Induction and Scientific Reasoning

Induction and Scientific Reasoning


SPEAKER 1: In the terminology
of standard textbook logic an inductive argument
is one that’s intended to be strong rather than valid. But this terminology
isn’t necessarily standard outside of logic. In the sciences in
particular there is a more common
reading of induction that means something
like making an inference from particular cases
to the general case. In this tutorial,
we’re going to talk about this reading
of the term and how it relates to the
standard usage in logic, and the role of inductive
reasoning in the sciences more broadly. In the sciences,
the term induction is commonly used to
describe inferences from particular cases
to the general case, or from a finite sample of
data to a generalization about a whole population. Here’s the prototype
argument form. It illustrates this notion
of inductive inference. You note that some individual
of a certain kind, a1, has a property, B. An example
would be this swan is white. Then you note that some other
individual of the same kind, a2, has the same property. This other swan is white. And you keep doing this
for all the individuals available to you. This swan is white. And this swan is white. And this swan over there
is white, and so on. So you’ve observed n swans
and all of them are white. From here the inductive
move is to say that all swans
everywhere are white, even the swans that you
haven’t observed and will never observe. This is an example of an
inductive generalization. And arguments of
this form or that do something similar, namely
infer a general conclusion from a finite example, exemplify
the way the term induction is most commonly used in science. Another example that
illustrates inductive reasoning in this sense is the
reasoning involved in inferring a functional
relationship between two variables based on a
finite set of data points. Let’s say you heat a metal rod. You observe that it
expands the hotter it gets. So for various
temperatures you plot the length of the rod
against the temperature. You get a spread of data
points that looks like this. What you may want
to know, though, is how length varies with
temperature generally so that for any
value of temperature you can then predict
the length of the rod. To do that you might try
to draw a curve of best fit through the data
points, like so. Looks like a pretty
linear relationship, so a straight line
with a slope like this seems like it’ll give
a good fit to the data. Now, given the equation for
this functional relationship, you can now plug in a
value for the temperature and derive a value
for the length. The equation for
the straight line is an inductive
generalization that you’ve inferred from the finite
set of data points. The data points, in fact,
are functioning as premises, and the straight line is
the general conclusion that you’re inferring
from those premises. When you plug in a value
for the temperature and derive a value for
the length of the rod based on the equation
for the straight line, you’re driving a prediction
about a specific event based on the generalization
you’ve inferred from the data. This example illustrates
just how common inductive generalizations are in science. So it’s not surprising
that scientists have a word for this kind of reasoning. In fact, the language of
induction used in this sense can be traced back to people
like Francis Bacon, who back in the 17th century
articulated and defended this kind of reasoning as
a general method for doing science. So how does this
kind of reasoning relate to the definition
of induction used in logic? We’ll recall in standard
logic, an argument is inductive if it’s intended
to be strong rather than valid. The key thing to
note is that this is a much broader definition
than the one commonly used in the sciences. That definition focuses on
arguments of a specific form– those where the premises are
claims about particular things or cases and the conclusion
is a generalization from those cases. But if you take the
standard logical definition of an inductive
argument, you find that many different
kinds of arguments will qualify as inductive
not just arguments that infer generalizations
from particular cases. So for example, on
the logical definition a prediction about the
future based on past data will count as an
inductive argument. The sun has risen every day
for as long as the earth has existed, as for as we know. So we expect the sun to
rise tomorrow as well. This is an inductive
argument on our definition because we acknowledge that
even with this reliable track record, it’s still possible for
the sun to not rise tomorrow. Aliens, for example,
might blow up the earth or the sun overnight. So this inference from the past
to the future is inductive, and most of us would say
that it’s a strong inference But notice that it’s not an
argument from the particular to the general. The conclusion isn’t
a generalization. It’s a claim about
a particular event– the rising of the sun tomorrow. So this kind of argument
wouldn’t count as inductive under the standard
science definition, but it does count under the
standard logical definition. Here’s a second example that
illustrates the difference. 90% of human beings
are right-handed. John is a human being,
therefore John is right-handed. Notice that the main
premise is a general claim while the
conclusion is a claim about a particular person. On the standard
science definition this isn’t an inductive
argument since it’s moving from the general
to the particular rather than from the
particular to the general. But on the logical
definition of induction this argument does count
since the argument is intended to be strong not valid. The relationship between the
two definitions looks like this. The arguments that
qualify as inductive under the standard
science definition are a subset of
the arguments that qualify as inductive under the
standard logical definition. So from a logical
point of view, there’s no problem with
calling an inference from the particular to the
general an inductive argument since all such arguments satisfy
the basic logical definition. But scientists are
sometimes confused when they see the
term induction used to describe other forms
of reasoning than the ones that they normally associate
with inductive inferences. There shouldn’t be
any confusion as long as you keep the
two senses in mind and distinguish them
when it’s appropriate. But if you don’t
distinguish them, then you may run into
discussions like this one that contradict themselves. These are the
first few sentences of the Wikipedia
entry on induction at the time of
making this video. The first sentence presents the
standard logical definition– inductive reasoning is defined
as strong reasoning, reasoning that doesn’t guarantee truth. The second sentence presents
the standard science definition of induction, defining
it as reasoning from the particular
to the general. Later on in the
article, they present a number of examples
of inductive arguments that satisfy the
logical definition but not the scientific
definition, such as inferences from correlations to causes, or
predictions about future events based on past events, and so on. These examples they use flat
out contradict the definition highlighted in yellow here. So if anyone out
there’s inclined, you might want to
edit that entry to clarify the distinction
we’ve been discussing here. I’ll summarize some key
points of this discussion. The first is that
we should be aware that there’s a difference
between the way the term induction is defined in general
scientific usage and the way it’s defined in logic. The logical definition
is much broader and is basically synonymous
with non-deductive inference. The scientific usage
is narrower and it focuses on inferences from
the particular to the general. Second, induction in the
broader logical sense is fundamental to scientific
reasoning in general. That Inductive reasoning
is risky reasoning. It’s fallible reasoning. Are you moving from known facts
about observable phenomena, say, to a hypothesis or
conclusion about the world beyond the observable facts? And the distinctive feature
about this kind of reasoning is that you could have all
the observable facts right, but you can still be wrong about
the generalizations you draw from those observations
or the theoretical story you tell that tries to
explain those observations. It’s a fundamental feature
of scientific theorizing that it’s revisable in light
of new evidence and experience. It follows from this observation
that scientific reasoning is, broadly speaking,
inductive reasoning, that scientific
arguments should aim to be strong rather
than valid, that it’s both unrealistic and confused
to expect them to be valid. The disciplines that
trade in valid arguments and valid inferences are
fields like mathematics, computer science, and
formal deductive logic. The natural and social
sciences, on the other hand, deal with fallible,
risky inferences and they aim for
strong arguments.

