Deduction Vs. Induction vs. Abduction
Deductive, inductive, and abductive reasoning are three basic reasoning types. Each works together to form a complete line of formal reasoning where deduction deals with certainty, induction with probability, and abduction with guesswork.
These three methods of reasoning, under which all other reasoning types essentially fall under or are a mix of, can be a little tricky to illustrate with examples… because each can work a variety of ways (thus any one example tends to be misleading; keep that in mind as you read through the examples below).
The core concept to remember is: deduction deals with certainty and certain conclusions, induction with probability and likely conclusions, and abduction with guesswork and formulating a hypothesis (a best guess or likely explanation that can then be examined). To put it another way, deduction deals with what is the case, induction deals with what is likely the case, and abduction deals with a best guess as to what could be the case.
Below are some longer explanations (see even longer ones here). The idea of this page isn’t to write an essay on reason (see our section on logic and reason for that sort of thing), it is to translate the gist of the three main reasoning types 😉
An Introduction into Deductive, Inductive, and Abductive Reasoning
Imagine you have a set of data. Logical truths, rules, statistics, etc. (a mix of all the different types of data you can imagine; which one generally gets from observation and measurement).
Now imagine you mix and match data points that seem to connect to draw conclusions from those data points organizing them in a way which creates a “logical argument,” like this:
- Data point #1
- Data point #2
- Any logically certain conclusion you can draw from comparing those data points is deductive, any likely conclusion you can draw is inductive, and any hypothesis you can form is abductive.
- The type of conclusion you draw acts as a tell (a hint) for the reasoning type used (as, for example, if your reasoning is done properly, only deductive reasoning can produce a logically certain conclusion).
- Any data point that is a logically certain truth like “black cats are black” might be thought of to be in the deductive category and any data point with even a hint of probability like “9 in 10 tests preformed showed a positive result” or “all ravens we observed have been black” might be thought to be inductive in nature.
- The way one reasons toward a conclusion and the type of conclusion help to define the reasoning type. Sometimes the same data can be reasoned through using different reasoning methods. If the argument is 1. Some cats are black, 2. No cats are green. I can conclude: deduction = this cat is not green, induction = this cat might be black, or abduction = perhaps something in cat genetics stop cats from being green, yet allow them to be black?
In other words, these are just three different ways to work through data to draw different types of conclusions.
Since deductive arguments / conclusions tend to be redundant, like “black cats are black” or “since some tests show negative results, not all tests are positive,” most reasoning ends up being inductive in nature. All that means is that one makes observations / takes measurements (or collects someone else’s) and then draws likely conclusion given those observations / measurements.
Induction is simply drawing likely conclusions from data (where each data point, like lab tests or citations helps to increase the certainty of a conclusion) and deduction is simply deducing logically certain truths.
Meanwhile, in a case where there isn’t enough evidence to support a conclusion, we can formulate a hypothesis using abduction. For example: I observe that this bird is white, I know that ravens are typically black, therefore it follows that this probably isn’t a raven. My hypothesis, or best guess, is that this bird is not a Raven (then we would build a case for it not being a raven to try to show that it wasn’t a raven using induction and deduction). In this sense abduction is essentially a form of induction where one doesn’t have enough data to draw a conclusion (but has the grounds for coming up with a hypothesis to which further testing can be applied can be applied).
- Something that is self evident and logically certain is deductive. Meanwhile, deductive reasoning is when we reason through data points toward a logically certain conclusion.
- When a case is being built with evidence to find the likelihood that something is the case it is inductive. Meanwhile, inductive reasoning is when we reason through data points toward probable conclusions.
- And, when the evidence isn’t there to support a conclusion, we can formulate a hypothesis using abduction. Meanwhile, abductive reasoning is the process of comparing these points and coming up with the best explanation.
So, abduction is guessing based on data, induction is determining likelihood based on data, and deduction is the act of determining redundant, tautological, logically certain truths.
Then, since abduction is just a guess in need of induction and deduction, and deduction is almost redundant, induction ends up being the glue that holds everything together and tells us what is likely true about the world…. yet since induction alone can never produce certainty and doesn’t lend itself to imagination (like abduction does) the three forms end up working together rather well when it comes to formulating arguments, critical thinking, and finding truths.
Deduction, induction, and abduction are like three parts of the same puzzle, and all formal reasoning is done using them and only them. Without abduction there is no hypothesis, without induction no testing, and without deduction no way to falsify; i..e. not only is there no logic or reason without these methods, there is no science (and essentially no philosophy). They are simply names for the aspects of human reason.
Deductive, Inductive, and Abductive Reasoning Defined
Above I tried to illustrate the types of reasoning by discussing them together, at this point it’ll likely help to offer full definitions of each:
Abduction: The reasoning method that deals with guesswork and produces a possible explanation. It is forming a hypothesis or likely explanation. The surprising fact, C, is observed; But if A were true, C would be a matter of course, Hence, there is reason to suspect that A is true. Ex. I see my dog’s bowl is empty; if my dog ate the food this would be the case, the likely explanation for the dog food being missing is that the dog ate the food. My hypothesis is the dog ate the food.
