TYPES OF REASONING
Reasoning within an argument gives the rationale behind why one choice, for example should be selected over another. Types of reasoning include:
 Abduction: the process of creating explanatory hypotheses.
 Analogical Reasoning: relating things to novel other situations.
 Cause-and-Effect Reasoning: showing causes and resulting effect.
o Cause-to-Effects Reasoning: starting from the cause and going forward.
o Effects-to-Cause Reasoning: starting from the effect and working backward.
o The Bradford Hill Criteria: for cause and effect in medical diagnosis.
 Comparative Reasoning: comparing one thing against another.
 Conditional Reasoning: using if...then...
 Criteria Reasoning: comparing against established criteria.
 Decompositional Reasoning: understand the parts to understand the whole.
 Deductive Reasoning: starting from the general rule and moving to specifics.
 Exemplar Reasoning: using an example.
 Inductive Reasoning: starting from specifics and deriving a general rule.
 Modal Logic: arguing about necessity and possibility.
 Pros-vs-cons Reasoning: using arguments both for and against a case.
 Residue Reasoning: Removing first what is not logical.
 Set-based Reasoning: based on categories and membership relationships.
 Systemic Reasoning: the whole is greater than the sum of its parts.
 Syllogistic reasoning: drawing conclusions from premises.
 Traditional Logic: assuming premises are correct.
Note that these are not all mutually exclusive methods and several give different lenses onto overlapping areas. In classical argument, for example, all arguments are framed as either inductive or deductive.
ABDUCTION
Description
A is observed. If B were true, then A would be true. Therefore B may be true.
Abductive reasoning, or abduction, is the process of explaining something that is experienced or observed in some way and where there is no existing knowledge to explain the phenomenon. It creates a hypothesis that may or may not be true and which may require further work to verify.
Example
A doctor, meeting a set of symptoms not met before, considers diseases that have similar symptoms and wonders if the presented condition is something similar.
A detective homes in on what seem to be important clues to a crime.
Discussion
Abduction was defined by semiotician Charles Peirce who defined it as 'the process of forming an explanatory hypothesis'. This is in contrast to inductive development of theories and deductivetesting of theories.
The process of abduction may well have a significant subconscious element, for example where an expert draws on tacit knowledge to explain a new phenomenon. Nobel Prize-winner Henri Poincaré said ‘It is through science that we prove, but through intuition that we discover.’
The principle of abduction aligns with the Constructionist view of the world. Shank (1998) suggests abandoning the pursuit of detail, preferring the development of 'craft skills' in abduction, through deliberately seeking surprise and the 'residue of the unexplained' in anomalies, inconsistencies and incongruities. Abductive reasoning may be a key skill in the paradigmatic process described by scientific historian Thomas Kuhn.
ANALOGICAL REASONING
Description
A is like B. M is in A. N is in B. So M is like N.
In analogical reasoning, an analogy for a given thing or situation is found, where the analogy is like the given thing in some way. Other attributes of the analogical situation are then taken to also represent other attributes of the given thing.
To use an analogy:
 Start with a target domain where you want to create new understanding.
 Find a general matching domain where some things are similar to the target domain.
 Find specific items from the matching domain.
 Find related items in the target domain.
 Transfer attributes from the matching domain to the target domain.
Example
This company is like a racehorse. It's run fast and won the race, and now it needs feed and rest for a while.
Today is like a day in paradise. We don't need an umbrella.
Dating it is like flying. At some point, your feet are going to leave the ground.
Discussion
Our brains work by patterns and association -- if a perception fits roughly into an existing pattern, then the existing pattern may be taken as definitive. For example, we see a half-hidden person and 'recognize' them as someone we know. We also use similarity in our thinking, where even distant fields may be used to help understand a given concept or situation. Although this can lead to fallacious associations, it can also be very helpful in extending understanding.
CAUSE-AND-EFFECT REASONING
Description
When you are presenting an argument, show the cause-and-effect that is in operation. Help the other person see why things have happened or will happen as they do. Show purpose. Link things to higher values. Show the inevitable linkage between what happens first and what happens next. Go beyond correlation (that may show coincidence) to giving irrefutable evidence of causality. If you cannot show causal linkage, then you may be successful just by asserting it, because few people will challenge a cause-and-effect assertion.
