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Essays

Principles of Critical Thinking

© Cary Cook 2018

I copyrighted this not because I want to own or control it,
but because I don't want somebody else to copyright it,
and claim that I got it from him.   Steal all you want.

Part 1:  Language

Intended as oral presentation with PowerPoint visual.
Paragraph breaks indicate next slide.

I've got a lot of material to cover.  And it's the kind of material no one can take much of in one sitting.  So when you get tired of it, we're done.  I can do the rest later for those of you who want to.  I will not make you wait until the end for comments and questions.  There will be intermitent discussion breaks, but they can't be allowed to tangent off subject.  Most of the learning that happens here will happen in the discussions.

The only people I'm talking to are rational truth seekers.  If you're not rational, I can't help you.  If you're not a truth seeker, I don't even want to help you.
By truth, I mean objective truth - the kind of truth that remains true regardless of the presence of any minds to believe it or know it.
If a person says there is no objective truth, there is no point in talking to him about objective truth.  The statement, "there is no objective truth" is an objective statement.  Therefore it can't be true.  It's a self-refuting statement.

If he restates it as a subjective statement, and says, "I think there is no objective truth" it's still an objective statement about what he thinks.  A denier of objective truth denies his own right to make any declarative statement - even a subjective one.  The existence of a subjective opinion is an objective fact.  There are living people, some of whom have PhDs, who talk as though they take themselves seriously, while denying truth of their own statements.  They are sophists, and not worth a truth seeker's time.

By rational, I mean you have and use common sense, and you accept deductive logic as reliable for determining propositional truth.  This is not to say that all logical syllogisms have true conclusions, but that all illogical syllogisms have false conclusions, though those conclusions may be coincidentally true statements.
By rational, I also mean that you not only use logic when it leads to conclusions you like, but you also submit to logic when it leads to conclusions you don't like.  That's when logic conflicts with self interest.  When logic conflicts with common sense, start over;  you've made an error in one or the other - usually a false premise.

By common sense, I mean the kind of probability judgment you use when you use inductive reasoning, rather than when you just want to say something cool.
By deductive logic, I mean that set of statements that is eternally and universally true of the relationships of variables.

Discussion break

I just proposed 4 stipulative definitions:  for truth, rational, common sense, and deductive logic.  A stipulative definition says, "by this term, I mean this concept in the context under discussion".  There are other kinds of definitions.  A dictionary definition tells us how people use terms - in general and in particular contexts.  Dictionaries rarely tell us when a term is used incorrectly.  They don't make that judgment, sometimes to the detriment of a language itself.

You probably know that Webster's Dictionary has recently added a new definition to the term literal.  They say it can now also mean figurative.  Note that they are not prescribing this definition;  they are just reporting on how people use the term.  But people who treat dictionary definitions as authoritative now think it is legitimate to use literal to mean figurative, thereby taking an unambiguous and useful word and making it ambiguous, thereby increasing confusion among all English speakers.  That is the reverse of normal and sensible language evolution.

Authorities (even legitimate authorities) can create bogus concepts in uncritical minds.

A stable epistemic foundation is always built on logic rather than authority.  It is always figured out rather than believed.  Now, am I claiming authority to make that statement?  It would self-refute if I were saying "I know what I'm talking about, therefore believe me".  But I'm not.  I'm saying that none of my statements in this presentation require authority.  I'm not asking you to believe any of them.  I'm not even asking you to figure them out.  I'm saying any truth seeker who remains one will figure them out whether he believes me or not.  He will also figure out the next statements beyond these.  I'm not here to change your path.  I'm here to help you get to where you're already going faster - unless you're already beyond this material, in which case I wish I had talked to you before writing it, and I will use your comments to revise it in my next draft.

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There are things, concepts, and terms, usually in that ontological order.  A thing represented in a mind becomes a concept.  The concept rarely matches the thing perfectly.  David Hume proved that the concept can't be shown to match the thing at all.  But even Hume didn't care, because he kept on talking and acting like it did; and so do we.  Assumed correspondence between thing and concept is necessary for any animal to seek food and avoid becoming food, much less talk about stuff.  In order to keep concepts in order, and communicate them, we label them with terms.