Induction: The reasoning method that deals with probability and produces a likelihood. It reasons from specific facts and probable rules “up” toward probable conclusions that don’t necessarily follow from the premises. It looks for patterns in data, reasoning by consistency and attempts to build a strong argument by collecting data that tells are compelling story. It is inferring B from A where B does not necessarily follow from A. Ex. Most A are B, and this C is A, therefore this C is likely B. Ex. Most dogs eat dog food, my dog is like most dogs, my dog would have eaten the dog food (that isn’t logically certain, it is just very likely).
Deduction: The reasoning method that deals with certainty and produces a certain truth value. It is a reasoning method that deals with certain conclusions (logically certain inferences). It reasons from certain rules and facts “down” to logically certain conclusions that necessarily follow the premises of an argument. It is inferring B from A when and only when B is a formal logical consequence of A. Ex. All A are B, and all C are A, therefore all C must be B. Ex. All dogs are mammals, all mammals need food, therefore all dogs need to eat food (a logically certain truth; almost redundant AKA tautological).
Here is everything above in one example:
The dog’s food was in the bowl, but the food is now it is missing (deduction; food was in bowl, food now not in bowl, certain truths). The likely explanation for the dog food being missing is that the dog ate the food (abduction; a hypothesis was formed as a best guess given the observation and that which is often the case). I am going to compile some inductive evidence to prove the dog ate the food. 1. the dog doesn’t seem to want to eat any more (he seems to be full). 2. he has dog food around his mouth. 3. when I ask him if he ate the food he looks guilty. I’ll conclude the dog likely ate the food (induction; I used inductive evidence to show it is likely that the dog ate the food; it isn’t certain, just likely). Oh wait… I just checked the security footage and it shows the cat ate the food while the dog sat there and looked sad. Since the cat did eat the food , the dog could not have eaten the food… that is logically certain conclusion (deduction).
FACT: Charles Sanders Peirce came up with Abduction to describe this odd sort of non-deduction that wasn’t exactly induction as it had been known. Otherwise deduction and induction are longstanding concepts worked on by philosphers over the years.
Deductive, Inductive, and Abductive Reasoning in the Scientific Method
The scientific method uses a mix of abduction (formulating hypotheses AKA making educated guesses), inductive reasoning (comparing data to draw likely conclusions AKA testing hypotheses and formulating theories), and deductive reasoning (for example, using data to falsify a hypothesis necessarily based on inductive evidence).
In this way deduction tends to be rooted in rationalism (working with what is logically necessary given the data), inductive reasoning tends to be rooted in empirical observation and measurement (working with what is likely given the data), and abduction is rooted in both (using inductive and deductive reasoning to reason by analogy, to formulate hypotheses).
In other words, how abduction, induction, and deduction work together in the scientific method (and often in reasoning in general) is like this: abduction forms the hypothesis, induction tests the hypothesis and helps us deduce what likely is, and then deduction helps us to understand what is logically certain given the inductive evidence (potentially “proving” or disproving our hypothesis).
Other Examples of Deductive, Inductive, and Abductive Reasoning
Here are some other examples of abduction, induction, and deduction so you can see other examples of what the above arguments could look like:
Alt. Deduction Ex. Premise 1: If it’s raining then it’s cloudy. Premise 2: If it’s cloudy then it’s not bright. Conclusion: It’s raining so it’s not bright.
Alt. Deduction Ex. Premise 1: It’s raining. Premise 2: It’s cloudy. Conclusion: It can rain and be cloudy at the same time.
Alt. Induction Ex. Premise 1: If it’s raining then it’s cloudy. Premise 2: It’s probably raining. Conclusion: It’s probably cloudy.
Alt. Induction Ex. Premise 1: If it’s raining then it’s probably cloudy. Premise 2: It’s raining. Conclusion: It’s probably cloudy.
Alt. Abduction Ex. Premise 1: If it’s raining then it’s cloudy.. Premise 2: It’s wet and raining. Conclusion: Perhaps when it’s cloudy it’s wet?
Here is another example
Abduction. 1+_=2 (no one knows what _ is, could be a formula, could be a single number; however, if it were 1 then it would all make sense… 1 is a solid guess).
Deduction. 1+1=x (it is logically certain that 1+1= 2; in terms of formal logic, x is certainly 2)
Induction. x equals 1 or 2 99% of the time, y equals 1 or 2 95% of the time AND it is the case that x+y=3 (it is likely that x is 1 and y is 2 or vice versa).
