Understanding the Different Types of Logical Reasoning Methods and Argumentation
We explain and compare the different types of reasoning methods including deductive, inductive, abductive, analogical, and fallacious reasoning.
With that in mind, we’ll also explain complex mixes and sub-sets of these reasoning types (AKA logic types, AKA argument types) including rhetoric, dialectics, skepticism, conditional, cause-and-effect, statistical, inverse versions, comparative, synthetic, and more.
A Quick Summary of the Many Different Types of Reason (All of Which are Forms of Deduction and Induction)
Here one should note that there are only two true forms of reasoning, deductive (deducing certain truth from other certain truths) and inductive (inducing likelihood of truth by comparing probable truths).
The rest are names for specific “forms, flavors, or mixes” of these (and some of these over-lap with each other).
Of these “forms, flavors, and mixes” the most notable is abductive (a type of induction that speaks to conceptualizing a hypothesis).
Also notable are reductive, conditional, analogous, fallacious, and the inverse forms (as they speak to important aspects of logic). The rest essentially just speak to methods of the aforementioned.
With that in mind, we could define the following methods of reasoning/logic/argument/inference:
- Deductive Reasoning: Starting with certain facts and comparing them to find other certain truths (determining truth-values with certainty based on certain truths). Facts that contain only certainty -> Pattern -> Conclusion based on certainty (produces more facts).
- Inductive Reasoning (Reasoning By Consistency): Starting with facts that contain uncertainty and finding what is likely true (determining probability and likelihood). Facts that contain uncertainty (like statistics) -> Pattern -> Conclusion based on probability (produces a theory).
- Abductive Reasoning: Starting with an observation and finding a good explanation for an event using facts and experiment (induction based on speculation or hypotheses). Hypothesis -> Facts and Experiment -> Confirmation or Invalidation of the hypothesis based on Facts (produces a theory).
- Reductive Reasoning (Reasoning by Contradiction): Starting with a conclusion or premise and using facts to prove it is not true (disproving a claim using facts to show it is “absurd”). The method of reductio ad absurdum attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible. Conclusion -> Facts -> the Invalidation of a conclusion (disproves theories).
- Analogous Reasoning: Reasoning by analogy (it is true for this system, real or metaphorical, perhaps it can tell us truth about this other system it shares properties/attributes with). Includes reasoning by metaphor; like using magnets to explain quantum interactions, or looking to a past historic event to help us understand a current event (by looking at properties the events share and speculating that it could share other properties and cause and effect chains).
- Deontic Reasoning: Reasoning where a conclusion logically follows from a single premise (a premise with a necessary conclusion). Ex. Lying is wrong; therefore one should not lie (the second premise, that one doesn’t want to act wrongly, isn’t needed, or is at least implied in the premise).
- Statistical Reasoning: Inductive reasoning using statistics (thus producing probable truth values based on statistical data).
- Comparative Reasoning: Reasoning by comparison (I reason I am short, because most people are taller than me). It is reasoning that establishes the importance of something by comparing it against something else (the comparing of two real systems to find similarities and differences; not just comparing by metaphor).
- Rhetoric: Using a mix of logical reasoning types (and a dash of appeals to emotion) to persuade people (persuasive reasoning).
- Abstraction (dialectic): Taking a concept and abstracting out other concepts (it is in essence the root behind deduction and the syllogism). One can also think of this as taking premises, arguments, or hypotheses and drawing out other premises and taking arguments and drawing out other concepts, premises, arguments, or hypotheses (it is essentially a form of analysis). From the concept of height comes short and tall (necessarily; to the extent that it is almost tautological). Or, for example, from the thesis of liberalism comes the anti-thesis conservatism, comes the synthesis centrism. Can be used to create spectrums and to discover new terms.
- Conceptualizing: Observing attributes to define terms. One can’t define a system without observing its properties. Without concepts there is nothing to reason with.
- Conditional Reasoning: If…then… logic. Logic where outputs change depending on variables. This is contingent reasoning that considers inductive and deductive logic based on variables (or “possible worlds”).