24 thoughts on “Induction and Scientific Reasoning

  • @ishwarrior Hey, thanks for the comment. On the point you make, I agree that as stated, it's a weak inductive argument, not a strong one. But your modification would make the final inference a deductive one, going from a general rule to a particular instance of that rule, and it would no longer be an example of an inductive argument. The question of what is necessary to make an inductive generlization strong is actually a deep one (I'm working on a tutorial course on this right now…).

  • @PhilosophyFreak so there are two steps: 1. induction 2. deduction. this distinction is actually very very important. many scientists nowadays are either ignorant or arrogant. either they are unaware of the first step, or hide step 1 from the public, selling it as "pure deduction". please help to educate future scientists properly, so that we don't get fucktards like Richard Dawkins.

  • @Heissenburger
    "many scientists nowadays are either ignorant or arrogant. either they are unaware of the first step, or hide step 1 from the public"

    Name one scientist who does that.

    "so that we don't get fucktards like Richard Dawkins"

    At least Dawkins doesn't claim things will pop into being once you put them into neat syllogisms, unlike what people like William Craig seem to think.

  • @Heissenburger The problem is that few science majors have to take a course that explains proper inductive process, qualifications, criteria, etc. It would be nice if every science major had to take a Philosophy of Science & Inductive Reasoning course their freshman or sophomore years, but that happens at only a few universities. So when they grow up and have to present results of their research, they screw up the terms.

  • Logic only has applicability in derivational tautological systems. Science has nothing to do with logic. Science is the study of existence via the Scientific Method and divorced from systems of logic.

    fatfist.hubpages com/hub/LOGIC-Its-Laws-Premises-and-LIMITATIONS

  • The problem is that an inductive argument is strong because of its probabilistic strength. Now, generalizing from a finite set of cases to an infinite set, mostly a nonenumerable set, of possible cases, makes probability stagger. In fact, any finite set within a nonenumerable set has probability 0.

  • Think of the many different heights from which an object can fall to ground. Each is a different case against which gravity has to be tested.

  • we're lucky science is flexible. If they find something that contradicts their inductions, they may change their conclusions. Religion, in the other hand, stays stuck in the same place whether evidence supports it or not…

  • Very clear, and very needed. ┬áIt's now my favorite presentation of how to understand that scientific IS inductive reasoning, but not all inductive reasoning is SCIENTIFIC. ┬áMany people (who you would think would know better) make the mistake of equating the two, and then make erroneous remarks like, "Inductive reasoning is reasoning from the specific to the general." ┬áThat's just one part of inductive reasoning. ┬áThank you!

  • What's meant by "strong" versus "valid"? What would be the difference between a "strong" argument versus say a weak argument? Is valid a logically consistent argument, whereas strong an argument that is highly likely to be true?

    "It follows from this observation that scientific reasoning is broadly inductive reasoning. That scientific arguments should aim to be strong rather than valid."
    Isn't the aim in conducting science to be both inductive and deductive? Isn't the use of statistics in science an example of deductive reasoning that must strive to be valid. The use of statistical hypothesis testing is a case where general rules (rules of probability) are applied to a particular case (the immediate study)? Similarly don't mathematical models also demonstrate vitally important areas of deductive scientific reasoning?

  • sry if it doesnt make sense but is it possible in the future to find some piece of iron which will not have the properties of iron we know today ? i mean we have make expiriments and find that iron when heated is expanding and we make the general statement that iron when is heated is expanding..but this is true bcs we havent find a piece of iron which doesnt expand when is heated? i mean the properties doesnt have relation with the definition of iron..am i right? sry for my bad english

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