Example
Say this Not this
If I help you, you will be more successful.
I will help you.
When the moon is high, things are abroad.
Things are sometimes abroad.
The new additive to fuel makes your car go so much further.
Add our new fuel additive to your car.
Discussion
We have deep needs for explanation and to be able to predict what will happen. We also need to be able to appear rational to others, and that they appear rational to us. When a person explains cause and effect, we are reassured that they are, indeed, reasonable people, and we hence trust them and their arguments more than we might otherwise do.
This need leads to psychological effects where you can offer a cause-and-effect argument that clearly has no real causal connection, yet it is surprising how many people will accept your argument without question. In a famous experiment, Ellen Langer et al were able to butt into a queue for a photocopier just by saying 'Can I use the photocopier because I want to use the photocopier' (yet without giving reason, the researcher was not allowed to jump the queue).
Cause-to-effects reasoning
Description
When describing a cause-effect situation, start with the cause and then add the effect or effects afterwards. This is particularly concerned with words in a single sentence, although the logic applies if spread across sentences.
Example
Say this Not this
The girl slapped the boy.
The boy was slapped by the girl.
If you send me the money, I will send you the goods.
I will send you the goods if you send me the money.
The people kicked the ball out of the field. It hit a passing police car.
A police-car was hit by a ball. It had been kicked out of the field.
Poverty is on the increase. People are desperate. Crime rates are rising.
Crime rates are rising because people are desperate due to increasing poverty.
Discussion
Cause-and-effect reasoning is generally persuasive as it helps answer the question 'why' something happens, making a statement objective and rational rather than a blind assertion. Starting with the cause is often linguistically easier than starting with the effect, making the sentence easier to both say and understand. Starting with the cause builds creative tension as an expectation is set up that something will happen because of it. This can make your audience more interested in what you are saying. There is also an assumption in this argument that one cause can have multiple effects. This can be used to show the power of a simple action. False cause-to-effects happens when we do not like something (for example handguns) and seek to create an effect to justify our beliefs (for example that having handguns will lead to many people becoming criminals).
Effects-to-cause reasoning
Description
When describing a cause-effect situation, start with the effect or effects and then work back to the cause of these. You can do this by asking 'why did this happen', creating curiosity and then explaining why. Using the word 'because' to connect effects to cause can be particular effective. 'If you want...then...' can also be useful.
Example Say this Not this
You lost the game because you did not listen to me.
You did not listen to me so you lost the game.
The economy is suffering. The President is too concerned with foreign policy.
The President's foreign policy is causing the economy to suffer.
If you want to rule the world, you have got to work hard now.
Work hard now and you will be able to rule the world.
Can I have a cup of coffee? I am very thirsty.
I am very thirsty. Can I have a cup of coffee?
Discussion
Cause-and-effect reasoning is generally persuasive as it helps answer the question 'why' something happens, making a statement objective and rational rather than a blind assertion. Putting the effects first anchors the statement in reality. It makes a statement that cannot be denied as it is a statement of known effects. The truth of the effects is then reflected into what may well be a hypothetical cause. When something happens, there is a deep human need to explain and answer why it has happened. Thus if you present a problem, people will start wondering why, thus making themselves more ready for your answer. Like the TV detective 'Whodunnit', the murder is committed and we are glued to the storyline to find out what happened. It is easy when trying to explain to latch onto something that is not necessarily the real cause, and our desperation for an answer can blind us to reality.
THE BRADFORD HILL CRITERIA
In 1965 Austin Bradford Hill described the minimal conditions establishing cause and effect in medical diagnosis.
Temporality
There is a time relationship between cause and effect in that the effect occurs after the cause. Also, if it is to be expected that there is some delay between cause and effect then that delay should also be observed.
Strength and association
Cause-and-effect may be observed by statistical correlation between these in repeated events or experiments. Full strength correlation has a coefficient of 1. A weaker association between cause and effect will see greater variation.
Biological gradient (dose-response)
In treatment, there might be expected to be a relationship between the dose given and the reaction of the patient. This may not be a simple linear relationship and may have minimum and maximum thresholds.