Notes on Semantics: In common language when people say “deduction” or “deduce” they mean “draw an inference using either deduction or induction.” If Sherlock considers probable evidence at a crime scene, but doesn’t witness the crime, and then he “deduces” (draws the inference) that it was “Mr. Mustard in the Parlor with the Candlestick,” he is using “induction” (he is comparing probable evidence to draw a probable conclusion about “what was the case”). Meanwhile, if Sherlock “deduces” (draws the inference) that “the victim was a bachelor, and was therefore was necessarily unmarried… because he is a bachelor (as unmarried is a property of all bachelors),” that is “deduction.” Meanwhile, if Sherlock “deduces” that it was the case that the victim was targeted because he was a bachelor, as other bachelors had recently be targeted, that would be abductive reasoning (which formulates a speculative hypothesis based on an interesting observation).
It Is About the Conclusions and the Way Facts are Reasoned Through… not the Qualities or Order of Premises
The point above being, it really doesn’t matter what order subjects and predicates are in, or the exact qualities and flavors of the premisses. If the line of reasoning deals with certainty, it is deduction. If it deals with probability it is induction. If it deals with best guesses, it is abduction.
Likewise, if the conclusion is certain, it is deduction. Probable, induction. A hypothesis or likely explanation, abduction.
I would say the above is true… even to the extent that we would consider abduction to certainly not be a form of deduction, but to essentially be a style of of induction where a weak inductive argument seems likely so we go ahead and apply further testing to the conclusion.
The reality is, in the inductive argument below, one can draw a deductive conclusion, an inductive conclusion, and an abductive conclusion given the inductive evidence (and that hints that it is the method and the conclusions drawn that tell us what type of reasoning it is, not just, or sometimes not at all, the qualities of the premises).
Deductive: Socrates is a mortal man (tautological necessary truth, simply a result of logical analysis). Inductive: All men are likely mortal like Socrates is (a likely rule based on a synthesis of the inductive evidence); NOTE: This is a weak argument, the evidence would become stronger the more instances we look at (so if we looked at 100 men, we could be more sure that all men are mortal). Abductive: Perhaps all men are mortal like Socrates is (a hypothesis gleaned from comparing an interesting observation to a fact).
TIP: See the classic syllogistic reasoning examples below. The problem with them is that while they work well to illustrate deduction, they only illustrate one style of induction, and they also don’t do a great job of differentiating between abduction and induction. It is the classic example that is paired with reasoning, but it doesn’t tell the full story (which means it can be confusing).
|Major Premise||All Men are Mortal (a certain fact about a class of things, could also be any certain fact about a specific thing or class of things.)||Socrates is Mortal (a fact about a specific thing, could also be a probable rule about a class of things.)||All Men are Mortal (a certain fact about a class of things, could be any type of premise.)|
|Minor Premise||Socrates is a Man (a certain fact about a specific thing, could also be a certain fact about a class of things.)||Socrates is a Man (a certain fact about a specific thing, could also be a probable rule about a class of things.)||Socrates is a Mortal (could be any interesting observation or idea.)|
|Conclusion (Inference)||It is certain that: Socrates is Mortal (Deduce a fact about a specific thing or class of things; produces a certain fact about a specific thing or class of things.)||It is likely that: All Men are Mortal (Infer a probable fact about a specific thing or class of things; produces a likely fact or rule about a specific thing or class of things.)||Perhaps: Socrates is a Man (Speculate a connection between the interesting observation and the certain or probable fact, rule, or observation, speculating a connection between the two premises; produces a speculative hypothesis.)|
NOTE: On this page you should consider every proposition (every statement in an argument) to be true. The study of arguments forms and types is not the study of the truth of specific propositions.
A Few Other Notes:
Bottom Up vs. Top Down: Induction is often called bottom-up reasoning because it generally starts with specifics facts/observations/measurements and/or probable rules (gleaned from comparing specifics) and reasons toward a generalization (a probable rule or likelihood). It is often called top-down reasoning because it generally starts with a certain rule about a class of things, compares that to a certain fact about a specific thing, and then reasons down towards a certain conclusion about a specific thing (although it can reason from specifics to specifics or rules to rules too. That said, one can do the inverse of any reasoning type (as noted above). For example with inverse induction, we would start with the conclusion and look for facts that proved the conclusion with certainty. Or with inverse deduction, we start with certain facts and look for a certain theory to support them. Bottom-up and top-down terminology aside, working with certain conclusions that follow from the premises only is deduction, and working likely truths that don’t necessarily follow from the premises is induction. Likewise, no matter what direction you go, comparing observations and specific facts to produce a speculative hypothesis is abduction.
Analysis / Rationalism and Synthesis / Empiricism: Deduction is a type of analysis (breaking a whole into parts) that is closely related to rationalism (the world of ideas), as it looks at what is logically and necessarily true about a given system (in this case a set of propositions; an argument). Induction is a type of synthesis (combining parts into a whole) that is closely related to empiricism (the world of material objects), because it compares data points that are generally obtained through observation/measurement to better understand how data does and doesn’t connect.