Induction involves using many individual observations to make a generalization.
This approach can be considered to be moving "from the bottom up".
Item X has characteristic W.
Item Y has characteristic W.
Item Z has characteristic W.
Therefore, all items in the same class as X, Y, and Z should also have characteristic W.
The Risk of the Inductive Leap
One could make many individual observations:
This bee stung me. It is a hymenopteran.
This wasp stung me. It is a hymenopteran.
This fire ant stung me. It is a hymenopteran.
And come to a general conclusion:
Therefore, all hymenopterans have stingers.
But you might already see a potential pitfall here.
A general conclusion made from many specific observations may not always be true.
Unless you test every every single hymenopteran species for stinging capability,
you might not discover an exception to your general rule.
In reality, many hymenopterans (stingless bees and ants, male honeybees, etc.) lack stingers.
Generalizations are certainly useful.
But a wise person knows there may be exceptions to a general rule.
It is even possible that the "general rule" might turn out to be wrong more often than not.
One can avoid this problem with deductive reasoning
Deduction starts with a general idea and determines whether it applies to a specific observation.
This approach can be considered to be moving "from the top down".
Every thing in class X has the characteristic Y.
This thing in my hand is in class X.
Therefore, this thing in my hand has characteristic Y.
Existing theories and hypotheses (generalizations) can be tested via deduction. Experimental observations (specific examples) are collected to test those generalizations.
A syllogism is a deductive argument with three simple steps:
All items of type X have the characteristic Y. (inductive generalization)
This thing in my hand is of type X.
Therefore, this thing in my hand has the characteristic Y. (specific conclusion)
All wasps have stingers. (inductively devised generalization)
This thing on my hand is a wasp.
Therefore, this thing on my hand can probably sting me. (specific conclusion)
To test this argument, you must now conduct a (potentially painful) experiment.
The results of your study may suggest further questions.
What types of hymenopterans lack stingers?
Which is the primitive condition: stinger or no stinger?
Why has stinglessness persisted? Is it adaptive?
The fun has just begun.
Hypothesis, Theory, and Law.
Science is different from other methods of seeking truth in that
Physical, observable evidence is required for formulation of hypotheses, theories, and laws.
Hypotheses and theories must be subject to falsification by means of experimental testing.
You may have heard an acquaintance say he has a "theory" about something.
This usually means they have a hunch based on little more than idle speculation or a "gut feeling".
In science, however, the terms hypothesis, theory, and law have very specific definitions.
A hypothesis is a tentative explanation for an observed phenomenon.
A prediction is based on past experience about the phenomenon. It's an "educated
guess" about what you expect to happen.
A hypothesis must be experimentally testable.
A scientific hypothesis cannot be proven to be true.
Results of an experiment allow the investigator to either
reject the hypothesis if experimental results do not support it
fail to reject the hypothesis if experimental results do not refute it
(More on this below, under "Science as Falsification".)
Multiple hypotheses make good science.
Considering only one possible explanation for an observation invites unintended bias!
A theory is a well-substantiated explanation of some aspect of the natural world.
It is an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena or observations.
A theory is constantly subject to testing, modification, and even refutation as new evidence and ideas emerge.
Theories also have predictive capabilities that guide further investigation.
Example: Darwin's theory of evolution by means of natural selection.
A natural law is described by a sequence of events in nature that has been observed to occur the same way, every time, under the same conditions.
Natural law is the basis of the experimental method in science, and is dependent upon cause and effect.
A natural law predicts that something will happen under a certain set of circumstances, but it does not explain why it happens.
Example: The Laws of Thermodynamics
Energy cannot be created or destroyed, but only changed in form.
All systems tend to move towards a state of greater disorder/chaos.
Science as Falsification
In his classic essay Science as Falsification, German philosopher Karl Popper explained why vulnerability to falsification--not repeated verification--is the hallmark of truly powerful hypothesis.
A falsifiable (Popperian) hypothesis can be put to a test that could possibly refute it.
In Popperian science, experiments are designed to rule out hypotheses that are clearly wrong.
In essence, this scientific method entails a process of elmination.
1. Make an observation about something in the natural world.
2. Pose competing hypotheses, each of which could potentially explain that observation
3. For each hypothesis, predict experimental results that would either support or refute that hypothesis.
4. Design and perform rigorous experiments to test each hypothesis.
5. Analyze whether experimental results support or refute the hypothesis being tested.
This process of exclusion is known as falsification.