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If a singular thing has a unique term, then the term labels the thing regardless of the concept.

The first time a mind figured out that some things have similarities that make them different from other things, he invented a category, which is a container to put concepts in.  Eventually he figured out terms with which to label his concepts and categories.

If a thing is an abstraction, then the thing exists in minds as well as external reality.  Logic for example:  It exists as verbally expressed laws in minds.  But if logic didn't also exist in ontological reality, the laws would not correspond to anything.  If A = A didn't exist in ontological reality, a cat would not necessarily be a cat.

I prefer not to define abstraction, because we usually understand it intuitively better than we understand it logically.  But if you require a definition, then an abstraction is an unchanging property of nature existing in various and changing instantiations of it, which are concrete by contrast.

When a physical thing exists in spacetime, it exists in a specific locality for a specific time period.  When an abstract exists in spacetime, it exist in multiple physical things in multiple places at the same time, and at different times.

Some abstractions exist only in minds, but that doesn't mean thing and concept are necessarily identical.  Beauty exists only in minds.  Beauty as a thing and a concept are identical in any particular mind.  Is beauty in one mind identical to beauty in another mind?  Things in the category of beauty certainly differ from mind to mind, but is beauty itself different?  I see no way to know.  Morality on the other hand differs from mind to mind, not only in its particulars, but in the concept itself.

Some say morality is whatever maximizes human well-being.
Some say it's whatever the Supreme Being likes
I say it's whatever maximizes the ratio of happiness over unhappiness in the universe.
But values are for a later presentation.

And mind is a dimension in itself, with at least 3 levels to keep straight.
You have a thought.
You have another thought about the thought.
You realize that this could go on indefinitely, unless there is such a thing as all thoughts, at which point it must stop.

When you think of a concept, and then the concept of concepts, you've jumped a level.  Concept of all concepts - you've done it again.  Not everything that is true of concepts is true of the concept of all concepts.

When you get to sets, you then jump to the set of all sets.  And that results in paradoxes if you don't keep these levels straight.  But that's for a later presentation.

An objectively existing abstraction may be a subjective concept concept – but no subjective concept can be shown to exist objectively.
Everything that exists exists objectively, including subjective concepts.
Everything that exists subjectively exists only in minds.
There is no subjective math and logic.  Beauty cannot be shown to exist objectively.  If it does exist objectively, nothing in the category is necessarily in it.  Even if there is a Supreme Being who is so anthropomorphic as to think some particular thing is beautiful, some creatures may disagree with him on it.  That doesn't mean they're objectively wrong.

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If a lot of people acknowledge the same abstraction, then it probably exists objectively.  The first few pages of a dictionary show many examples:  But the popularity of a term or concept doesn't guarantee that it is legitimate in the sense of existing objectively.  We have terms for abstractions that don't even exist.  More on that later.

A subjective interpretation of an abstraction may be different from the objectively existing abstraction.  e.g.  A person may not know that there is a difference between logic and common sense.  He might think they're both correct thinking, and conflate them in his mind.  But they remain distinct objective concepts - not in his mind, but in objective reality.  Justice and morality:  different concepts.  Moral right and legal right: different concepts.  They're all over the place.  It would be a tangent to address them now, but I hope to get to them in future presentations.

If a thing is not abstract, what is it?  The term generally used is concrete rather than physical.  So time and space, and everything dependent on time and space are concrete.  But some abstract concepts can also be taken in a concrete sense.  Consider the concept "tomorrow".  Not the term;  the concept.  Is it abstract or concrete?  Well, you can mean it either way.

As an abstract, tomorrow is always a day away.
As a concrete, tomorrow is only a day away.
So now maybe we can get that song straight.

We could say that a thing may be concrete or abstract.

Or we could say that only concrete things can be things, and abstracts must be concepts.  Both paradigms have problems, which you will discover if you try to make a consistent paradigm.

We could say that abstracts may be real or imaginary.
But trying to draw a line between real and imaginary, even a stipulative line, reveals a paradigm problem.  At least it's beyond my ability.
Are future events real or imaginary?
There are no rules on what we could say.

When you hit an epistemic dead end, you don't keep banging your head on it.  You go and seek truth elsewhere - unless you're a quantum physicist.