- Modal Reasoning: Reasoning by qualifiers. Conditional reasoning is one example of this. For example, since A then necessarily B. This is what Hume’s fork expresses essentially. Things are either possible if and only if it is not necessarily false (regardless of whether it is actually true or actually false); necessary if and only if it is not possibly false; and contingent if and only if it is not necessarily false and not necessarily true (i.e. possible but not necessarily true); impossible if and only if it is not possibly true (i.e. false and necessarily false).
- Cause-and-effect Reasoning (Casual Reasoning): Reasoning what could or should happen given an effect or cause (what would happen if there was no taxes starting tomorrow?) See types and modes of causal reasoning.
- Temporal Reasoning: reasoning based on the qualifier of time (where something can be true some times and then false other times).
- Inverse (Deduction, Induction, Abduction): Doing the inverse of any reasoning type, for example with deduction we would start with the conclusion and look for facts that proved the conclusion with certainty.
- Skepticism: Poking holes in arguments by trying to falsify, invalidate, weaken, provide counter-arguments, or generally use reductive reasoning (questioning inferences and premisses).
- Synthetic Reasoning: Looking at the spaces in between things (considering relations by analogy and forming hypotheses from that). A sort of mix of induction, abduction, and analogy.
- Critical Thinking: A name for employing all these thinking methods and pairing them with imagination to practice philosophy (natural and moral). Thinking “what is,” “what might be,” and “what ought to be” to draw out more truth from what is known.
- Fallacious Reasoning: Reasoning based on false beliefs (reasoning based on beliefs that are not actual facts).
- Butterfly Reasoning: A way to describe the common reasoning method people use where connections are drawn based perceived associations (that don’t necessarily connect logically). It is the assumption of a relation without proof of a relation (a type of fallacious reasoning). This form of reasoning can produce compelling arguments, but uses unsound, invalid, weak, or uncogent arguments. It was defined by the very useful website “changingminds.org” to describe the sort of reasoning people use in the every day (and, as a side note, the sort of reasoning conspiracy theories often use).
TIP: Any of the above reasoning types can generally be transposed onto a syllogism or onto a conditional if…then… statement.
TIP: Deductive logic, deductive argument, deductive method, deductive reasoning, deductive inference, and deduction all generally mean the same thing (but not exactly the same thing in all contexts; i.e. pay attention to context). They describe the act of comparing two or more certain statements and drawing a certain inference. In logic a single term is often used for many different concepts, like the term “inference,” just as often many different words are used for one single general concept. Deductive is an example of a term that applies to all the aforementioned (where its meaning differs depending on context). The answer to why this is the case is generally found in the limits of the human language, the way our language works, and what makes sense in the context of the ongoing field of logic.
With that basic introduction covered, let’s look at this all in more detail to better understand the different types of reasoning/argument/logic.
- First we’ll introduce you to the basics of logic and the syllogism (so you can understand the types of reasoning and argument).
- First we’ll offer general definitions for each reasoning type (this won’t be an exhaustive list of every reason type named in the cannons of philosophical and mathematical logic, but will be a solid foundation of important types).
- Then we will compare deductive reasoning and inductive reasoning, to find out the difference between deductive and inductive reasoning (as these are the two primary forms of reasoning; and arguably the only real forms of reasoning, with the rest being sub genres of these two).
- Then we will compare and contrast the other forms of reasoning.
The Basics of Deductive and Inductive Logic and Reason
What is reason? Reason in this sense is another name for the process of using logic and reason to compare terms (concepts like “A”), construct logical arguments (and state propositions AKA statements like “A=B” and “B=C”), and draw reasoned inferences (make conclusions like since “A=B” and “B=C” therefore “A=C”). See an explanation of logic and reason.
Introducing the Syllogism
All forms of reasoning and argument can essentially be transposed onto a syllogism. A version of the classic syllogism looks like this:
- Premise 1: All humans are mortal.
- Premise 2: All Greeks are a human.
- Conclusion: All Greeks are mortal.
It which looks like this with explainers:
- Major Premise: All humans (subject term; middle term) are mortal (predicate term; major term). (a logical proposition that uses the categorical terms “all humans” and “mortal,” where “are” tells us their relation; we can reasonably assume all humans are mortal using inductive reasoning).
