Wason’s 2-4-6 task
• Wason's (1960; 1977) 2-4-6 problem: participants have to discover a rule the experimenter has in mind.
• The number sequence 2-4-6 conforms to the rule.
• The participant must generate number triples to try and discover what the rule is.
• The experimenter replies "yes" if a triple conforms to the rule, and "no" if the triple does not conform to the rule.
• The participant can test as many triples as they like and should only announce what they think the rule is when they feel confident that they have the right answer.
• If they are not right, the experimenter encourages them to keep trying by testing more triples – announcing more rules – and so on….
• The 2-4-6 triple is deliberately chosen to suggest a specific rule to the participants such as "numbers ascending in twos"
• The actual rule held by the experimenter is "any ascending sequence".
• Wason & Johnson-Laird (1972) found that:
- only 21% announced a correct rule first time
- 28% never announced a correct rule at all
- 51% made at least once incorrect announcement before coming up with the right rule
People appear to:
• Formulate an initial, incorrect hypothesis (e.g.., "numbers ascending in twos")
• Suggest triples that confirm their initial hypothesis, rather than generating triples that could potentially falsify their hypothesised rule.
In order to make progress on this task subjects need to:
• Test triples which could falsify their current hypothesis (i.e., use disconfirming triples)
- e.g., 2-3-4.
• Another way to make progress on the task is simply to vary your hypothesis.
Wason called the tendency to test a hypothesis with positive examples a confirmation bias.
Criticisms of the confirmation bias account and the role of positivity bias
• Do participants intend to achieve confirmation, or is such a strategy only ineffective because of the nature of the task?
• Evans (1989): participants are not attempting to confirm their hypothesis, but are unable to think of testing a hypothesis in a negative manner.
• Klayman and Ha (e.g., 1987): people have a bias to test positive instances of their hypothesis. In some situations (e.g., the 2-4-6 task) positivity bias can lead to difficulties.
• But in other situations, positive testing can lead to successful discovery of rules.
• The relation between the subject’s hypothesis and the target rule is all important!
There are in principle 5 such relations:
- The subject’s hypothesis (H) and the target rule (T) are the same: You think that the rule is "ascending by 2", and it is.
- H is less general than T: Your H is "ascending by 2" and the rule T is "ascending numbers".
- H is more general than T: Your H is "ascending by 2" but T is "even numbers ascending by two".
- H and T overlap: Your H is "ascending by 2" but T is "three even numbers" (each set will contain triples that are not in the other set).
- H and T are disjoint: Your H is "ascending by 2" but T is "descending numbers"
• The original 2-4-6 task is an example of the second of these relations.
• Positive testing will lead to permanent "yes" feedback and will therefore look like confirmation bias – when, in fact, it might not be.
• Positive testing will lead to identification of the target rule in some of the H-T relations. (e.g., situation 3).
• Klayman and Ha argue that positive testing is generally a rational strategy in cases where we cannot know the exact relation between H and T.