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Back to things:
All concepts are things.  All things in minds are concepts.
A thing is not what it causes, or what causes it.
A thing is not what it's part of, or what's part of it.
Some things are; and some things aren't:
what they appear to be,
what they were, or what they will be.
The only things that are identical to what they were and will be are eternal things.

What is true of all things in general is also true of all concepts in general.  But what is true of all particular things may not necessarily be true of their respective concepts.

e.g.  Which came first; the thing or the concept?  If the thing is not produced by a mind, then the thing came first.  e.g.  There were molecules before there was ever a mind to have the consept of a molecule in it.
If the thing is produced by a mind, then the concept came first.  There was the concept of a car before there was ever a car.

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A concept is a single unit of thought.  It may be composed of parts, but no part equals the concept.  It may have subsets, but no subset equals the concept.

Tree is a thing and a concept.  Trunk, branches, and leaves are parts of it.  Each part is a thing and a concept, containing other parts and concepts down to quantum level and maybe beyond.

A concept may contain subconcepts, but no subconcept is the same as the original concept.  Since it's a category now, we'll call them subsets.  A concept may be divided into pieces or fractions, but none of that diminishes the fact that it is a single unit of thought.

If it's more than one unit of thought, it's more than one concept.  Otherwise no physical thing can be conceptualized, except possibly a quantum, because all physical things are composed of other physical things.

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This one is to remember.
Conflating concepts continually causes confusion.
Note that I didn't say conflating concepts constantly causes confusion.
Constantly and continually are different concepts.

A constant event is one that never stops as long as it remains constant.
A continual event is one that happens repeatedly as long as it remains continual.
If you conflate constantly and continually, you may cause confusion - or not depending on context, and mutual common sense with whomever you're talking to.

No concept is a member of 2 mutually exclusive categories simultaneously.  Example:
Voluntary acts and involuntary acts are mutually exclusive categories.

No act is a member of both of them simultaneously.  What about blinking and breathing?  Well, sometimes they're voluntary;  sometimes they're involuntary, but never both at the same time.

Calling an act semi-voluntary does not create a category between voluntary and involuntary acts.

It just creates a category that's sometimes one, and sometimes the other.  Many of the terms we use conflate mutually exclusive categories, thus creating bogus concepts in our minds.

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There are bogus terms and bogus concepts.  And sometimes you can't even tell which is which.  A bogus term is one that can't be conceptualized.  e.g.  square circle.
A bogus concept is one that takes 2 or more legitimate concepts, and mushes them together.  e.g.  belief

Belief is a term that has come to denote 2 different concepts – at least 2. That means it's an ambiguous term.  Because the term is ambiguous, a bogus concept is often generated.  This term should not be ambiguous, but it has been made so by the New Testament.  Belief should simply mean probability judgment.  If you believe X is true, then you think X is probably true.  Probability judgment is an involuntary act.  It happens in the mind without any conscious decision.  But that definition doesn't work in some parts of the NT.  The Greek word translated belief is also translated faith, and it usually indicates a voluntary act - a decision to trust or not trust that something is true.  Hence belief has become an ambiguous term, and must be disambiguated in order to speak about it sensibly.  But when belief is supposed to be voluntary and involuntary at the same time, it's a bogus concept.

God is an ambiguous term.  You already know it means 2 different things depending on whether the G is capitalized.  Lower case g denotes a created being inside this universe.  Obnoxious atheists deliberately ignore this distinction. Even with the capital G, God is still ambiguous. It can mean, among other things:

  1. Supreme Being: that which created the first created thing
    who may or may not be the same as
  2. Creator of this universe
    who may or may not be the same as
  3. Creator of mankind
    who may or may not be the same as
  4. Judge of mankind
    who may or may not be the same as the God of some set of scriptures
Obnoxious Christian apologists deliberately ignore this distinction.

Discussion break

What is an attitude?  French word...  originally meant the angle of something relative to the ground - or at least relative to something more stable than itself.

Aristocrats no doubt liked this word because it let them criticise subordinates without a specific accusation.  Like "I'm the stable mountain of importance, and he's trivial.  His angle relative to me is what matters."
And by angle he meant an expression on a scale between worship and defiance of an emotion on a scale between adoration and hatred.  Which mattered - the emotion or the expression?  Not clear.