- Minor Premise: All Greeks (subject term; minor term) are a Human (predicate term; still the middle term). (logical proposition; again we can reason that All Greeks are human via inductive reasoning).
- Conclusion: Therefore, All Greeks (subject term; minor term) is mortal (predicate term; major term). (reasoned inference; we draw the logical conclusion or reasoned inference that All Greeks are mortal because they are human and “all humans are mortal”).
The Mood of a Syllogism
The syllogism above is a thing of deductive reasoning and is an “AAA” “universal” categorical syllogism made from categorical propositions; categorical: because it uses categories of things and not specific names and, universal: because the subject term applies to the predicate in each premise and conclusion (i.e. the subject is distributed to the predicate; it is not undistributed, meaning it applies only to “particular” cases).
Further, it is affirmative, because each statement is denoting that the claim is true (if it was “aren’t” instead of “are” it would be negative).
Another way to say this is each proposition and the conclusion are all Universal Affirmative (A). All valid “AAA” syllogisms have a constant truth-value.
In other words, there is a logical rule-set behind reasoning where each proposition or conclusion is either in the form of:
- Universal Affirmative (A). All A are B.
- Universal Negative (E). No A are B.
- Particular Affirmative (I). Some A are B.
- Particular Negative (O). Some A are not B.
The above is always true for deductive reasoning (because it speaks to certainty), but can only loosely be applied to inductive reasoning (because it speaks to likelihood).
In other words, the style of a syllogism works for both deductive and inductive logic/reasoning/argument, but the bit about mood only directly applies to deductive reasoning (one of the ways in which these two forms of reasoning are different).
TIP: To be clear “AAA” means a universal major premise, a universal minor premise, and a universal conclusion. Learn more about figure and a term which describes the position of the middle term, mood.
Deductive Reasoning Vs. Inductive Reasoning
The structure of a syllogism works for both inductive and deductive arguments, but these two types have a key difference.
Deductive reasoning produces constant truth-values, inductive doesn’t (it produces probable truth-values AKA likelihoods).
With that in mind, an inductive syllogism (a non-deductive or statistical syllogism) might look like this:
- Almost all Adult Humans are taller than 25 inches.
- Socrates is an Adult Human.
- Therefore, it is “highly likely” Socrates is taller than 25 inches.
With deductive reasoning we can know whether an argument is true or not based on figure (as long as we confirm our logic is sound). That means we can create a logic rule-set that always works.
It doesn’t work the same way with inductive reasoning (as we aren’t just working with certain truths).
In other words, there are different metrics that apply to deductive and inductive reasoning respectively. So let’s cover those now to further illustrate the difference between these two main logic types.
Deductive Reasoning and Validity and Soundness Vs. Inductive Reasoning and Cogency and Strength
- Deductive arguments are either sound or unsound and either valid and invalid.
- Inductive arguments are either cogent or uncogent and either strong or weak.
All of that speaks to whether or not the parts (subject, premisses, predicates, etc) of the logic make sense together (that the connect logically).
TIP: For more reading see: Deduction and Induction from Patrick J. Hurley, A Concise Introduction to Logic, 10th ed.
The following is true for deductive arguments only:
- A valid deductive argument is an argument in which it is impossible for the conclusion to be false given that the premises are true.
- An invalid deductive argument is a deductive argument in which it is possible for the conclusion to be false given that the premises are true.
- A sound argument is a deductive argument that is valid and has all true premises (if it isn’t true for all premisses, it is “unsound”).
- An unsound argument is a deductive argument that is invalid, has one or more false premises, or both.
The relationship between the validity of a deductive argument and the truth or falsity of its premises and conclusion can be illustrated by the following table:
Meanwhile, the following is true for inductive arguments only:
Unlike the validity and invalidity of deductive arguments, the strength and weakness of inductive arguments is expressed in degrees of probability.
- To be considered “strong,” an inductive argument must have a conclusion that is more probable than improbable (there must have a likelihood of greater than 50% that the conclusion is true).
- The inverse is also true (i.e. argument is therefore “weak” if it has less than 50% probability).
- Thus, an uncogent argument is an inductive argument that is weak, has one or more false premises, or both.
