# Induction vs. deduction in science

1. Jun 14, 2010

### jackson6612

Bacon did not propose an actual philosophy, but rather a method of developing philosophy. He argued that although philosophy at the time used the deductive syllogism to interpret nature, the philosopher should instead proceed through inductive reasoning from fact to axiom to law. Before beginning this induction, the inquirer is to free his or her mind from certain false notions or tendencies which distort the truth. These are called "Idols" (idola), and are of four kinds:

* "Idols of the Tribe" (idola tribus), which are common to the race;
* "Idols of the Den" (idola specus), which are peculiar to the individual;
* "Idols of the Marketplace" (idola fori), coming from the misuse of language; and
* "Idols of the Theatre" (idola theatri), which result from an abuse of authority.

The end of induction is the discovery of forms, the ways in which natural phenomena occur, the causes from which they proceed.

The difference between inductive and deductive reasoning is mostly in the way the arguments are expressed. Any inductive argument can also be expressed deductively, and any deductive argument can also be expressed inductively.

I have to confess the deduction and induction always confuses me. I'm not a science or maths student so please keep your answers simple.

Deduction proceeds from a general to specific and in induction the order is reversed. Any object thrown upward falls back to the ground. So a ball will fall back because it's an object (Deduction). All the balls thrown upward fall back to the ground, and as ball is an object therefore all the objects will do the same. What is Bacon trying to say? In maths, we first prove a formula for some specific cases (because we have no other option - we cannot proceed backward from general case n), then proceed to a general case n. Even if we have reversed the order, the argument would still be that much valid. If it holds for nth terms, then obviously it will hold for n=1,2,3,...

I hope you get what I'm trying to say. Thanks.

Sources:
http://en.wikipedia.org/wiki/Francis_Bacon
http://www.sjsu.edu/depts/itl/graphics/induc/ind-ded.html [Broken]

Last edited by a moderator: May 4, 2017
2. Jun 14, 2010

### vandegg

From http://en.wikipedia.org/wiki/Baconian_method

"Bacon suggests that you draw up a list of all things in which the phenomenon you are trying to explain occurs, as well as a list of things in which it does not occur. Then you rank your lists according to the degree in which the phenomenon occurs in each one. Then you should be able to deduce what factors match the occurrence of the phenomenon in one list and don't occur in the other list, and also what factors change in accordance with the way the data had been ranked. From this Bacon concludes you should be able to deduce by elimination and inductive reasoning what is the cause underlying the phenomenon."

This was an attempt to come up with some sort of scientific method back in the 1600's when there was no widespread uniform body of methods to govern experiments and such.

3. Jun 14, 2010

### mikelepore

This is my understanding of it. Someone please correct me if I said this wrong.

Deduction: Answering a question by going from the general to the specific -- "We're going to have a baby. Wiil it be warm-blooded?" -- "Yes, because it will be a human, and all humans are warm-blooded."

Induction: Answering a question by going from the specific to the general: "Are all humans warm-blooded?" -- "Yes, we checked a million humans and found them all to be warm-blooded, so our tentative conclusion is that all humans are."

Science must use both.

4. Jun 15, 2010

### K^2

The deductive part of science is called mathematics.

5. Jun 15, 2010

### JoeDawg

Try this:
http://www.iep.utm.edu/ded-ind/

"Because deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises, if the argument is a sound one, the truth of the conclusion is “contained within” the truth of the premises; i.e., the conclusion does not go beyond what the truth of the premises implicitly requires. For this reason, deductive arguments are usually limited to inferences that follow from definitions, mathematics and rules of formal logic. For example, the following are deductive arguments:

There are 32 books on the top-shelf of the bookcase, and 12 on the lower shelf of the bookcase. There are no books anywhere else in my bookcase. Therefore, there are 44 books in the bookcase.Bergen is either in Norway or Sweden. If Bergen is in Norway, then Bergen is in Scandinavia. If Bergen is in Sweden, the Bergen is in Scandinavia. Therefore, Bergen is in Scandinavia.

Inductive arguments, on the other hand, can appeal to any consideration that might be thought relevant to the probability of the truth of the conclusion. Inductive arguments, therefore, can take very wide ranging forms, including arguments dealing with statistical data, generalizations from past experience, appeals to signs, evidence or authority, and causal relationships.

Some dictionaries define “deduction” as reasoning from the general to specific and “induction” as reasoning from the specific to the general. While this usage is still sometimes found even in philosophical and mathematical contexts, for the most part, it is outdated. For example, according to the more modern definitions given above, the following argument, even though it reasons from the specific to general, is deductive, because the truth of the premises guarantees the truth of the conclusion:

The members of the Williams family are Susan, Nathan and Alexander.
Susan wears glasses.
Nathan wears glasses.
Alexander wears glasses.
Therefore, all members of the Williams family wear glasses.

Moreover, the following argument, even though it reasons from the general to specific, is inductive:

It has snowed in Massachusetts every December in recorded history.
Therefore, it will snow in Massachusetts this coming December."