After a while, the expression became conflated with the emotion behind it.  But the expression is voluntary, and the emotion is involuntary.

So what does that produce?  Is faking humility a good attitude?  Is faking grattitude a good attitude?  If a token is all that’s required – sure.  But usually a good attitude is seen as sincere and voluntary at the same time; and that rarely happens.  Either you express a faked emotion, or you simply have an emotion, and don't try to hide it.

Popular usage of terms creates bogus concepts in uncritical minds.

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Popular usage of terms creates bogus concepts in uncritical minds.

Some parents do it deliberately to their kids.  Like when they tell them to say they're sorry whether they are or not.  If the kid is not sorry, you're ordering a lie - possibly punishing for not lying.  And though you are preparing your kid for life in a corrupt world, you're also perpetuating the corruption.

Some parents have figured that out.  So they say,  "Ok, you don't have to say you're sorry, if you're not.  But you still have to apologize."  That works, as long as the kid doesn't ask, "What do you mean by apologize?"

Do you mean: No matter how you define apology, you may be telling your kid to think or feel something he doesn't.  And you may be doing the same thing yourself, and choosing to ignore it.

Now maybe social harmony is more important than speaking the truth, or sometimes more important.  I'm not addressing which is more important.  I'm addressing what the term means.  Apology has evolved by popular usage specifically to confuse an honest expression with a socially sanctioned lie.

Evolved from what? Apology in Greek literally means "from word", or from any of the other things logos can mean.  It denoted a verbal defense.  It had nothing to do with being sorry, or regret for having done something regretable.  All of that evolved later.

Discussion break

A definition is a description that isolates a term or concept.  Now technically, definitions apply only to terms.  Concepts aren't defined; they're clarified.  Definition is to terms as clarification is to concepts.  However, if I use the correct term every time I switch between thing and concept in this presentation, it would get unnecessarily tedious and convoluted.  So I'm going to say that things and concepts are both defined.

Too much precision can be detrimental to communication.  More precisely, there exists a degree of precision, which if exceeded, can add irrelevant detail to a point, or cause an interlocutor to lose track of the logic of a statement or set of statements, or simply cease to care what is being said.

That's not a critical thinking principle; it's a pragmatic principle, known in the military as KISS, "keep it simple stupid".

So, a term definition disambiguates that term so you know what concept it refers to.
A concept definition clarifies the boundaries of that concept enough to have it make sense in the context in which it occurs.  But it doesn't necessarily describe the inner workings of the concept, or its relationship to other concepts.

If a definition isolates a concept from all other concepts, it is an exhaustive definition.  If it isolates a concept just enough to identify it in the context under discussion, it is a sufficient definition.  If it doesn't even do that, it is an insufficient definition.

Sufficiency of a concept definition is determined by the context in which its term occurs, and mutual understanding between dialogers.  There are no rules for determining such sufficiency.  We have only common sense.  There is no authoritative referee for term definitions in English;  it's a wild west shootout.  People make stuff up, dictionaries record it, and the people think the dictionary definitions are official.  There is no English Academy like the French Academy to standardize our language.  So English keeps evolving.  But a concept never evolves, unless the thing it denotes evolves.  An abstract concept doesn't evolve at all.  Though our understanding of it may evolve, and the term we use to label it may evolve.

Apology was an example of that.  First it meant verbal defense.  Then gradually it included expression of regret for having done the act being defended.  Now it just means expression of regret, with or without a verbal defense.

One thing we truth seekers can do is clarify concepts if we are so motivated.  I've begun such a clarifier on my website.  It's a work in progress, and not ready for publication.  But it would be of great benefit to the world if it were worked out by a team of linguistic philosophers and published.

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What if a term is vague?  Well, technically terms aren't vague,

but the concepts they denote may be vague.

Our understanding of a term may be vague.  In fact, our understanding of most terms is vague.  But that's because understanding is a vague concept.  It has a sliding scale of degrees.

Gray is not a vague term;  it denotes a vague concept.  But we might as well call it a vague term, because we're living in a world that's accustomed to calling things what they're not.  It's good to know what's correct, but saying everything correctly often hinders communication.  We"re back to 'keep it simple stupid".