Consistency
One apparent success does not prove a general cause and effect in wider contexts. To prove a treatment is useful, it must give consistent results in a wide range of circumstances.
Plausibility
The apparent cause and effect must make sense in the light of current theories and results. If a causal relationship appears to be outside of current science then significant additional hypothesizing and testing will be required before a true cause and effect can be found.
Specificity
A specific relationship is found if there is no other plausible explanation. This is not always the case in medicine where any given symptoms may have a range of possible causing conditions.
Evidence
A very strong proof of cause and effect comes from the results of experiments, where many significant variables are held stable to prevent them interfering with the results. Other evidence is also useful but can be more difficult to isolate cause and effect.
Analogy
When something is suspected of causing and effect, then other factors similar or analogous to the supposed cause should also be considered and identified as a possible cause or otherwise eliminated from the investigation.
Coherence
If laboratory experiments in which variables are controlled and external everyday evidence are in alignment, then it is said that there is coherence.
COMPARATIVE REASONING
Description
Comparative reasoning establishes the importance of something by comparing it against something else. The size of the gap between the things compared indicates importance. Compare against a high standard to make something look undesirable. Compare it against a weak example to make it look good. To create a logical argument, first establish the validity of the comparison benchmark. For less logic, the benchmark may be assumed.
There are many ways to compare, for example:
 Compare what people have got (or not got) against what others have.
 Compare the past with the future.
 Compare what is actual with what is ideal.
 Compare words and actions against values.
Example Say this Not this
I guess your wife will want something good-looking. How about this one?
This is the right one for you!
How will we know when we have succeeded? Let's discuss this first...
Success means maximum profits.
Our manifesto says we must help those who cannot help themselves. Now, can this person help himself?
We should not help this man.
Discussion
Comparison is a very natural form of judgement as we find it difficult to evaluate something on a stand-alone basis. We want to know if it is better or worse -- but better or worse than what? For persuasion, if you can establish the benchmark against which better and worse is judged, then the rest, as they say, is history. Not only is there a common assumption that the given benchmark item is the right thing to compare against, but the assessment of how much better or worse things are is also assumed to depend on the size of the gap between the item being compared and the benchmark. Several sequential requests make use of this principle, setting a benchmark and then using the contrast of the ensuing gap to prompt desired action.
CONDITIONAL REASONING
If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false. In effect you also need a statement of the form 'If not A then ...'.
A classic form of conditional reasoning is in using syllogisms, where a general major premise is combined with a more specific minor premise to form a conclusion. Syllogisms are easy to get wrong and there are many fallacies.
The card trap
A classic trap was used by Wason and Johnson-Laird (1972) to show how poor we really are at reasoning.
Four cards are laid out as below:
E
K
4
7
The conditional statement is now given: 'If a card has one vowel on one side, then it has an even number on the other side.' The question is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. More than half of people questioned said E and 4. To affirm the antecedent, E is correct. E is a vowel and thus should have an even number on the other side. If there was an odd number on the other side, the statement would be false, so E must be turned over to check for this. But choosing 4 is affirming the consequent. Even though 4 is even, it can have a vowel or consonant on the other side and the statement is not falsified. Only 4% said E and 7. The 7 could deny the consequent and hence must be checked. If there was a vowel on the other side, the statement would be false. And what of K? There is nothing to say that a card cannot have letters on both sides. If there is a vowel on the other side, then the statement is also wrong.
So what?
Be careful about if-then statements, both in your own use and in those that others use. It does, of course also mean that you can make statements that are logically false and few people will challenge you.
CRITERIA REASONING
Description
Start by defining the criteria by which the outcome of a decision will be judged, and then identify the best decision, given these constraints. In a logical argument, you will spend much time establishing the criteria as valid first. In a less logical situation, you may assume the criteria are correct, minimizing the time spent on any discussion about them. Criteria which appeal to common values are likely to be easily accepted.
Example Say this Not this
I guess your wife will want something good-looking. How about this one?
This is the right one for you!
How will we know when we have succeeded? Let's discuss this first...
Success means maximum profits.