In Popperian science
a hypothesis can NEVER be proven true.
a hypothesis can ONLY be (1) rejected or (2) not rejected.
A hypothesis not falsified by experimental results can be provisionally accepted as a potential explanation of the observation.
However, failure to falsify a hypothesis does NOT prove that the hypothesis is true.
Falsification: An Illustration
An ancient North American explorer
arrives at the Pacific Ocean for the first time.
He knows that fish live in other bodies of water such as lakes and streams.
Hypothesis: There are fish in this new body of water.
Alternative (competing) hypothesis: There are no fish in this new body of water.
To test the hypotheses, he sweeps a dip net into the ocean and pulls it out.
He repeats this procedure hundreds of times, and never catches a fish.
Does this mean "There are no fish in this new body of water" is TRUE?
The essence of Popperian Science is falsifiability.
None of the explorer's hundreds of trials has falsified the "no fish" hypothesis.
However, the next trial might yield a fish.
The "no fish" hypothesis can be provisionally accepted because observable evidence does not indicate otherwise.
But the "no fish" hypothesis cannot be said to be TRUE.
The falsification might still be out there.
All it takes is the capture of ONE FISH for the "no fish" hypothesis to be rejected.
The explorer has NOT proven his "no fish" hypothesis to be correct.
Rather, the explorer has failed to prove his "no fish" hypothesis to be incorrect
This is a subtle, but critical distinction.
The explorer must remain open to the possibility that his unrefuted hypothesis might, at some future time, be refuted.
Of course, dipping a net into the ocean isn't a very high-tech way to address this problem.
But with more advanced technology such as
He might be able to refute the "no fish" hypothesis.
Science marches on as technology improves.
Popperian Hypothesis: An Analogy
One might compare a Popperian hypothesis to castle or fortress.
It appears well built and perfectly sound.
Which is the better way to test the strength of the castle?
List the ways the castle is fortified to be strong.
Attack the castle and try to break it down.
Listing castle fortifications is analogous to listing bits of evidence that support a particular hypothesis.
Attacking the castle is analogous to performing an experiment that could refute that hypothesis.
No matter how well built the castle might be, until you actually try to break it down, you don't know if it will stay up.
If the castle was not "true", it may end up looking something like this.
Strong Inference: Competing Hypotheses
In 1964, John R. Platt coined the phrase strong inference to describe a straightforward, powerful method of addressing a biological problem: posing multiple, competing hypotheses, any of which could potentially explain an observation.
In its separate elements, strong inference is just the simple and old-fashioned
method of inductive inference that goes back to Francis Bacon. The steps are
familiar to every college student and are practiced, off and on, by every scientist.
The difference comes in their systematic application. Strong inference consists of
applying the following steps to every problem in science, formally and explicitly
1. Devising alternative hypotheses that potentially explain an observation
2. Devising a crucial experiment (or several of them), with alternative possible
outcomes, each of which will, as nearly as possible, exclude one or more of the
3. Carrying out the experiment so as to get a clean result;
4. Recycling the procedure, making subhypotheses or sequential hypotheses to
refine the possibilities that remain, and so on.
It is like climbing a tree. At the first fork, we choose--or, in this case, "nature" or
the experimental outcome chooses--to go to the right branch or the left; at the
next fork, to go left or right; and so on. There are similar branch points in a
"conditional computer program," where the next move depends on the result of
the last calculation. And there is a "conditional inductive tree" or "logical tree" of
this kind written out in detail in many first-year chemistry books, in the table of
steps for qualitative analysis of an unknown sample, where the student is led
through a real problem of consecutive inference: Add reagent A; if you get a red
precipitate, it is subgroup alpha and you filter and add reagent B; if not, you add
the other reagent. B; and so on.
Posing only one hypothesis to explain an observation can lead to confirmation bias, the tendency to interpret evidence as confirmation of one's own pre-existing ideas about that observation.
Posing competing hypotheses to explain an observation can help prevent confirmation bias.
If Hollywood TV writers can do it, so can you.
About thirty years ago there was much talk that geologists ought only to observe and not theorise;
and I well remember some one saying that at this rate a man might as well
go into a gravel-pit and count the pebbles and describe the colours.
How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!
-- Charles Darwin, in On the Origin of Species
The "view" Darwin cites above is the hypothesis.