So if a term is too vague to be understood in context, a stipulative definition may be required, to draw an arbitrary boundary around the concept denoted, or at least between 2 concepts, so you don't conflate them.  Easy in pictures, but often difficult in words,  and often impossible if your target audience is not in sync with your common sense.  In arguments, when your target audience is hostile, a vague term can cause an end of discussion - or worse yet, a protracted discussion that tangents off into whateverland, or goes around in worthless circles.

"Truth seeker" is a vague term.  Defined broadly, everything with a mind seeks some truth - at least enough to be sufficiently comfortable with the amount it knows.  Defined narrowly, a philosopher might exclude all non-philosophers.  An environmentalist might exclude all non-environmentalists.  Etc.

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Can truth be vague?
Note that I'm not asking this question because anyone cares about the answer;  I'm asking it just to show you where critical thinking can take you if you follow it.  Ideologues and faith seekers may use critical thinking to get to where they want to go.  Truth seekers follow critical thinking to see where it goes.
So can truth be vague?  Our understanding of it usually is, but what about truth itself?  Too difficult.  What about some particular kind of truth?  Can a thing be vague?  Or is it only our mind's concept of it that's vague?  We could say vagueness applies only to concepts - and then only some of them.  But If we want to reserve the term "vague" for concepts alone, then we still can ask.  "can a thing have indistinct boundaries?  Or does it just look blurred because of our defective vision?"

How about a cloud?  Does a cloud have indistinct boundaries?  Well, some edges look blurred and some look hard.  But that's just appearance.  What about the cloud itself?

A cloud is an object made of atoms and molecules, mostly air, but what distinguishes it from the air around it is mostly water molecules.

Whether or not a particular water molecule is in it or out of it depends on the stipulated boundary of that particular cloud.

No matter where the boundary line is drawn, there may be water molecules straddling it -

unless the boundary line is drawn ad hoc, specifically to avoid molecules.  So technically, unless you draw a boundary specifically around all the borderline cases, some objects can be blurred.  To a quantum physicist, maybe they're all blurred.  Probability cloud, whatever the hell that means.

Is the general concept of a cloud vague?  Weird question.  How do you draw a line around a general concept?  Once you draw a line, it's no longer general.

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But remember, truth is an abstract, so the thing and the concept may be the same... thing.  Can an abstract be vague or blurred?  Again, poor understanding can make any abstract look vague, but can an actually existing abstract be vague or blurred?  I can't think of any definite examples.

And what if our concept of an abstract is defective?
That can happen - remember?  That means a legitimate abstract, and our concept of it can be different.  So even if our concept of an abstract is vague, the abstract itself may not be.

Let's put the question, "Can an abstract be vague?" in the Who cares? file, and go do something else.  Not the trash can, because we might want it later.  Critical thinking has a lot of compartments, and we have to examine them in the right order.  Some may not be worth exploring at all.  That's not a principle of critical thinking, but it's an important pragmatic principle that critical thinking reveals.

So can truth be vague?  Probably goes in the same file, but let's try another approach.

Truth is a property of a statement that corresponds to reality, or to some particular part or subset of reality.

But now I've introduced a new term:  property.  So now we have to detour into that.
Disambiguation first:
Here's a Google definition of property.  I'm talking only about the second.  So feathers are not properties of birds; having feathers is a property of birds.

There are substances and properties of those substances.  The Google definition of substance doesn't even address concepts or abstracts.  Neither does Wikipedia.
Though there are references to abstract substances, I'm not aware of any references to abstract substances having properties.  Some abstracts obviously have properties.  Ambiguity is a property of some terms.  Vagueness is a property of some concepts.

So, if properties are things had by substances, and statements are abstractions, then either some substances are abstractions...
Or... abstracts can have properties, and we don't even need to address substances.
Critical thinking does transcend dictionaries and Wikipedia.

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Can a property be vague?  Yes.  Gray is the standard example for a vague concept; and gray is a property.

So can truth be vague?

If truth is a property, and some properties are vague, is truth vague?
Not necessarily.

And that's not even what we're asking.  We're asking if some truth can be vague.  But it doesn't work this way either.
The only way to know is to find an example of a vague truth, that doesn't just look vague because we don't see it clearly enough.