Our manifesto says we must help those who cannot help themselves. Now, can this person help himself?
We should not help this man.
Discussion
Establishing criteria provides legitimacy for any future argument, as the criteria form the rules by which right and wrong are judged, even when criteria are assumed to be true without discussion.
The easier criteria are to accept as reasonable, the less likely it will be that people will question them. Using common values helps this. A problem with criteria is highlighted by the question 'by what criteria do you select the criteria'. This argument could be given again, should criteria for selecting criteria be agreed. In this way, criteria reasoning, though useful in many ways, may be build on sand.
DECOMPOSITION
Description
Break the item in question down into its component parts. Analyze those parts and how they fit together. And then draw conclusions about the whole.
Example
I want to find out how a Rubic Cube operates. I pull it apart to see its hidden workings. By reassembling it slowly, I am able to explain its apparently magical cohesion as a whole in terms of three-dimensional geometry.
I listen to your argument and take note of each element. I then argue against each element in turn. Having destroyed the parts, I then assume I have destroyed the whole argument.
Discussion
Much of science takes a decompositional approach to things, breaking them down into parts, atoms and smaller still. The notion that a thing is the sum of its parts and no more hence has a highly credible air. A problem with decompositional thinking is that the whole thing can easily be more than the sum of its parts. A person is more than bone and muscle. You cannot understand a car by studying each item in isolation. A trick in effective decompositional reasoning is to use it as lens, understanding the parts but not assuming that they fully describe the whole. The biggest trick is in
understanding the relationship between the parts. The problem with this is that relationships increase with the square of the number of parts, making full understanding of even a simple device potentially very difficult. Decomposition is a very useful lens and often does tell the whole story, but there are many situations where this is an inadequate approach.
DEDUCTIVE REASONING
Description
Deductive reasoning, or deduction, starts with a general case and deduces specific instances. Deduction starts with an assumed hypothesis or theory, which is why it has been called 'hypothetico-deduction'. This assumption may be well-accepted or it may be rather more shaky -- nevertheless, for the argument it is not questioned. Deduction is used by scientists who take a general scientific law and apply it to a certain case, as they assume that the law is true. Deduction can also be used to test an induction by applying it elsewhere, although in this case the initial theory is assumed to be true only temporarily.
Example Say this Not this
Gravity makes things fall. The apple that hit my head was due to gravity.
The apple hit my head. Gravity works!
They are all like that -- just look at him!
Look at him. They are all like that.
Toyota make wonderful cars. Let me show you this one.
These cars are all wonderful. They are made by Toyota, it seems.
There is a law against smoking. Stop it now.
Stop smoking, please.
Discussion
Deductive reasoning assumes that the basic law from which you are arguing is applicable in all cases. This can let you take a rule and apply it perhaps where it was not really meant to be applied. Scientists will prove a general law for a particular case and then do many deductive experiments (and often get PhDs in the process) to demonstrate that the law holds true in many different circumstances. In set theory, a deduction is a subset of the rule that is taken as the start point. If the rule is true and deduction is a true subset (not a conjunction) then the deduction is almost certainly true. Using deductive reasoning usually is a credible and 'safe' form of reasoning, but is based on the assumed truth of the rule or law on which it is founded.
Validity and soundness
Deductive conclusions can be valid or invalid. Valid arguments obey the initial rule. For validity, the truth or falsehood of the initial rule is not considered. Thus valid conclusions need not be true, and invalid conclusions may not be false. When a conclusion is both valid and true, it is considered to be sound. When it is valid, but untrue, then it is considered to be unsound.
EXEMPLAR REASONING
Description
Exemplar reasoning is the use of examples in argument. The example may be told as a story or may be a short comparator. It may be a duplicate of the situation or may be a relatively distant
metaphor. It may be of a known person, known situation or something not directly known to the other person.
Example
You should go out more often. I have a friend who used to stay in and was never really happy.
You know I had a dog like yours and he wouldn't fetch things either. I found that rubbing some jam on the stick worked.
You want to be a pop-star? Look at Jules Markam and how hard he worked. Are you prepared to put in the hours?
