What are some necessary and sufficient conditions for a true or false statement to be a "fact" and not an "opinion"?

Question

Motivation

Perhaps we are trying to formalize some informal definitions of the English words "fact" and the English word "opinion".

Suppose that someone wanted to make some arguments related to the idea that there is no such thing as good or bad (ethical nihilism).

Specifically, the concepts of good and bad are a sort of linguistic error.

As an example, men, women, and children often say, "homosexuality is evil" instead of saying "I personally do not like homosexuality".

There are people on earth who have difficulty disambiguating between their own internal world and the external world around them.

Thus, an error is committed in which some people assume that everyone on earth enjoys or dislikes the same thing that the individual enjoys or dislikes.

For example "I personally prefer stainless steel chrome alloy forks over sterling silver forks" becomes "stainless steel forks are good and "silver forks are bad".

To digress, one justification might be that silver forks tarnish more easily than chrome alloy.

---

Some people suppose that their personal opinions are actually facts of nature.

What are some necessary and sufficient conditions for somthing to be a fact and not an opinion?

---

Consider the following sufficiency criterion....

A Sufficiency Property for FACTS
For any true statement x, we have that if x describes things external to the thoughts that are internal to the human mind, and x describes visible things, audible things, or tangible things, then it is sufficient for x to be a "fact".

In short, after all men, women, and children are dead, the stones will remain.

A fact is somthing external to the minds of men.

Begin Examples

Content of Example	Baseless Claims and Notes for the Margins	Name(s) of the Example
σ₁ = "For any sufficiently large rock R, if R is sufficiently small, and if R is sufficiently cold, and R is sufficiently motionless, then rock R does not make much noise"	The string of text σ₁ is either a true statement or string of text σ₁ is a false statement Medium-sized rocks have an existence external to thoughts inside of the human mind sufficiently small and sufficiently large might mean bigger than a baseball and smaller than the moon orbiting planet earth It is true that sufficiently medium size, motionless, very cold rocks do not make much noise	Example One The Rock Example
σ₂ = "At least one cloud of mostly water (with some small impurities) is in the sky"	The string of text σ₂ is a true or false statement statement σ₂ is true or false Note that the imperative command "get me an empty archival folder" is not a true or false statement (mkdir in BASH script) Clouds of slightly impure water do not pertain to the innermost thoughts inside of the human mind (contemplate the difference between an inner world of thought versus external world of things) It is true that at least one cloud of mostly water (with some small impurities) is in the sky"	Example Two The Cloud Example

---

However, it is not necessarily (¬ □) the case that things internal to the human mind are not facts.

For example, it might be a fact that a very specific child almost always enjoys eating pan dulce (dessert bread or bread with added sugars).

The statement that "my son enjoyed the taste of pan dulce over the last five years" might be classified as a fact just as the statement "It snowed at the Southernmost tip of South America, on at least one day, in the year 2025." A statement about one single man, or one single woman, or one single child is almost a statement about localized geography, instead of geography as a whole. We make a statement about one person, and not a statement about all people on earth.

---

What are necessary and sufficient conditions for somthing to be a fact and not an opinion?

Answer 1

I swear, if there's one word that has caused more trouble, confusion, and heartache than any other in the modern world, it's the word 'fact'. Pesky pugnacious term… The problem is that people want to use the term 'fact' as a definitive answer to an unasked question — the question: "Why should we accept this?" — but it rarely if ever works as intended.

When we use the term 'fact' we mean one of two things (and in practice we are not always clear with ourselves about which we mean):

1. A 'fact' (simple fact) can be an observed empirical event, without theoretical embellishment. For instance, if we see a stone fall, that constitutes a pair of 'facts': the observation of a stone, and the observation of downward movement. These kinds of 'facts' don't need any sort of explanation, they exist prima facie by virtue of being observed.
2. A 'fact' (induced fact) can be an established and validated theoretical proposition. For instance, the Theory of Gravity is often taken to be a 'fact' because it is validated by an extensive number of simple facts that conform to its predictions.

Note that induced facts (°2) are of a different order entirely from simple facts (°1). Simple facts depend on the validity of perception; induced facts depend on the validity of reasoned induction.

So coming back to the broader question, a 'fact' is merely a certain type of opinion. Either it's:

• a simple assertion that one subjectively experienced a certain event: e.g., "it's a 'fact' that I saw Jenny slap Lou across the face", or…
• a provisional assertion based on reasoning from experience: e.g., "given the preponderance of evidence it is a 'fact' that Bronson committed the murder".

We would all like to think that a 'fact' is more than that — that a 'fact' reflects some underlying and indisputable ontological condition — but that's mere idealism masquerading as epistemology.