So until then, file it.  We discovered that we can't answer the question by critical thinking - at least I can't at my present level.  But even if we fail to answer the question we asked, we may find good stuff along the way.  Look at the principles we've accidentally stumbled on.

Even if all known members of a particular category have a particular property, it is not proven that all members of that category have that property.

The only known way to prove that something has a particular property is to show an example of that property in that thing. You can't know if all members of a category have a particular property unless you can examine all of its members.

If all known members of a particular category have a particular property, does something shown to be in that category probably have that property?  This is a question we will have to address when we get to inductive reasoning.

Understanding of critical thinking is cumulative.  The more you figure out, the more you can figure out.  But you also discover that some things you thought you had figured out were just accepted on faith.

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Definitions can be categorized according to content:

After defining something genetically, you may have to further define it compositionally or attributively in order to distinguish it from other things in the same genetic category.

For any of these 3 categories, a list of examples does not define a concept, unless that concept is a category containing nothing but those examples.

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Definitions can be categorized according to usage:

Definitions can be categorized according to precision:
They can range from broad to narrow.  There may be no distinct categories here, but just a sliding scale, arbitrarily assigned and intuitively understood.

e.g.  What is a beard?  Does it have to be on a chin?  How many hairs does it take to make one?  How long does each hair have to be?  Where does a moustache hair become a beard hair?  Totally arbitrary.

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Here's a stipulative definition of critical thinking:  Systematic identification of objective truth, and the knowledge of how to apply it.  I wish I could call that an official definition, but I don't have that right.  I can't even call my definition of definition authoritative.  I don't know of a single philosophical term that has an official definition.  Definitions arbitrarily agreed on by whomever is dialoging are all we've got.  I'm totally convinced that my definitions should be considered official, but people who disagree with me think the same of their own definitions.  Science has official definitions accepted by the general public:  Salt is sodium chloride.  But philosophy has few if any outside of math and logic.

I defined deductive logic as that set of statements that is eternally and universally true of the relationships of variables.  Many people object to that.  They prefer to think logic is a human construct - a tool to use when desired, and ignore when not desired.  And they may back up their objection by refering to dictionaries.

If you are such a person, what do you call that set of statements that is eternally and universally true of the relationships of variables?  If you want to call it something other than logic, that's fine.  Just substitute that term whenever I say logic, and we'll communicate.  But if you assert that there is no set of statements that is eternally and universally true of the relationships of variables, I can prove you wrong simply by listing a few.  e.g.  If all A = B, and all B = C, then all A = C.  That would be objectively true if there were no minds to know it or believe it.

Principle:  If people won't accept your definition of a term, tell them the concept you're talking about, and let them assign a term to it.

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Ignoring the term/concept distinction can cause problems.  e.g.  "What is X?" is an ambiguous question.  Are you asking what the term means or what the concept is?  i.e.  Are you asking:  Of all the concepts conventionally labeled X, which one do you mean?   or   What are the boundaries of concept X?  The first is an effort to disambiguate. The second is an effort to minimize vagueness.

Ignoring term/concept distinction can also cause problems when asking questions of the form "Is A in category B?"  e.g.
Is America a Christian nation?  You can quote founding fathers all day, and never arrive at an unchallengeable conclusion.  Assuming you agree on what America is, and what a nation is, the question is still unanswerable until Christian is defined.  And even after Christian and nation are sufficiently defined, "Christian nation" may be ambiguous enough to require further definition.  Define all these things sufficiently, and the question is answered.  Getting your opponent to agree on a definition is the hard part.

Is atheism a religion?  Which atheism?  Classical atheism or the new agnostic atheism?  The latter isn't even a philosophical position.  It's just a statement of one of many things a person doesn't do.  Classical atheism may say gods don't exist, or God (capital G) does not exist.  Is classical atheism a religion?  Now you have to define religion.  You can define it broadly or narrowly or in between.

Here are 3 Google definitions of religion.  I won't bother reading them all.  The first definition is narrowest;  the 3rd is broadest, though religion can be defined more narrowly and more broadly.  By the 3rd definition, even agnostic atheism is a religion to some people.  Even your career or political position could be a religion by the 3rd definition.  Any pursuit or interest could be a religion, if religion is defined broadly enough.