6. Jun 15, 2010

### jackson6612

Thank you very much, everybody. Joe, your link is very helpful. I'm trying to formulate my own definition using different sources. I will need some time to assimilate the information. Thanks a lot. And if anyone of you have a better explanation, or suggestion, then please let me know.

7. Jun 15, 2010

### apeiron

This is the basic insight. And it is easy to understand why it works.

If you start from what seems a most general truth, then you can of course find a whole set of more specific sub-truths within it. The big truth guarantees any small truths that can be derived from it.

So big truths - the global constraints of a system, the universal laws of nature, the fundamental axioms of a system - are of particular value. But we have to find some justifiable way of discovering them.

Some people believe divine relevation can be a path. Some believe that "pure rational argument" can deliver them. But Bacon and others who argued for empiricism said we need to go the other way and construct big truths. We have to build up to them in additive fashion, taking many small truths (local observations) and constructing a sturdy, deduction-supporting, general truth out of them.

And so we arrived at the standard definition that induction is the move from the particular to the general, deduction is the move from the general to the particular.

Why then do people confuse the elegant and clarity of this sure system for gaining knowledge by making statements like....?

Well perhaps every generation wants to be seen to be saying something knew? Who knows.

But anyway, while these examples attempt to rewrite logical arguments so that the natural form of the arguments appear reversed, the efforts are plainly contrived.

How can we be certain that the Williams family consists of Susan, Nathan and Alexander? Well someone must have checked. And they are probably right unless they missed Boris hiding in the closet. So we have a truth from inductive enumeration, the set style statement [Williams [Susan, Nathan, Alexander]] in which the global constraint is "family relationship" and a series of local instances composes that family.

Now what further truths can be derived from this bare general statement? Well, we can guess they are all human (Nathan is not the family cat), they all live in the same house (perhaps), but this would be abduction, not deduction - reasonable guesses based on other knowledge that would need to be confirmed inductively.

So one process of enquiry has established [Williams [Susan, Nathan, Alexander]]. But it says nothing about glass wearing. We can deduce nothing safely from this first "premise". It is really a piece of knowledge that floats off to one side of the argument that follows.

But then it seems, the enquirer wants to say something further about this family and decides to focus on the question of glass wearing.

Well, why? What would motivate this? It is not a deduction that naturally suggests itself. It can only be that we want to generalise the new notion of the [Williams family] even further to include their common properties as well as their familiar bonds.

So clearly we are moving from a more general notion of family to an enquiry about a particular example of a family. We cannot deduce a common property like glasses from any understanding of the notion of family, although our prior knowledge of the world (families tend to be humans and humans can be glass wearers, families tend to share defective eyesight, etc) could be employed to make an abductive guess.

Anyway, the enquiry then procedes by induction (checking each known Williams family member in turn) to arrive at this general truth [Glasses [Susan, Nathan, Alexander]].

Because we then end up with two sets that are congruent, we are now justified to make the further general statement (about this particular family) - the Williams wear glasses. And from that in future we can derive deductions from the general to the particular.

Whoops, they found Boris. By deduction, he will also be wearing glasses. No he isn't. Damn. Empiricism wins again. Which would not be so surprising as there was never any strong logical, causal, reason why being a Williams and wearing glasses would be common properties.

Anyway, it is plain that this example of "deduction from specific to general" is not a single argument but a pair of inductive arguments combined.

One establishes the generality of the Williams family, the other the generality of glass-wearers. Then the two sets of observations are merged to create a richer truth about the generality of glass-wearing Williams.

Again, this just doesn't work as advertised.

If you have accumulated enough observations to form the rule - it always snows in Massachusetts in December - then it is a deduction to say it will snow this December. The greater truth must contain this lesser truth by definition.

Of course, what this example smuggles in to confuse you is the obvious fact there is no necessity of snow each December in the general rule. There may well be some necessity involved (just because of lattitude, rain fall, etc). But really we have to wait and see if it snows to be certain, and so what we actually can derive from our prior knowledge, our general rule, is an abductive best guess.

So the situation is that we have a weak general rule formed by an inductive history (specifics adding up to construct a general). And its deductive strength is uncertain because while we have established a strong correlation, we cannot see the rule as having a causal force. It says nothing about the world which clearly constrains future events. At best, it gives grounds for abduction as to why the regularity has occured in the past and must occur in the future.

Bacon and others of course were concerned with creating strong structures of knowledge. And so that is why the definition of abduction, induction and deduction - the crucial triad of epistemology - should not be muddied by confused statements.

The inherently logical direction for deduction has to be from the general to the particular as the smaller must be found within the larger, while the only way that humans, as located and specific observers (unable to tap into universal truths in any direct fashion such as revelation or "nous"), can safely establish global generalisations is by constructing upwards from the accumulation of specific intances. And to begin things, we must just leap in with a best guess.

8. Jun 18, 2010

### jackson6612

Hi Iron

Thanks a lot for this explanatory reply. I have few questions which I would ask soon. Once again, thanks.

Best wishes
Jack