Many articles discuss the process of logical argument in select situations, presenting logic as an “alternative” method of decision making. This article’s premise is that logic can be used in many more contexts, and ultimately is the only valid method of resolving all arguments in real life. Unfortunately, logic is not used in many cases because of time constraints and lack of knowledge about its use.
Common pitfalls in arguing:
You may recall being in situations where an argument escalated to raised voices, insistent repetition, off-topic distraction, emotional blackmail, and similar tactics. Perhaps you’ve attempted those tactics yourself in the past. Now give it some thought: If a statement is made louder, is it any more or less true? What if it is repeated using different words? What if the person says “trust me” before making the statement, or “I’ll bet with you”, or “how could you possibly think otherwise”? If it doesn’t affect the truth of the statement, then why do people so often resort to these tactics?
Consider a person’s emotions regarding an argument. If someone makes a statement that they feel strongly about, does that affect its truth? Does it matter how upset they are? How angry? How much they want to be right? What about the past? Does it make any difference how “right” or “wrong” a person has been previously? How often they’ve argued about the same topic? Does how upset they are about previous arguments, misunderstandings, or other wrong-doings, change the truth of their statements? Why is emotional context so common in arguments if it doesn’t impact the truth in any way?
Perhaps the greatest difficulty in logical arguments is detecting non-relevant factors. Off-topic distractions can be subtle, they can be flustering, they can certainly be frustrating. It may take a significant amount of experience, expertise, confidence, and patience, to remain focused and reach a logical conclusion.
So are you saying that emotion has no place in logical arguments?
No. In fact, many arguments would be pointless were they not to take emotions into account. However, it is important to acknowledge that emotions don’t affect truth. How emotions can and should be integrated into logical arguments so as not to affect the universality of results is discussed further below.
Before arguing logically:
Consider your audience: Logical arguments may not be viable in many cases. For a logical argument to reach a conclusion, the person you are arguing with must:
- Be willing and motivated to argue logically
- Be capable intellectually of logical argument
- Have the time and patience to see the argument through logically
- Be knowledgeable in the process of logical argumentation
So for example, there is not much point in arguing with someone who is too emotional to think straight, has nothing to gain from seeking the truth, or does not have an open mind. By the same token, if you go into any argument for the purpose of “winning” it, then you are going in for the wrong reasons yourself: A logical argument’s purpose is to deduce the truth, whether you like the end result or not.
Intellectual capacity is also an important factor. Rational thinking does require significant wherewithal, focus, and memory. Someone who is too young, or too old and “set in their ways”, may not have the capacity to carry out an argument logically. Note that if memory is the only issue, then a good solution is to carry out the argument in writing.
Logical arguments can take a lot of time, perhaps spanning multiple sessions. Thus logical arguments may not be viable where time is of the essence. But perhaps most importantly, logical arguments require the cooperation of the audience – ie, they must be knowledgeable in the process, and follow it as you do, while being open to correction and guidance. If this is not viable, as with a politician addressing the electorate, a lawyer examining an opposing witness, or a marketing manager delivering a public relations message, then there is little point in proceeding.
If you are having difficulty reaching a consensus with someone – your spouse, a family member, coworker, friend, or other acquaintance – and feel that a logical approach may help, then hand them this guide. If you have been handed this guide by someone else, do not feel insulted. Few people receive training in logical argumentation in their schooling or career. On the contrary, if someone hands you this guide, then they must feel that you have the intellectual capacity to carry out a logical argument – a compliment!
Alright, I’m ready, willing, and able, and my audience is too, let’s get the show on the road!
To make a logical argument in real life, we take the tenants of logical argument from the theoretical worlds of philosophy and math, and apply them to day-to-day situations. A logical argument consists of 4 components:
1. A question / decision to be made
2. A set of facts, also known as “assumptions” (or premises)
3. Application of logical rules to those assumptions – called the “argument”
4. Derivation of the result, which is the logical “conclusion”
Assumptions are basically any statement that (a) is relevant to the argument, and (b) all parties involved agree on. The reason why they are called “assumptions” rather than “facts”, is that it is not – strictly speaking – necessary that they be “true”, but only that we agree that they are “true”.
The process of gathering assumptions in preparation for the argument can be the most difficult part of the process. With practice, it becomes easier to determine in advance what facts are relevant, and which ones aren’t. But the important part is getting agreement.
Where not all parties agree on a particular statement, that statement cannot be used as an assumption. In this situation we do something called “take a step back”:
- If you feel that a statement is necessary for the argument to proceed, but you cannot get agreement up front, then think of it as a separate argument.
- Think about what facts and argument could be used to derive this statement. Explore which of those facts you can get agreement on.