A term (or concept) must be defined broadly enough to include everything you're talking about, and narrowly enough to exclude everything you're not talking about.

You can't know if a particular thing is in a particular category until both are sufficiently defined.

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A category is a set of concepts identified and labeled by something they have in common.  A category may be labeled by several terms.  The set of all left handed people in the room may be the same as the set of all blonds in the room.  If so, they are the same category called by different names.  A category is the sum of its members regadless of how it is named.

Further ambiguity:
When asking, "Is A in category B?", if A is a single and recognized thing, it's already sufficiently defined.  Is Fred a man?  Assuming you agree on the definition of man, and you know what Fred you're talking about, then you can answer the question easily.  But if A is a vague concept, or B is a vague category, then you have to define both enough to answer the question.

That may imply assigning arbitrary boundaries.
After that, you may have to clarify "is".  Do you mean always is, generally is, or sometimes is?
If A is a category, then do you mean all A, most A, or some A?

This produces 9 possibilities.
And there are more, but we don't need to list all of them:  "Is A now in category B?"  "Ever in category B?"  "Potentially," etc.

When talking about non-controversial things, context and common sense are usually sufficient to communicate.  But with controversial discussions, your opponent may pretend not to know what you're talking about even if it's obvious.  If you and your opponent can't agree on definitions, the truth seeking is over.  Discussion beyond that point is game playing.

Principles:  Every ambiguity or vagueness of every term is an obstacle between you and knowledge of truth.  It's also an obstacle between you and communication.
You can't think or communicate propositionally any more precisely than your language allows.

Discussion break

Do all terms have to be sufficiently defined?  Let's see.  What does "is" mean?  We just listed some adverbs to modify it, but what does the word itself mean?  We can't define the term or the concept without assuming we already know what it means.  But we can identify 4 different subsets of it.

There are 4 kinds of is:
  1. is identical to (ontological)
  2. is a property of (ontological)
  3. is in the category of (epistemological)
  4. is equivalent to (axiological)

Equivalence is usually axiological, but not necessarily.  2 nickels are equivalent to a dime only in the sense that they have equal value.  They are not equivalent in any ontological or epistemic sense.  But 2 statements are epistemically equivalent if they have the same meaning.  Two statements can't be ontologically equivalent because equivalence is not an ontological concept.  But 2 things or concepts can be ontologically equivalent.  e.g. Any given amount of mass is ontologically equivalent to a certain amount of energy.

But the intended meaning "is" is almost always obvious by context.  When it is obvious, there is no point in talking to a person who demands a definition of "is" before answering a question in which the term "is" occurs.  Just as there is no point in discussing objective truth with a person who refuses to recognize its existence.

We must accept the fact that some terms are indefinable, because they cannot be defined without using terms which are themselves defined by the term in question.  I don't know if there is a term for these terms, so I'm choosing to call them epistemically basic terms, and they denote epistemically basic concepts.

Here's a list of some:

Sometimes there are mutually defining terms which together denote an epistemically basic concept.  And sometimes they're not even synonyms.  When you define each in terms of the other, you have the illusion of having made a sensible statement, without having isolated the concept.

Most synonyms do not denote an epistemically basic concept, but still denote the same concept.  And some of them don't appear to be synonyms, because they have different connotations.
Normal and ordinary - same concept - part of the majority.  Yet nearly everybody wants to be normal, but hardly anybody wants to be ordinary.
Justification and warrant - same concept.  Each term is used to define and legitimize the other.  But neither term says any more than the other already said.
Ethics and morality - same concept - the set of values pertaining to conduct.  But like the previous examples, they have different connotations, so people like to say they mean different things.  Like one means community imposed, and the other means individually imposed.  But they disagree on which is which, so they're all tap dancing.  It's an effort to sell their own preferred distinction as an official distinction.

It might be nice to have an official language, so we would all know what is being said.  It would make question dodging more difficult.  But who's going to be the referee?  Some government bureau?  That may be acceptable to people accustomed to authoritarian rule.  But most Americans are too American to stand for it.

