Almost every website that talks about it says, “Inductive reasoning is a bottom up” approach while “deductive is a top down approach”.
Can anyone explain to me the THE DIFFERENCE? What makes these two forms of reasoning so different? Examples are always appreciated as well.
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Deductive reasoning (top down) is when you use a rule to form a conclusion. For example, a rule could be A=B. So, if you see an A, the conclusion is that it is also B.
Inductive reasoning (bottom up) is when you use a conclusion to create a rule. So, let’s say you examine a bunch of A’s, and by observation realize that they are also B. With that info, you theorize that A=B.
The terms bottom/top up refer to how the conclusion relates to the rule. The rule is on top, the conclusion is on the bottom. When use a rule to determine the conclusion, that is from top to bottom (deductive). When you use a conclusion to make the rule, you are going from bottom to top (inductive).
Deductive reasoning uses the rules of logic to prove things are true. Math is a form of deductive reasoning.
Inductive reasoning is when you use samples of cases and expect the rule to always be true even though you can’t look at every case.
Deductive: Shapes with just three sides are triangles, this shape has three sides therefor its a triangle.
Inductive: The people I know like cheese, if I put cheese on this hamburger, people will like it.
Inductive reasoning: Suppose I have very large set of items. I want to prove that some property is true for all the items. I first start by proving its truthfulness for the first item, then I prove that for every item for which the property is true, the property holds for the next item as well.
Example: I have a very long strip of LED lights. I want to prove that every single light is set to red. If I can prove that 1) the first light is red and 2) a light cannot turn red unless the light next to it is already red, then I don’t need to check every light color to know the entire strip is lit up in red. That’s inductive reasoning, going from the specific to the general. This example might be a bit unnatural, but many things use inductive reasoning. Pollsters make generalizations about what the population thing based on small sample sizes. It’s the same 2 step process: 1) 60% of a picked sample of people think speed limits are lame 2) what is true for a properly chosen small sample of society must hold true for a larger set of people. So we use induction to say that 60% of everyone thinks speed limits are lame.
Deductive reasoning is simply the reverse process, and it seems very trivial because it’s how we always reason. If I know that all items in a set satisfy a condition, then I know that condition is true for every individual item as long as I can prove it is indeed part of that set that I just described.
If I know that all light sources in a room are blue, and I find a glowstick, then I know that glowstick must be blue as well without needing to turn it on and verify, because a glowstick is a light source. The reasoning goes from the general (all lights are blue) to the special (glowsticks are blue)
I think the examples demonstrate the points better than the definitions, but I’ll inclide the definitions too.
Deductive reasoning uses general observations to come to a specific conclusion.
Example: I take a coin out of my purse. The coin is small, looks like copper, and it has a portrait of Abraham Lincoln on it. Pennies are known to have all of these features. Therefore, I deduce that it is a penny.
Inductive reasoning uses specific observations to make a generalization.
Example: I take a coin out of my purse, and it’s a penny. I take another penny out. Then another penny. Then another penny. I make the generalization from this pattern that all the coins in my purse are pennies.
Deductive: you eliminate possibilities one by one, sometimes using prior things you have eliminated to eliminate others, until you get to a conclusion.
Inductive: you start from something known, and then logically build by pointing out implications of what is known, and implications from those implications, until you get to a conclusion.
If everyone tells you that you will most definitely burn your hand if you touch the stove, your inductive reasoning will lead you to the conclusion that if you put your hand on the stove you will get burned.
With your superior intellect’s deductive reasoning, you figure out that a pot that’s been on the stove for a while and has burned its contents will also burn you.
Deductive reasoning: if all the premises in an argument are true, then the conclusion MUST be true.
E.g. All humans are mortal. I am a human. Therefore, I am mortal.
If it is indeed true that all humans are mortal, and that I am a human, then I must be mortal. There is absolutely no way that I am not mortal if I am a human and all humans are mortal. It is logically impossible.
Inductive reasoning: if all the premises in an argument are true, then the conclusion is PROBABLY true, but could be false.
E.g. I’ve seen a million swans. Every swan I’ve seen has been white. Therefore, all swans are white.
Sure, seeing a million white swans might be a good reason to think all swans are white, but it is still possible that other coloured swans exist, and I just haven’t seen them yet. Despite the fact that my evidence gave me a good reason to believe the conclusion, it is still possible for the conclusion to be false.
I’ll give you an example that happens in physics all the time.
Acceleration and force.
If you know the individual forces acting on an object you can find the net force. Then with the net force you can absolutely determine the acceleration they will create. You use the forces to deduce the acceleration.
This is like when you see a person push a box. You see the push, know how hard it was pushed, and knowing the mass of the box you can calculate the acceleration.
If you see an object accelerate you can infer a net force was present. But you can’t be absolutely certain as to the individual forces that make it up.
In our box scenario you’d see the box accelerate, then make a claim as to how hard it was pushed. But you may have forgotten about friction…
Even more odd, you see a box rise into the air, slow and then gain speed on the way down. You don’t see anything touch the box. So you *infer* that a force must be accelerating it downwards (gravity) even if you can’t see the source of it. This is a sound inference, as the only other times you see acceleration are when a direct force is applied (pushing/pulling).
Hey, former philosophy instructor here.
The difference concerns the kind of relation purported to exist between the premises and the conclusion.
In a deductive argument, the premises are purported to guarantee the truth of the conclusion. As such, the premises either guarantee the truth of the conclusion or they don’t. The argument is either good or it isn’t.
In an inductive argument, the premises are purported to make the truth of the conclusion more likely. As such, inductive arguments aren’t just good or bad; they can be better or worse.
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