- Keep “stepping back” to more and more basic assumptions until you reach agreement on those statements necessary to derive all of the assumptions that you would like before proceeding.
- Once you have agreement on all the preliminary statements needed to derive the assumptions you want, then go ahead with an argument for each of those, get agreement on the conclusions, and then they can be entered as assumptions in the original argument.
This process has behind it the implied assumption that there is a set of facts that all parties can agree on that is sufficient to derive the logical conclusion. If this is not the case, then the argument cannot proceed. Be patient. Even when agreement seems hopeless, chances are that all parties agree on a lot of statements (think: “the sky is blue”, “1 + 1 = 2″, “the purpose of this argument is to determine the truth”, “the basic tenants of logic are correct”, etc). And don’t forget about the power of empirical knowledge: Not all facts can be derived from previously known facts. Some, arguably most facts, can only be determined empirically, through research and observation. If you can’t get agreement on an assumption deductively, then think about how it can be derived inductively.
The argument is the process by which new statements (additional facts) are derived (deduced) from existing statements. The final new statement derived, is the conclusion.
Some of the simplest rules of logic include:
- New statements, such as the steps of the argument, and the final conclusion, can only be derived from existing statements – starting with the assumptions. The assumptions therefore, must include deductive and/or inductive statements, from which additional statements can be derived.
- If something is true, then its negation cannot also be true. Therefore, if a contradiction is found, then at least one of the assumptions, or perhaps one of the steps of the argument, must be incorrect.
- Deductive reasoning: Say we have the following statements: (1) “All Y is Z” and (2) “X is Y”, then we can derive the new statement: “X is Z”. Example: If all swans are white, and this is a swan, then it must therefore be white.
- Inductive reasoning: Say we have the following statement: “All known Y are Z”, then we may derive the new statement: “perhaps all Y are Z”. Example: If all swans that we’ve ever seen are white, then we hypothesize that all swans are white.
In practice, any previously derived statements or rules, such as the rules of logic, math, or science, may be added as assumptions, and used to derive additional statements during an argument. Then those derived statements can be used to derive yet more statements, and so on. Here is an example:
(1) All chemical mixtures obey the laws of physics
(2) Humans are a chemical mixture
(3) Humans do not obey the laws of physics (they have will power)
- If (1) All chemical mixtures obey the laws of physics, and (2) Humans are a chemical mixture, then (4) Humans obey the laws of physics
- If (4) Humans obey the laws of physics, and (3) Humans do not obey the laws of physics, then (5) we have a contradiction
Deriving a contradiction means that at least one of the assumptions must be incorrect. It doesn’t however, tell us which one. Determining that requires more analysis.
Arguing something in real life means trying to reach a consensus about something – ie, making a decision, answering a question, determining truth. If the statement is phrased as a question – eg, “do humans have will power?”, then the conclusion hopefully answers that question.
In the above example, the conclusion was that one of the assumptions is false. Ideally though, the conclusion would be the answer to the question originally asked. Phrasing the topic of an argument as a question implies an open mind by all parties involved in the argument, and a desire to seek the truth, so this is the recommended approach.
Let’s try the above example again, this time with a more open mind:
Question: Do humans have will power?
(1) All chemical mixtures obey the laws of physics (without exception)
(2) Humans are a chemical mixture (and nothing more)
(3) Will power is the ability to disobey the laws of physics
- If (1) All chemical mixtures obey the laws of physics, and (2) Humans are a chemical mixture, then (4) Humans obey the laws of physics
- If (3) Will power is the ability to disobey the laws of physics, then (5) anything that has will power does not (strictly speaking) obey the laws of physics
- If Humans have will power, and (5) anything that has will power does not obey the laws of physics, then Humans do not obey the laws of physics, a contradiction with (4), therefore:
(6) Humans do not have will power.
Note that without agreement on the assumptions, the argument cannot proceed. Here is another example:
“Abortion is wrong”
(1) Killing living humans is wrong
(2) Killing non living humans is not wrong
(3) A fetus is a living human
- If (1) Killing living humans is wrong, and (3) A fetus is a living human, then:
(4) Killing a fetus is wrong
On the other hand:
“Abortion is not wrong”
(1) Killing living humans is wrong
(2) Killing non living humans is not wrong
(3) A fetus is not a living human
- If (2) Killing non living humans is not wrong, and (3) A fetus is not a living human, then:
(3) Killing a fetus is not wrong
This example demonstrates that if you don’t agree on the assumptions, then a logical argument cannot proceed. In fact, the argument on the morality of abortion cannot be settled until all parties involved agree on all the assumptions. If they cannot agree on assumption (3), then it’s time to “take a step back”, and look for assumptions that everyone is willing to agree on, such as how to define whether or not something is “living”, or perhaps even what circumstances may permit killing living humans after all.