- Meanwhile, A cogent argument is an inductive argument that is strong and has all true premises; if either condition is missing, the argument is uncogent.
The relationship between the strength of an inductive argument and the truth or falsity of its premises and conclusion can be illustrated as:
TIP: As you can see inductive reasoning follows rule-sets like deduction does, but it doesn’t produce certainty like sound and valid moods of syllogisms do. Instead it only offers insight. This is due to the probable nature of induction.
TIP: With both deductive and inductive logic we should consider how the terms of propositions relate to each other, do they follow necessarily? Are they tautological (do we need to say All Greeks are mortal, isn’t mortality a property of the categorical class “All Greeks” in the first place)? You can learn more about that on our page on Hume’s Fork, it doesn’t speak directly to the differences between reasoning types, but it is very important to understand (so let’s discuss that quickly).
Modality and Hume’s Fork
Here are some other important things to know about the terms we are using and about the modality (the relations) between subjects, predicates, premisses, and arguments.
- Proposition: A logical judgement about two or more terms (a subject and a predicate; ex. “a bachelor is sitting in the chair” is a proposition or judgement about the subject, “a bachelor”, “sitting in the chair,” the predicate). In other words a proposition is a proposed logical judgement about at least two terms.
- Premisses and Conclusions: Two types of propositions where a premiss is a proposition that leads to a conclusion (another proposition).
- Empiricism: Knowledge through empirical evidence (information from the senses). Facts about the world. What we observe. We observe something and form a concept by observing its attributes. All real objects and real attributes and the real relations of objects are empirical.
- Rationalism: Knowledge through ideas (information originating in our minds). Facts about ideas. Everything that isn’t material, and is therefore formal, is rational. All argument involves rationalizing about rational and empirical concepts.
- Skepticism: In this case, being skeptical that rationalism (pure reason) can result in true knowledge about the world. Can be interpreted broadly as skepticism about both empirical and rational knowledge. For instance, Kant suggests fusing the two styles as, “our senses themselves could be tricking us.”
Types of Propositions:
- Analytic proposition (or judgement): a proposition (AKA logical judgement) whose predicate concept is contained in its subject concept. A statement that is true by definition. Ex. “All bachelors are unmarried.” The bachelor is unmarried because he is a bachelor.
- Synthetic proposition: a proposition whose predicate concept is not contained in its subject concept but related. True by observation. Ex. “The bachelor is sitting in a chair” (nothing about sitting in a chair makes one a bachelor).
- a priori proposition: a proposition whose justification does not rely upon experience. Moreover, the proposition can be validated by experience but is not grounded in experience. Therefore, it is logically necessary. What Hume called a tautology. Ex. “1 + 2 = 3,” or “all bachelors are unmarried.” It stands to reason all bachelors are unmarried, but I can’t meet every bachelor to confirm this empirically.
- a posteriori proposition: a proposition whose justification does rely upon experience. The proposition is validated by, and grounded in experience. Therefore, it is logically contingent. Ex. “The bachelor is sitting in a chair” (yes, I can confirm the bachelor is in the chair empirically, via my senses, by looking).
This gives us four possibilities:
- An Analytic a posteriori which are experience based propositions that can be shown to be true by their terms alone.
- A Synthetic a posteriori which are experience based propositions that can be shown to be true by their terms alone.
- An Analytic a priori which are propositions not based on experience that can be shown to be true by their terms alone.
- A Synthetic a priori which are propositions not based on experience that can’t be shown to be true by their terms alone.
Furthermore, we have these modal relations:
- A necessary proposition (necessarily true): Any proposition which is necessarily true or necessarily false (the white cat is white; or, the white cat is not black). A necessary proposition is one where the truth value remains constant across all possible worlds.
- A contingent proposition (dependent on more information): Any proposition in which the truth of the proposition depends on more information. They are propositions that are neither “true under every possible valuation (i.e. tautologies)”, nor “false under every possible valuation (i.e. contradictions)”.
- Tautological proposition (necessarily true but redundant): That which must be true no matter what the circumstances are or could be (ex. the black cat is black; it is redundant to say the black cat is black).