Discussion
Examples are often very persuasive as they contain evidence of 'real world' situations. We believethe evidence and so set up a pattern of believing that leads us to agree with the overall argument. The assumption in the use an example is that it can be generalized to the situation about which you are talking. This is not necessarily true and may be resisted with arguments of the form 'Ah, but this is different...'. Examples used may be direct, as above, or indirect, such as using them as metaphor of some kind to map between domains or models, bringing analogical richness to the situation.
INDUCTIVE REASONING
Description
Inductive reasoning, or induction, is reasoning from a specific case or cases and deriving a general rule. It draws inferences from observations in order to make generalizations.
Inference can be done in four stages:
1. Observation: collect facts, without bias.
2. Analysis: classify the facts, identifying patterns o of regularity.
3. Inference: From the patterns, infer generalizations about the relations between the facts.
4. Confirmation: Testing the inference through further observation.
In an argument, you might:
 Derive a general rule in an accepted area and then apply the rule in the area where you want the person to behave.
 Give them lots of detail, then explain what it all means.
 Talk about the benefits of the parts and only get to the overall benefits later.
 Take what has happened and give a plausible explanation for why it has happened.
Inductive arguments can include:
 Part-to-whole: where the whole is assumed to be like individual parts (only bigger).
 Extrapolations: where areas beyond the area of study are assumed to be like the studied area.
 Predictions: where the future is assumed to be like the past.
Example Say this Not this
Look at how those people are behaving. They must be mad.
Those people are all mad.
All of your friends are good. You can be good, too.
Be good.
The base costs is XXX. The extras are XXX, plus tax at XXX. Overall, it is great deal at YYY.
It will cost YYY. This includes XXX for base costs, XXX for extras and XXX for tax.
Heating was XXX, lighting was YYY, parts were ZZZ, which adds up to NNN. Yet revenue was RRR. This means we must cut costs!
We need to cut costs, as our expenditure is greater than our revenue.
Discussion
Early proponents of induction, such as Francis Bacon, saw it as a way of understanding nature in an unbiased way, as it derives laws from neutral observation. In argument, starting with the detail anchors your persuasion in reality, starting from immediate sensory data of what can be seen and touched and then going to the big picture of ideas, principles and general rules. Starting from the small and building up to the big can be less threatening than starting with the big stuff. Scientists create scientific laws by observing a number of phenomena, finding similarities and deriving a law which explains all things. A good scientific law is highly generalized and may be applied in many situations to explain other phenomena. For example the laws of gravity was used to predict the movement of the planets. Of course when you find a law, you have to spend ages proving it and convincing others that it is true.
Inductive arguments are always open to question as, by definition, the conclusion is a bigger bag than the evidence on which it is based. In set theory, an inductively created rule is a superset of the members that are taken as the start point. The only way to prove the rule is to identify all members of the set. This is often impractical. It may, however, be possible to calculate the probability that the rule is true. In this way, inductive arguments can be made to be more valid and probable by adding evidence, although if this evidence is selectively chosen, it may falsely hide contrary evidence. Inductive reasoning thus needs trust and demonstration of integrity more than deductive reasoning. Inductive reasoning is also called Generalizing as it takes specific instances and creates a general rule.
MODAL LOGIC
Description
Describe things in terms of possibility and necessity. Also explore how there intertwine.
Do not state things in terms of absolute truth, but say how likely it is.
For necessity, talk about how necessary something is. Thus use words like can, may, should, ought, must, have to.
Talking about how true or necessary something is gives you more potential in arguments as you now have an analogue continuity of alternatives, rather than the black-and-white binary decision of simply whether something is true or false, necessary or unnecessary.
Example Say this Not this
The door might be open.
The door is open.
You must do it.
You do it.
They could come here.
They will come here.
Discussion
Traditional logic is based on extension, in that the truth of the logic is found within the supporting statements. Modal logic are based on intention, in that truth is where you find it, and that the reality of many situations is that it is impossible to determine exact truth.
Thus:
 A sentence is possible if it might be true (or might be false).
 A sentence is necessary if it must be true (and cannot possibly be false).
 A sentence is contingent if it not necessarily true. (a contingent truth is true in the given case, but might not have been true).
