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This is a question that my friends asked me a few times. I am confused, because I have been trying to answer this question myself, but I can't seem to come up with any valid answer. For example, what I used to believe is, nothing in life is certain except death. How can I be certain of what I believe? I hope someone would help me answer this question in a straightforward and understandable manner.

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We cannot be certain of anything. Entertain the following scenarios:

  1. The universe was created 5 minutes ago. When your brain was constructed, neurons were arranged in such a way that you have many memories about the past. You could not tell the difference between living since birth, and false memories.
  2. Information from the outside world reaches your brain through your senses (seeing, feeling, hearing, tasting, smelling). How would we know our eyes are real, and not hooked up to a small computer that just simulates a world? Of course we can feel our eyes are real. But what if our arms, legs, other senses were also controlled and fed directly into the brain? Again we could not tell the difference.
  3. You think you know what's in your fridge right now, but what if someone took something out just now while you weren't looking. Your brain contains an approximation of the fridge the last time you looked inside. It's close, but not the truth. It's like how Google maps can differ from the actual world, because a new street was created a minute ago.
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If you have a belief about the matter (elementary particles) that is outside the domain of their existence you can be certain (or uncertain, what you wish) about your belief. If it involves statements about this matter itself (like how elementary particles behave or how many of them are in a certain region of spacetime), then your beliefs can be proven right or wrong.
It's getting a bit more difficult if your belief concerns the nature of the elementary particles themselves. If they contain more than just dead stuff, if they can form (non-causal) aggregates that are more than the sum. Or even if they can be influenced by a non-physical cause.
This belief can be proven or not. If it can't be proven, then your belief is again certain (or uncertain, again, what you wish). If it can be proven (like the non-causal connectedness of particles in an aggregate) then yo can be certain or not.

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Many teenagers in a high school math class will study a model of a baseball being thrown into the air, and then falling.

A lot of these mathematical models of baseballs are different from reality.

When creating a mathematical model, a baseball might be a perfect sphere.

Real baseballs are not perfectly spherical, there are ridges and dents.

Some mathematical models also do not account for air-friction.

The mathematical model of baseballs being thrown, or falling, is an overly simplified view of reality.


Well, people have other models as well.

One model is the view that statements are either true or false.

Consider the statement,

Bob went to bed at 10:00PM (STATEMENT A)

Well, what if Bob actually went to bed at 9:58PM?

Is the statement about Bob's bedtime true or false?

Sarah ate nothing today. (EXAMPLE B)

Well, what if Sarah ate nothing today, except for a breath mint while waiting for an appointment at in a doctor's office?

You asked, when can we have certainty in what we claim to know?

The view of world where we know somethings and not know others, is a very black-and-white view of the world.

The black-and-white view of the world is a tool.

Wood carpenters have many tools:

  • Flat-bladed screw-drivers
  • Phillips head screw-drivers.
  • coping saws
  • squares
  • chisels
  • micro-planers
  • sanding blocks
  • etc...

Different tools are good for different things.

A lot of people do not understand that the mental tools they use the most often are not the only mental tools available.

If you always view stuff as:

  • knowable or unknowable
  • correct or incorrect
  • true or false

... then you are like a carpenter who uses a Phillips-head screw driver for all screws. Even when the screw is supposed to use something called a "torque bit" or maybe a square-headed tipped driver, you continue trying to use a Phillips-head screw driver.

There is an issue with questions like:

  • Is it possible to truly know anything with absolute certainty?

Is "heck" a swear word or not a swear word?


Are doughnuts a type of bread?


Is this plate clean?

Questions like that are a bit like asking at what time $t$ a baseball will hit the ground when you forgot to account for air-friction.

All of the quesitons are examples of loaded questions.
The questions presume that a black-and-white view of the world is the only view of the world.

"Mysophobia" is a word used to describe people afraid of germs. If you had a dinner plate cleaned by a Mysophobic person, in most cases, a scientific laboratory could use an electron microscope to locate, and take a photo of at least one bacterium or mold spore on the plate.

That is, even very clean plates are not 100% clean.

The following two questions are problematic for the same reasons:

  • Is a clean plate really clean?
  • Can we know anything with absolute certainty?

The questions assume that:

  • things are either knowable or unknowable
  • statements are either true or false
  • Something is either bread, or not bread.

Suppose you had a percentage somewhere between 0% and 100%

There exists a way of rounding percentages where anything less than 100% becomes 0%.

For example 47.3% is rounded down to 0%.