- Contradictions (necessarily not true as it contradicts itself): That which must necessarily be untrue, no matter what the circumstances are or could be (ex. the bachelor is in a chair and not in a chair).
- “Possible” proposition (is true under certain circumstances): Are true or could have been true given certain circumstances (ex. x + y = 4).
Remember we also have affirmative, negative, universal, and particular (as covered above).
We now have the basic building blocks down. As you can see, some things are necessary (like we find in deductive logic) and some things are probable (like we find in inductive).
General Definitions for Each Reasoning Type
Below are general definitions for some key types of reasoning, in the next section we will explain each using a syllogism. The rest of the information on this page is really just meant to help hammer in what we already discussed above and shed more light on abductive reasoning and other reasoning types using examples…. remember, at its core, this is all just deduction and induction in different forms.
Inductive reasoning (AKA induction) is reasoning based on a set of facts and likelihoods from which we can infer that something likely true. For example, A is almost always equal to C, B is almost never equal to C, therefore it is very likely in this instance A=C.
Deductive reasoning (AKA deduction) is reasoning based on a set of facts from which we can infer that something is true with certainty. For example, A is always equal to C, B is never equal to C, therefore A doesn’t equal B.
Those are the only two true types of reasoning, induction “expands knowledge in the face of uncertainty,” deduction is a logical ruleset for drawing inferences from propositions (statements/facts/judgements) we are already certain about.
All other forms of reasoning are sub-sets of those (and almost all those subsets are subsets of inductive reasoning).
Abductive reasoning (AKA abduction) is a form of inductive reasoning where one starts with a observation, and then seeks to find the simplest and most likely explanation (going on to form a hypothesis; it is like the first step of forming a hypothesis). With abduction we are comparing likeness (how one system is like another system). For example, every-time we multiple something by A we get the output zero, this gives us reason to suspect that A=0 (we have the hypothesis that A=0, we can now use induction to verify the likelihood that this is true).
FACT: The American philosopher Charles Sanders Peirce (1839–1914) introduced abduction into modern logic. He went in circles trying to define and re-define it. It turns out to be useful, but really it is just a sub-genre of inductive reasoning (itself with many subsets). Consider the following table which explains abduction in Peirce’s terms
|Deduction. Rule: All the beans from this bag are white.
Case: These beans are from this bag.
Therefore Result: These beans are white.
|Induction. Case: These beans are [randomly selected] from this bag.
Result: These beans are white.
Therefore Rule: All the beans from this bag are white.
|Hypothesis. Rule: All the beans from this bag are white.
Result: These beans [oddly] are white.
Therefore Case: These beans are from this bag.
Or the same thing again, this time in Peirce’s terms.
- Hypothesis (abductive inference) is inference through an icon (also called a likeness).
- Induction is inference through an index (a sign by factual connection); a sample is an index of the totality from which it is drawn.
- Deduction is inference through a symbol (a sign by interpretive habit irrespective of resemblance or connection to its object).
In other words,
- Abduction compares similarities to find a hypothesis (hmm photons have polarity, maybe all quanta do? That is my hypothesis).
- Induction seeks to draw inferences with probability by comparing a set of facts (this person smoked, they ate red meat, they lived in a polluted city, they never exercised, it is likely they will develop health problems).
- Deduction seeks certainty by drawing inferences from know facts.
So, so far, inductive and deductive are true reasoning methods that draw inferences from facts (or in logic speak, propositions).
Where, generally speaking, inductive is probable, deductive is certain (with some special rules).
Meanwhile abductive is a notable subset of induction that speaks to the first steps of formulating a hypothesis.
There are specific rule-sets for all these forms of reasoning, but deductive reasoning is the only form of reasoning which has a perfect logical rule-set that produces constant truth values. The other methods generally produce probabilities. With that in mind, like Peirce helped us see above, all of this can be laid on-top of the structure of a syllogism.
The rest of the forms of reasoning are debatably not separate from the above, but let’s quickly note them anyway.