Integrating emotions into logical arguments:
An important feature of a logical argument is its “universality”: Based on the same assumptions, any 2 people, anywhere in the world, and at any time period, will always reach the same conclusion.
As such, keep in mind the following about integrating emotions into logical arguments:
- Emotions may only be included as assumptions, they may not be used to alter the rules of the argument itself.
- Statements about emotion should be “objective”; eg, through quantification, measurement, or “emotional currency”.
- Consider that emotions change over time, while the rules of logic do not. As such, use context-sensitive statements. For example, instead of “I am angry, therefore I don’t want to help you”, use “when I am I angry, I don’t want to help you”.
Here is an example:
Question: Should I throw this computer at the wall?
(1) I am angry right now
(2) This computer is the source of my anger
(3) Throwing this computer at the wall will make me feel better
(4) Anything that will make me feel better is something I should do
If (4) Anything that will make me feel better is something I should do, and (3) Throwing this computer at the wall will make me feel better, then:
(5) I should throw this computer at the wall.
At first blush, there is not much wrong with this argument or its conclusion, even though all of the assumptions incorporate emotion. However, it is worth noting some issues:
- Assumptions (1) and (2) are irrelevant to the argument – neither are used.
- Assumption (3) is not context-sensitive, and may be questionable across time. For example, throwing a computer at a wall may provide short-term gratification, but longer-term, it will cause damage, expense, a mess to clean up, and possible social ramifications (scaring, upsetting, or annoying others). Hence it may not, ultimately, be true.
- The assumptions provided fail to suggest any alternatives. Perhaps changing the question to “what is the best way to reduce my anger?”, and adding other options, such as “wait until I calm down” or “burn off steam by doing some exercise” or “try upgrading the program that isn’t working” would make a difference to the conclusion.
You’re having an argument with your spouse: One of you wants to go out to a nice restaurant, the other wants to stay home. Many statements are thrown around: “It’s cheaper to eat at home”, “We hardly ever go out”, “I’m too tired to go anywhere”, “I’m too tired to cook”, “I want to watch TV”, “I want to have a nice conversation”, etc. These are all valid statements of fact (assumptions), some of which are emotionally based. However, they fail to achieve a satisfactory resolution much of the time. Perhaps in a healthy relationship, a compromise will be reached – both of you cook and have a nice conversation over dinner, or you go to a cheap restaurant that shows a local sports broadcast, or you agree to do one thing today, and the alternative tomorrow. In an unhealthy relationship, maybe the louder voice gets their way. How can this argument be resolved logically?
Part of the problem is that we don’t have agreement on the assumptions needed to proceed. To move forward, we need to “take a step back”, and start with what everyone agrees on. For example: “We want the greatest overall level of happiness between us.” An important technique for reaching agreement on emotional statements is quantifying, or measuring an emotion. An easy way to do this would be to rate emotions on a scale of 1 – 10. However, for an argument to be valid, the scale should be calibrated so that values mean the same thing to both parties involved.
To accomplish this, we use something called “emotional currency”: Each person suggests something that they would be willing to trade to get their way, and something that they would be willing to accept in exchange for capitulating to the other person’s desires. Here it is worked out:
- Person #1: Wants to go out, willing to give a 30-minute back rub to go, or accept a 30-minute foot massage to stay.
- Person #2: Wants to stay home, willing to give a 40-minute foot massage to stay, or accept a 40-minute back rub to go.
In this case, it works out that staying home would be the optimal solution for both parties. Using a currency such as back rub or foot massage time provides a calibrated, quantifiable measure for logical evaluation. Any quantifiable currency can work: Money, time together, time apart, gifts, favours, chores…
There are many reasons not to argue logically:
- It takes too long
- The topic is too complex
- Inability to remove emotion from the argument portion
- Not enough information
The alternative to arguing logically is not to argue logically – or rather, to argue non-logically (irrational argument). But are there any circumstances under which it makes sense to argue non-rationally? Consider the following:
- Irrational arguments have all the same problems as rational ones: They do not resolve complexity, deal with emotion, or fill in missing information any better than rational argument – rather they circumvent these problems, implying that somehow non-rational debate can resolve them.
- Irrational discourse relies on logical “sounding” arguments anyhow: There are statements of fact (often unsubstantiated), a line of (inconsistent) argument, and a conclusion. Any time someone makes logical statements, they are engaging in rational discourse – why not be consistent about it and arrive at correct conclusions?