Necessity and possibility have aspects of a Boolean relationship in that:
It is not necessary that X is true = It is possible that X is not true
It is not possible that X is true = It is necessary that X is not true
The modalities of possibility and necessity are also known as alethic modalities.
Deontic logic is the specific logic about duty, where necessity is has a moral quality to it.
PROS-VS-CONS REASONING
Description
Pros-vs-cons reasoning seeks to weigh up the arguments for a case (pros) against the arguments against the case (cons).
The argument will usually end up with a conclusion of whether the pros or cons are stronger, thus precipitating a 'reasonable' conclusion. Things that will make a 'pro' stronger (and vice versa) include:
 More logical arguments.
 More evidence being displayed (including actions and perceptions of other people).
 Greater emphasis being put on key words.
 More arguments for the case.
Starting with the favored side allows you to fill the other person's mind with the key points, such that the second list becomes less easy to absorb. Starting with the disfavored side allows you to make it sound reasonable, then knock down each of the disfavored arguments with stronger arguments for the contrary case.
You can also choose between giving all of one side and then all of another, or alternating between each side (the latter is good for comparing related for-and-against points).
Example
Say this Not this
It is useful and cheap, but on the other hand it won't last long and will make you look ungenerous.
It won't last long and will make you look ungenerous.
James likes it, Jan likes it, Bill likes it, Fred likes it. Only Sam and Alice don't like it.
Most people like it.
Look at the list of features on this...But when you try it at home, you may find that...
When you try it at home, you may find that...
Discussion
Offering arguments both for and against a case makes the arguer seem even-handed, neutral and hence trustworthy. It also takes the wind out of the sails of a counter-argument if you have already discussed the point.
Quantity and quality are often confused, and more arguments for one side can make it look like that side is the better choice.
RESIDUE REASONING
Description
Prove something by showing that all other possibilities are not possible. This can be done with drama, striking off the alternatives from a figurative list. Then emphasize that the remaining option must be true. In more detail, you can start with the problem, highlighting the issue. Then do analysis that shows the causes of the problem and so lead to options and disproving all except your chosen alternative. A way of doing this is through Pros-vs-Cons Reasoning.
Example
She is not outside. She is not upstairs. She is not on the ground floor either. There can only be one conclusion: There is a cellar in this house and she is there.
Discussion
Sir Arthur Conan-Doyle's famous detective Sherlock Holmes said 'When you have eliminated the impossible, whatever remains, however improbable, must be the truth.' This classically summarizes the principle of residue reasoning.
This approach assumes of course that the speaker's list of options is a complete set of options. If an opponent shows further possibilities, then the argument (and perhaps the arguer) is destroyed.
If residue reasoning does not reach a final conclusion, then at least it may reduce the number of options, such that you can then compare the remaining possibilities using another form or reasoning.
SET-BASED REASONING
Description
Set-based reasoning is founded on Set Theory. Its arguments range around whether things are members of named groups or not, thus 'A dog is an animal but not a vegetable'.
The basic assumption is one of membership, that an item can be categorized into a given group or set. This also assumes that both the item and the set exist in the first place. The following argument then may include consideration of the overlap between sets and the implications of this.
Set reasoning often thus includes statements along the lines of:
 A is a B
 If A is a B then...
 A is not a B, but it is a C
 A is both C and D, therefore...
Example
Say this Not this
He works for Microsoft. Microsoft people are intelligent. Therefore he is intelligent.
He works for Microsoft and is intelligent.
If this is an international standard CD then it will use ISO standard encryption coding.
ISO encryption will be used here.
If he is both Italian and lives in New York, then he is likely to be fond of pizza.
He probably likes pizza.
Discussion
Set theory makes careful distinction about what a thing is and what it is not. It is thus very precise about definitions and puts a lot of focus here. It also is concerned with membership relationships and hierarchies, seeking higher and lower members of an order.
The verb 'to be' is important here. When we say an item 'is' a member of a set, we assume it has allthe attributes of the set. A common error set-based is when we say to a person something like 'you are silly'. The person (or others) may take this description to indicate that they are nothing but silly, having all the attributes of silliness. This can cause significant psychological effects.