Analogical reasoning is reasoning by analogy. It is where one looks at shared properties of a thing and assumes other shared properties (by analogy). This is also a type of inductive reasoning, it has aspects of abduction, and can just be said to be “reasoning by analogy or metaphor.” Ex. 1. S is similar to T in certain (known) respects. S has some further feature Q. Therefore, T also has the feature Q, or some feature Q* similar to Q.
Synthetic reasoning is reasoning where one looks at the spaces between facts (so to speak) to synthesize one or more idea. It is when one looks at two or more sets of facts and attempts to draw conclusions about other things. It is therefore a mix of analogical and abductive reasoning, and is most certainly (like those) also a type of induction. Ex. All A are A and never B, All B are B and never C, perhaps all D are D and never E (if A, B, and C behave this way, perhaps D and E do)?
Fallacious reasoning is reasoning based on a fallacy… which is deductive or inductive reasoning based on a fallacy. Which is just akin to not having one’s facts straight.
Reductive reasoning is a subset of argumentative reasoning which seeks to demonstrate that a statement is true by showing that a false or absurd result/circumstance follows from its denial. Reductive reasoning speaks to the very important skepticism.
Conditional reasoning is “if… then…” reasoning. Like the syllogism most logic can be transposed onto this form (it is how computers work after-all). In other words, most logic can be transposed on the statement: “if A then B.” This can result in direct proof (if A then B, and we suppose A is true, then B is true), contrapositive proof (if A then B, suppose B is false, then A is false), or proof by contradiction (if A then B, suppose A is true and B is false, therefore C the conclusion is true and C is false… which is a contradiction and therefore the premise is wrong). All inductive reasoning will result in something “likely” being a true or not (either all the time or in some instances), all deductive reasoning will result in something being proven true or not (either all the time or in some instances).
Inductive Reasoning Explained With Examples
Inductive reasoning is reasoning in which the premisses are viewed as supplying strong evidence for the truth of the conclusion (assuming something about a thing based on something similar). This sort of reasoning results in probabilities and likelihood.
1. 25% of beans are red, 2. 75% are blue, 3. the bag has a mix of randomly selected beans, 4. it is therefore likely that some beans in the bag are red and some are blue.
We can’t be sure there is both red and blue beans in the bag, but it is likely given the facts (we could calculate the probability of this with Bayes’ theorem.)
- Premise: All Greeks have been human so far.
- Conclusion: The next Greek born will be a human.
Given the fact that all Greeks are human, it is likely (but not certain) the next Greek born will also be human.
Deductive Reasoning Explained With Examples
Deductive reasoning is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion (comparing two things). This sort of reasoning results in absolute truth-values.
1. 25% of beans are red, 2. 75% are blue, 3. the bag has a mix of beans of different types, 4. therefore there are red and blue beans in the bag.
We deduced that the bag must contain both red and blue beans for sure given the facts.
- Premise 1: All humans are mortal.
- Premise 2: All Greeks are human.
- Conclusion: All Greeks are mortal.
Since all Greeks alive today are human (we have assumed we have already confirmed this; or we have at least accepted the inductive logic used to come to this conclusion), we can know with 100% certainty that all Greeks are mortal (they are human, so they are mortal).
TIP: Deductive reasoning can also be probable, this is because it is only certain when the argument is 100% valid. If we were unaware of an immortal Greek, then our conclusion would be false, even though our logic was sound. If our logic isn’t sound (if our subjects and predicates don’t pair sensibly or if our premises don’t; then our conclusion will be unsound). One can arrive at a true conclusion using unsound logic and invalid reasoning by luck, but that is not the main point here.
Abductive Reasoning Explained With Examples
Abductive reasoning (or retroduction) is like “educated guessing” or reasoning by hypothesis. In other words, abductive reasoning is a form of inductive reasoning which starts with an observation then seeks to find the simplest and most likely explanation (finding the simplest explanation). The reason it is distinguished from inductive reasoning is because it tries to find the best conclusion by attempting to falsify alternative explanations or by demonstrating the likelihood of the favored conclusion. Abductive reasoning is the reasoning method using in the scientific method.
1. there is a bag with 1,000 beans in it which are either 99% red and 1%blue or 1% red and 99% blue, 2. we randomly pull out ten beans and they are all blue 3. therefore it is very likely that the bag contains 1% red and 99% blue beans.