- Informal weight factors are used in place of formal ones: Instead of quantifying risk, emotion, and unknowns, irrational arguments rely on unrelated factors to sway opinions based on what “sounds” important, rather than what is. This is hardly an improvement.
Note that the question above itself is suspect: “are there any circumstances under which it makes sense to argue non-rationally?” – the term “makes sense” implies “logical”. Rephrasing the question to “is it ever logical not to be logical?” – the answer is clearly no. This is also an example of how logical “sounding” statements can enter into non-logical arguments without being acknowledged.
Now, if non-rational argument results in the same conclusion as logical argument, then there is no issue. But where the results differ, logically they cannot both be correct simultaneously. The risk of arguing non-logically is arriving at an incorrect conclusion.
Consider a simple case as an example – noting that the principles here apply to any decision: Suppose that you are considering whether or not to invest money in a particular project that you think might provide a good return on investment. This decision involves an enormous amount of unknowns and probably emotion as well (eg, “intuition”, “desire”, and “fear”). Yet any financial investor would agree that this is a matter of a purely rational decision: Any venture capitalist, bank, or shareholder making such a decision asks for a business plan, calculation of net present value, risk assessment, and corroborative evidence (eg, market research) – the more information the better. In spite of enormous amounts of unknowns, financial investors do not rely on non-rational decision criteria because doing so adds risk of making bad decisions. Instead, unknowns are incorporated into the decision making process as risk – a quantifiable, measurable factor.
A common example of non-rational argument is a debate. Debates can be formal (eg, political debate), or informal (eg, 2 people yelling at each other). Seemingly debates have the same purpose as rational arguments: To make the best decision / determine the truth. However, in practice debates fail to achieve this, because in fact, the real goal of participants in a debate is to take a side, and “win”. As such, the “winner” of a debate is often unclear, and in cases where the winner is “clear”, it is often because of their delivery rather than the validity / truth of their position.
In contrast, the purpose of arguing logically really is to determine the truth. Participants in a debate enter the contest with an equal opportunity to “win”. In contrast, participants in a logical argument recognize that it is not possible for 2 contradicting positions to both be true simultaneously – ie, only one conclusion can be correct – and the purpose of the logical argument is to determine which it is. As such, participants can work together, rather than against each other, to poke holes, test assumptions, check accuracy, and arrive at a single logical conclusion that is agreed to by all parties as the only logical conclusion possible given an agreed-upon set of assumptions.
Arguing in writing:
In addition to time, many skills are necessary for successfully resolving an argument logically:
- Experience detecting / translating equivalent statements to logical form
- Experience proposing relevant statements and the steps to reach a conclusion
- Knowledge of the field – including empirical data, risk analysis, decision factors, etc
This can be very demanding, even to an expert. A highly recommended approach, whenever practical to do so, is to argue in writing. Arguing in writing helps to remove emotional factors from the process, reduce setbacks from imperfect memory, and provides time for participants to revise their statements, collect needed data, and think thoroughly through their argument. A forum that removes time constraints, permits a collaborative approach (ie, allows participants to edit / improve previous work without conflicting with other participants’ requirements) is ideal. An example of a public (multi-participant) forum that fulfills these criteria is a wiki. However, nearly any method of arguing in writing tends to improve on verbal debates, and would be recommended over typical non-formal methods.
You may have heard in the past something along the lines of: “One thing I like about math is that there is no room for interpretation – there is only one right answer.” Since math, science, and logic are really 3 sides of the same coin, this can be extended to apply to much more than just basic arithmetic. Using logic in day-to-day decision making, it can be extended to essentially any question.
Logic has the property of there being “only 1 right answer”. In logic, it is not possible for 2 contradictory statements to hold true simultaneously, and as with math, truth is universal. So just as the question “how much is 1 + 1″ has only one right answer, and any other answer is wrong, so is the case with any question that might come up in daily decision making, such as “what is the best route to work”, “what is the best place to invest my money”, “which political candidate should I vote for”, and “is there a God”. Granted, in the vast majority of cases, we don’t have sufficient information to be certain of the correct answer, but we can still use logic to do our best with the information available, while accounting for unknowns.
The requirements for successful logical argument as outlined earlier, are extensive, including time, will, and an open mind. For example, court proceedings often rely heavily on logic to deliberate (although consistency is an issue in practice), and they are notoriously lengthy. One good piece of news however, is that with practice, it is possible to become more efficient at it. More importantly, not arguing logically can often take much longer, be much more difficult, and lead to poor results. The practicality of logical argument in real life situations is often underestimated, but ultimately, more often than not, it is actually the most practical approach.