99% is rounded down to 0%.

No matter how close a percentage is to 100%, even 99.999998%, is rounded down to 0%.

Inputs are any percentage, such as 68%, and outputs are always either 0% or 100%.

You have encountered the percentage rounding machine if you:

  • went to school
  • took a multiple choice test
  • the multiple choice test asked a true or false question.

If a statement is 99% true, did you mark it true or false on an exam?

Phillips-head screw drivers are useful for somethings, but not useful for others. It is time for you to learn how to use some of the other tools in the tool-shed.

One tool that is nice to use, are relativistic comparisons.

Is a cartoon dog a dog? There is something wrong with the question.

A cartoon dog is more like a dog, than a cartoon cow, relatively speaking.

Jack says that he is wearing a new pair of shoes. However, the shoes were bought three days ago, and he wore the shoes yesterday. Are Jack's shoes truly new?

Well, the shoes Jack is wearing today are newer than any of the other shoes which Jack owns, relatively speaking.

Ethan's grandfather is 72 years old. Is Ethan's grandfather old?

Well, Ethan's grandfather is older than me (relatively speaking)

Can we know anything with absolute certainty?

Relativistic comparisons can be made mathematically tractable. Using relativistic comparison will not force you to sound like a hippie who is tripping and walking through the clouds.

Relativistic comparisons are usually transitive

That is, if a is related to b, and b is related to c, then a is related to c.

For example, if Bob is older than Sarah, and Sarah is older than me, then Bob is older than me.

School teachers could write the following disclaimer at the top and bottom of every page of an exam:

IMPORTANT INSTRUCTION for true/false questions: if a statement is more than 90% true, then mark it as true. Do not worry about teeny, tiny exceptions. Only mark the statement as false if the statement is often not true.

Many many school teachers spot the exception to the rule half of the time, but not the other half.

If a student can see all of the exceptions to the rule ("but what about when...?"), then they will often fail the exam.

If a students answers based on whether the only exception are tiny and pedantic, then they will fail the exam.

Most school teachers attempt to convince their students that there is only one mental model of the world. Usually, the teacher's believe it themselves.

There is a branch of mathematics referred to as fuzzy logic

In fuzzy logic statements are not just true and false.

In fuzzy logic there are statements which are 96% true, and statements which are 47% true, etc...

I have a degree in math, and I think like fuzzy logic has some issues, but I am trying to show you that there are views of the world which are not black and white.

The problem with fuzzy logic is that mathematicians can squish and squash the real-interval (0, 1) as much as they want. Afterwords, the statement "Bob is bald" is only 46% true, when it used to be 84% true. However, for any two people P and Q if P was balder than Q before we messed up the numbers, then P is still balder than Q after we're done squish and squashing the real-interval (0, 1).

The problem with fuzzy logic is that exact numbers (percentages) do not matter.

There is something known as thee "sorites-paradox"

If we keep removing hairs from someone's head, is there a point at which they suddenly transition from being not bald, to being bald?

The removal of a single hair will not turn a non-bald man into a bald one.

Instead of black, and white, please try to see the shades of grey.

You asked, when can we have certainty in what we claim to know?

For more than a hundred years, British and German philosophers defined a piece of knowledge as a "justified true belief".

That is, if you believe that a cartoon Micky Mouse makes you breakfast in the morning, that belief is not a form of knowledge. People believe things which are not true.

What if you believe something which is true, but you chose it randomly? I pick a number between 1 and 1000. I ask you to guess the number. you guess correctly.

Well, that is not knowledge, because it is not justified

In 1963 Edmund Gettier showed the world's philosophers that there exist examples of knowledge which are not justified true beliefs.

In order for something to be knowledge, it must be a belief, it must be truer than thinking mickey mouse cooks your breakfast, and it must be justified.

Maybe conditions are necessary, but not sufficient, to describe what knowledge is.

Attorneys often define what is and what is not an X

In the United States, Section 508 (c) of the American with Disabilities Act, Title V states that:

A "wheelchair" is a device designed solely for use by a mobility­-impaired person for locomotion, that is suitable for use in an indoor pedestrian area.

philosophers, and mathematicians usually describe one of the following:

  • conditions necessary for X to be a Y
  • conditions sufficient for X to be a Y.

It is difficult to find a set of conditions which are both necessary and sufficient
You asked, when can we have certainty in what we claim to know?

Well, I am certain that I have a computer less than 100 feet from my present location as I write this post for the philosophy branch of stack exchange.

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