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# Inductive and Deductive Reasoning/ Natural Sciences + Mathematics

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## Maliha K

on 11 October 2013

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#### Transcript of Inductive and Deductive Reasoning/ Natural Sciences + Mathematics

Strengths and Limitations of Inductive and Deductive Reaso ning in Natural Sciences and Mathematics.

-Inductive reasoning has its place in the scientific method.
Specific observations and measurements may begin to show us a general pattern.
-This allows us to formulate a tentative hypothesis that can be further explored
-We might finally end up making some general conclusions with deductive reasoning.

Personal connection: Binomial Nomenclature: (SL Biology)
Induction involves the formulation of generalizations from specific examples. Humans must make tentative generalizations because otherwise, we would have no use of language.
For example: The word "Canine" is a generalization of a certain breed of animal (a dog). This allows for a quick reference for biologists.
Inductive
Can be used as a basis for justification
Produces concrete conclusions about nature that are backed by a variety of observational evidence.

Can’t ever give us anything certain, only things that are likely to be the case.
-Hasty Generalizations
Most inductive reasoning is not based upon exhaustive evidence, and therefore the form is incomplete.

-Scientists do not work inductively, but use intuition ahead of facts to conjure a hypothesis.
-A hypothesis is always tested deductively, as it is taken for the moment as truth.
-Statements in science can never be verified because of the uncertainty in induction. They can only be falsified or refuted by evidence.
Allows scientists to specify their observation instead of generalizing it

False Premise

One can start off with a generally accepted axiom, or statement, and deduce conclusions based on that axiom.
Deductive reasoning can make permanent the logical fallacies we have today. In other words, if you use an axiom to deduce a variety of conclusions, and that axiom turns out to be false, all of the conclusions following that axiom are false as a result.

Use inductive reasoning to make a conjecture about the next figure in the pattern

If you have carefully observed the pattern, this is the next figure in the pattern

In Mathematics
Inductive reasoning in math involves the process of arriving at a conclusion by observing patterns
Deductive reasoning in geometry is the process by which a person makes conclusions based on previously known facts.
Deductive
Inductive
inductive reasoning can never be used to provide proofs.
ACCORDING TO KARL POPPER...
HOWEVER! Science is open to being falsified and is able to be tested.
In the Natural Sciences
:

Charles Darwin:

-Proposed that the finches all shared a common ancestor, and evolved and adapted, by natural selection, to exploit vacant ecological niches.
-This resulted in evolutionary divergence and the creation of new species, the basis of his 'Origin of Species'.

Realized Finches, a species of birds
varied across the Galapagos Islands
INDUCTIVE REASONING: He started with a specific piece of information and expanded it to a broad hypothesis. He then used DEDUCTIVE REASONING to generate testable hypotheses and test his ideas.
One can
therefore
conclude...
Strengths:
Limitation:
Deductive
Limitation
Strengths
Circular reasoning
GEOMETRY
Given that a certain quadrilateral is a rectangle, and that all rectangles have equal diagonals, what can you deduce about the diagonals of this specific rectangle?
Limitation
Strengths
Limitation
Strengths
Instead, inductive reasoning is valuable because it allows us to form ideas about groups of things in real life
Example:
All metals expand when heated
A is a metal
Therefore A expands when heated
Deductive Reasoning
Inductive Reasoning:
Reasoning from the particular to the general.
Example:
Metal A expands when heated, as does metal B and C
Therefore, all metals expand when heated.
Reasoning from the general to the particular

They are equal....
Personal Connection From IB Biology
If A is true, B is true. If B is true, A is true. Therefore, both are true.
Allows for the simplification of various things, based on patterns observed
End
“The only situation that is impossible is a a valid argument with true premises and a false conclusion"....An argument can be valid and still not be true!
Furthermore...
To what extent can science be verified by reasoning?
Knowledge issue:
Example 2:

THEN a square is a quadrilateral.

Example 1:
PROOFS:
If you double a whole number you always get an even number:
ex: 13+13=26

If you multiply two odd numbers you always get an odd number:
ex: 5x9=42
according to mathematical induction some things are always "fundamental truths"

Do proofs provide us with completely certain knowledge? (especially in mathematics)
Extracted knowledge issue from "fundamental truths" by mathematical induction:
Maliha Khan
TOK II
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