SYSTEMIC REASONING
Description
Understand something by considering it as a whole system. Analyze not just the parts but also the relationships between the parts. You can use decompositional reasoning to identify parts, but go beyond this in considering the additional things beyond just the parts.
Example
I argue for a new square in the middle of town by considering the aesthetics of space and the relationships between the empty square and the tall buildings around it. I also consider the dynamics of movement and pauses of people during parts of the day and weekend, including in other squares.
Discussion
A 'system' is a set of connected parts, each of which may be considered as system in its own right. An individual part can have any number of different relationships with any other part of the system. Thus there are relationships between me and the seat I am sitting on based on space, friction, electromagnetism, gravity, and so on. A closed system assumes that there is no external influences. Science likes closed systems as this allows deterministic answers. An open system assumes that everything can be connected to everything else. The ultimate open system is the universe, with any part being able to influence any other part. This is much harder to analyze and understand, but it is also much more real. Systems also may consider whether or not each part of the system has purpose and will. Thus, for example, a company is made up of people, all of whom may have purpose beyond that of the company (and thus making achieving the company's purpose more complex than it might at first seem).
SYLLOGISTIC REASONING
Syllogisms are arguments that take several parts, typically with two statements which are assumed to be true (or premises) that lead to a conclusion. This takes the general form:
Major premise: A general statement. Minor premise: A specific statement. Conclusion: based on the two premises.
Syllogistic reasoning is concerned with using syllogisms to draw conclusions from premises.
Syllogistic traps
We each make many statements in both conversation and writing where we imply logical connections between unrelated points. Sadly, the logic and truth that we assume is not always there.
Consider the following statements and conclusion:
Statement 1: All men are animals
Statement 2: Some animals are aggressive
Conclusion: Some men are aggressive
This seems to be a reasonable conclusion, but then consider the following:
Statement 1: All men are animals
Statement 2: Some animals are female
Conclusion: Some men are female
Now the conclusion appears to be ridiculous and false - yet the reasoning is exactly the same as in the first example. The first example thus has a false conclusion. The animals who are aggressive arenot necessarily men. What is happening here is that we are using what we know to be true as a substitute for the logic of the statement. In less certain situations, we use the same unspoken assumptions and beliefs to less acceptable ends. There are a number of other syllogistic fallacies that can trap the unwary logician.
Using Venn diagrams
Syllogistic reasoning uses rational logic and hence set theory applies and the best way to visualize it is to draw a Venn Diagram. The diagram below is a valid drawing that explains the first two statements in the example.
The conclusion of the example falls into the traps of making the assumption that the 'aggressive animals' and 'men' subsets necessarily overlap, whereas there is no necessity for this in statements one and two. Although the conclusion could be true it does not have to be true.
So what?
Beware of making linked assertions that seem reasonable but in fact are logically incorrect.
You can, of course, make such assertions deliberately, using logic that seems valid to persuade. If you do this, of course, you run the risk of the other person exposing your false logic.
TRADITIONAL LOGIC
Description
Start with premises that are assumed to be true. Then use only logical rationale to derive a conclusion. Be careful that it is applied correctly. Keep emotion well out of it.
Example
Say this Not this
All people have potential. You are a person. You have potential.
Some people have potential. You are a person. You have potential.
Some bananas are yellow. Some bananas are green. I don't know if there are any green and yellow bananas.
Some bananas are yellow. Some bananas are green. Therefore some bananas are green and yellow.
Murder is wrong. Shooting someone dead is murder. Therefore shooting someone dead is wrong.
Shooting someone dead is murder. Murder is wrong. Therefore shooting someone dead is wrong.
Discussion
Traditional logic, as originated by Aristotle, obeys formal rules and is bivalent -- that is, it is about truth and falsehood with nothing in between. A logical flaw or fallacy is one in which the laws of logic are not followed (irrespective of whether there is real truth there or not). This can often be seen through the use of Set Theory. An argument that has a logical flaw in it is invalid. A valid argument that is actually true is alsosound. Logical arguments fall down when the premises are false. It is also possible to get snared in a complex logical argument that seems to follow logical rules, but is in fact a fallacy.