We hypothesized that this was the bag with mostly blue beans because we pulled 10 beans from the bag at random, and that would have been very unlikely if only 1% of the thousand beans in the bag were blue.
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.
Socrates didn’t die like the rest of the Greeks;
- If some Greeks weren’t mortal, this could explain why Socrates didn’t die,
- Hence, we can can suspect that not all humans are mortal.
Here the hypothesis is framed, but not asserted, in a premise, then asserted as rationally suspect-able in the conclusion.
TIP: So, is this really different from inductive logic? -Ish, not really… at the end of the day we are still comparing facts and inferring likelihood like we do with inductive logic. The difference is the order in which we approach the problem. That brings us to the even less accepted synthetic reasoning (not to be confused with Kant’s analytic-synthetic distinction).
Analogical Reasoning Explained With Examples
Analogical reasoning is reasoning from the particular to the particular (by analogy). It is often used in case-based reasoning, especially legal reasoning.
- Premise 1: Socrates is human and mortal.
- Premise 2: Plato is human.
- Conclusion: Plato is mortal.
Since Socrates is human and mortal, and since Plato is human, it stands to reason that Plato is also mortal.
This is a sort of inductive reasoning that produces “weak arguments” in many cases due to its structure. Consider the next example which produces an invalid result.
- Premise 1: Socrates is human and male.
- Premise 2: Cleopatra is human.
- Conclusion: Cleopatra is male.
Just because Socrates has two properties and shares one with Cleopatra doesn’t mean he shares all properties with Cleopatra, if he did, he wouldn’t be the unique person Socrates, he would be a categorical term.
Synthetic Reasoning Explained With Examples
Synthetic reasoning is a form of reasoning where one compares the difference and similarities between propositions and attempts to synthesize them to draw an inference (looking at the space in between two ideas so to speak). It is essentially a hybrid form of analogical and abductive reasoning.
- Premise 1: In every nation people seem to divide themselves into two groups (observation).
- Premise 2: These groups tend to have some constant left-right viewpoints (observation).
- Premise 3: These viewpoints seems to line up with the archetypical male and female personas (observation).
- Conclusion: Perhaps the political left and right are naturally occurring and are a reflection of the archetype male and female (grounds for hypothesis)?
And with that we have grounds to formulate a hypothesis and begin the process of speculation. Here our hypothesis is based on the “synthesis” of two ideas. Thus, synthetic reasoning is really just a flavor of abduction.
- Premise 1: All humans are mortal.
- Premise 2: All Greeks are human.
- Conclusion: All Greeks are mortal.
- Synthetic Reasoning: But wait, oddly we find that the flat worm is [essentially immortal], so what if there is a sub-class of humans who break this rule under special circumstances? <— Again, with that we have grounds to formulate a hypothesis and begin the process of speculation.
In other words, synthetic reasoning is just a term that speaks to looking at the spaces in between, the relations of things. It could easily be considered as a part of induction and abduction and is generally talked about alongside abduction, or even as a synonym for abduction, if at all.
NOTE: Synthetic reasoning is not widely accepted as a form of reasoning.
Fallacious Reasoning Explained With Examples
- Premise 1: The fair coin just landed on heads 10 times in a row.
- Conclusion: Therefore the coin will likely land on tails next time; since it is due.
This reasoning is invalid because it is based on the gamblers’ fallacy. In other words, if one bases their premise on a fallacy then deductive, inductive, or abductive reasoning is by its nature invalid.
TIP: As you can see, all reasoning is really just inductive or deductive. Inductive deals with probability, deductive deals with absolutes (but can be probabilistic since its elements often rely on induction). The rest of the forms essentially speak to the specific mechanics of how we compare terms and whether we start with observations, terms, judgements, inferences, hypotheses, or theories.
- Types of Reasoning
- 11.3 Persuasive Reasoning and Fallacies
- reductio ad absurdum
- Statistical Syllogism
- Deduction and Induction from Patrick J. Hurley, A Concise Introduction to Logic, 10th ed
- Analogy and Analogical Reasoning
- Three Ways to Prove “If A, then B”