Principles:
Every term that is defined is defined in terms that ultimately rest on epistemically basic concepts.  Their existence must be accepted in order to make sense of propositions.

Otherwise ultimate justification for epistemology is impossible, because the effort to tie up the loose ends just creates more loose ends.
That last one is not really a principle.  It's more of a pragmatic boundary beyond which critical thinking stops providing useful information.

Discussion break

Some terms appear to denote different concepts, but when examined critically, prove to denote the same concept.

Wisdom and sanity are denotatively the same concept.  But you'd never know it by looking them up in dictionaries.  Here are the Google definitions of wisdom and sanity.  They do not clarify the concepts.  They only tell us how people use the terms.  If we were trying to clarify the concepts they denote, we could easily pick these definitions apart.  But I'm not going to bother with it now.

Here's what these 2 concepts actually mean.
Wisdom and sanity both mean knowing how to get what you want without doing things that will get you more of what you don't want later.
Wisdom is the high end of sanity.
Sanity is the low end of wisdom.
The wiser you are, the saner you are.
I'm not going to defend this definition.  I'm just going to leave it in the air, for the benefit of truth seekers, so that when you're ready for it, maybe you'll figure it out sooner.

Sometimes a term denotes a concept that means only the absence or opposite of another concept, which is the absence or opposite of it.
Sometimes with a neutral midpoint
Some concepts can be defined only in terms of what they are not.  If something is defined in terms of what it is not, the definition is sufficient if the audience has the same intuitive understanding.  It's exhaustive only if there is nothing else that is not those same things.  If you say A is not B, that's not a sufficient definition - unless the audience understands what you mean in context.  If you say A is the only thing that's not B, that's an exhaustive definition.

What does "perfect" mean?  Having no defects.  What is a defect?  An imperfection.  What makes something a defect?  Some mind judging it to be so - possibly not even a human mind.  Some animals kill offsring which they judge to be defective.  What if perfect is defined as being complete?  What does complete mean?  Is a 3 legged dog incomplete?  Only if dogs are defined compositionally or attributively, and the definition includes having 4 legs - in which case no 3 legged animal is a dog, regardless of its parents.

In order for perfect to be a meaningful term, it must be defined as conformity to a given standard.  That standard will necessarily be arbitrary.  Is God perfect?  Well... to what standard does he conform?  No, you can't say that!  God is the standard of perfection.  Fine, then all you've said is that God is what he is.  Everything is what it is.  Saying God is perfect says nothing.

Sometimes a concept is understandable only in contrast to supposed antonyms. What does "actual" mean?

1.  existing as opposed to apparent
2.  existing as opposed to imaginary
      A.  existing as opposed to fictitious
            i.  existing as opposed to hypothetical
3.  existing as opposed to possible
4.  existing as opposed to potential

Discussion break

Another principle:  Epistemically basic concepts are to concepts as axioms are to propositions.
Epistemically basic concepts can't be defined.  Axioms can't be proven.
Understanding of epistemically basic concepts must be assumed in order to think and communicate anything that is based on them.
Axioms must be accepted as true in order to think and communicate anything that is based on them.

Why are geometric axioms not called geometric laws?  Because they cannot be proven.  Does that mean laws can be proven?  What about laws of physics?  If we call them laws, surely they must be provable.  Does our inability to find an exception to a law prove it to be a law?  If so, why does our inability to find exceptions to geometric axioms not make them laws?

Here's what's going on.  The people who decided on what to call things didn't think it out.  We critical thinkers owe them nothing.  Though we are stuck with their rules and terminology when talking to strangers, we have the right to make improvements with which to think, and communicate among ourselves.  But this does not justify using PhD jargon when talking to people who don't know what it means.  People who do that are not trying to communicate, but to impress.

Here's another example:  What about the laws of thought?
We can't prove any of them.  We just accept them as laws because we can't think of exceptions.  Can any law be shown to exist?  Or are all assumed laws only axioms?  Of course there are judicial laws, but that's a different concept called by the same term.  Other than that, I can't think of a single assumed law which does not prove to be anything more than an axiom upon examination.  But if I now assert that all assumed laws are only axioms, I fall into the same error that I have just exposed.

The next part of this series will be on epistemology.

Final discussion