A hypothesis is a "tentative proposition...subject to verification
through subsequent investigation....In many cases hypothese are hunches
that the researcher has about the existence of relationships between
variables." (Verma and Beard, 1981)
The hypothesis is the cornerstone of science.
Hypotheses can be constructed and used in different ways.
When one first makes an observation that generates a question, that question can evolve into what is sometimes known as the overall hypothesis about the observation.
For example, you might notice that in a population of wild goats
some males have curled horns
other males have straight horns
all females have straight horns
This is your observation.
You might wonder:
"Does the shape of a male's horns affect his some aspect of his natural history?"
This is your question.
You pose multiple hypotheses to explain the variation in male horn shape:
"The shape of a male's horns affects his attractiveness to females."
"The shape of a male's horns affects his ability to fight other males."
"The shape of a male's horns affects his ability to ward off predators."
("Insert your clever hypothesis here.")
Any of these can be considered an overall hypothesis.
Each of these could and should be tested.
For now, we'll choose the first hypothesis: attractiveness to females.
Experimental (Statistical) Hypotheses
To make an overall hypothesis testable, it can be re-phrased as two mutually exclusive, experimental (statistical) hypotheses:
Your observation of male goat horns led to a hypothesis that there is a relationship between two things:
horn shape and attractiveness to females.
To determine whether these two things are actually related, you must
design a rigorous experiment
statistically analyze your results
reject or fail to reject each of your experimental hypotheses
The null hypothesis states that there is no relationship between the two things:
"Female goats are equally attracted male goats with straight horns and male goats with curly horns."
The alternative hypothesis states the opposite of the null hypothesis, that there is a relationship between the two things:
"Female goats are not equally attracted to male goats with straight horns and male goats with curly horns."
The alternative hypothesis may be either
two-tailed (does not specify how the two things vary together) "Female goats are not equally attracted to curly-horned males and straight-horned males."
one-tailed (specifies a direction for the relationship)
"Males with curly horns are [more/less] attractive to females than males with straight horns."
The results of your experiment will indicate which of these hypotheses will be rejected, and which you will fail to reject.
Model Organisms Help Us Understand Biological Systems
A model organism is a non-human species used to study a particular biological phenomenon.
Model species are studied not because the investigator wishes to understand only how that species works, but because discoveries made in them may apply to the workings of other organisms, including humans.
Model organisms generally
are easy to raise and maintain
have a short generation time
are used when human (or other species) experimentation would be unfeasible or unethical
Typical model organisms used in biological research include...
Various species of bacteria
Escherichia coli is usually the star of the show, but many other species contribute to our genetic knowledge. One obvious advantage is their extremely rapid rate of reproduction.
Saccharomyces cereviseae and other species.
Arabidopsis thaliana is considered the "fruit fly of the plant kingdom".
It is used extensively in studies of plant biological systems.
Its name means "black bellied sugar lover." But you will meet many mutant forms with colors and shapes to amaze you.
Zebra fish are commonly used to study the biology of development, including
genetic defects in development
evolutionary development (EvoDevo)
The genome of Mus musculus is oddly compatible with that of Homo sapiens, and for this reason it makes an almost ideal model mammal for genetic studies.
...among many others.
Remember: A model organism is a tool used to study a biological phenomenon that may be similar in other species.
When you use onions to study mitosis, you're investigating mitosis, not onions.
When you use yeast to study enzymes, you're investigating enzymes, not yeast.
When you use Betta splendens to study agonistic behavior, you're studying agonistic behavior, not fish.
Scientific Method Redux
Scientific progress proceeds differently from progress in other fields:
observation - The investigator notes a phenomenon that poses a problem/elicits a question.
hypothesis formulation - The investigator poses multiple, competing hypotheses that could potentially explain the observation.
prediction - The investigator makes a statement about what s/he
believes will happen when each hypothesis is put to the test.
experimental design - The investigator designs an experiment to generate data that will allow the investigator to either reject or fail to reject each hypothesis.
data collection - Experiments are run, data are collected.
data analysis - Data are subjected to rigorous analysis to determine whether any
deviation from the prediction is truly meaningful, or merely due to chance.
conclusion - The investigator determines whether the outcome of the experiment refutes or fails to refute the hypothesis.
requires observable, physical evidence
devises experiments designed to falsify, not verify a hypothesis
has a willingness to modify or even reject long-held ideas that turn out to be wrong
These set science apart from faith in things that cannot be observed or falsified.