Answer 2

To a reasonable person, facts are not subjective; opinions are subjective to the person holding them.

“Reality is that which, when you stop believing in it, doesn’t go away.”

In at least some sense, the only necessary and perhaps sufficient condition for something to be a fact is that it cannot be argued; that is, it isn’t subjective to who you are or what else you believe, it just is. Opinions, conversely, do depend on who you ask, and in that case act as “subjective truths”.

---

For example, take the fact “the Earth is round like a sphere”. To a reasonable person (ahem…) this is obviously true: we’ve seen it from space, we’ve locally measured its curvature, and we’ve had to build rail lines and undersea cables that deal with that curvature.

I can also take the stance that “the Earth isn’t round, it’s flat” is a fact. Unfortunately for Flat Earther me, that doesn’t make it any more true that the Earth is flat; it is a fact, by all reasonable knowledge (e.g. excluding the possibility that an alien race is mind-controlling astronauts and construction workers and physicists into seeing obviously-flat data as obviously-round data), that the Earth is round, and saying otherwise doesn’t falsify that idea.

---

Meanwhile, I could hold the opinion that “I wore a fun quirky outfit yesterday.” If I say this, it becomes true in my eyes (unless I’m lying; for our purposes, assume nobody lies). In my perception of reality, this is a fact.

However, my coworker, Mr. Kerman, could hold the opinion that “they wore a boring regular outfit yesterday”. If he says this, it becomes true in his eyes; in his perception of reality, that is a fact.

---

The key thing is that the opinions here are contradictory but no issue is produced. It’s okay for me and Mr. Kerman to hold completely-different sets of opinions, and for those opinions to (subjectively) apply as truths in the same way facts do. Meanwhile, facts cannot be contradictory in the same way no two contradictory logical propositions can coexist in the same theory: two facts contradicting each other implies that one or both is wrong, whereas two opinions contradicting each other is a non-issue.

Answer 3

Discussion and not an answer: the issues regarding "truth" have been debated in Western world (but not only, obviously) since ate at least Parmenides (5th century BCE). Thus, it is quite hard to imagine "clear and simple" definitions.

A first difficulty is about terminology: IMO facts "as opposed to theories and to values, are part of the furniture of the world", while statements are linguistic entities.

According to a common sense view, a statement is true when it corresponds to a fact.

But a different approach is that about beliefs: there are factual beliefs vs opinions (opinion beliefs). Maybe not so different: we can talk about statements of fact vs. statements of opinion, or factual claims vs. opinion claims.

Examples:

“Fact: statement of actuality or occurrence. A fact is based on direct evidence, actual experience, or observation.

“Opinion: statement of belief or feeling. It shows one’s feelings about a subject. Solid opinions, while based on facts, are someone’s views on a subject and not facts themselves.”

Maybe the first definition is too narrow: each of us share well-know facts about Napoleon, but they are not "based on direct evidence, actual experience, or observation." Histrical facts are facts after all.

Thus, a possible refinement is: “A fact is a statement that can be proven true.”

But the refernce to Truth can easily lead to circularity: "The basic idea of the correspondence theory [of truth] is that what we believe or say is true if it corresponds to the way things actually are – to the facts."

Current discussion about fake news is also rlevant [see e.g. Keith Raymond Harris, Real Fakes: The Epistemology of Online Misinformation (Philosophy & Technology, 2022) ]: genuine news (as opposed to fakes) are subject to fact-checking. Thus, again, we presuppose a strict relation between what is true/reliable and what is going on, what happened, what is corresponding to facts.

Answer 4

In physics (and for physicians) that would be measurement.

You state that this ball is larger than that one - this is an opinion. Once you measure them, which one is larger becomes a fact.

To some extent, models are "opinions". You invent/guess/extrapolate/... something and call it a "model" - your opinion about how stuff behaves.

You then make measurements and compare them to the predictions of your model. If they fit, the model gets closer to a "fact". A good model has boundaries outside which it is expected it will fail (for instance you can claim that if a train goes x km/h and you run in the train at y km/h in the same direction, your speed as measured from the ground is x+y km/h if x and y are "small enough")

Answer 5

This is an important question, and (similar to Ted Wrigley's answer) I think it comes down to the term 'fact' being both poorly defined and also overloaded (meaning it is context sensitive and also can mean different things to different people.)

I think the easiest way to make sense of this is first discuss a related but much more specific and unambiguous term: 'factual claim'. A factual claim is statement about objective reality. "The moon orbits the earth" is a factual claim, for example. "The earth is flat" is also a factual claim. While people may dispute (and they do) the veracity of both of these claims, it's not correct or reasonable to refer either of these statements as 'opinions'.

An opinion is a subjective statement such as "chocolate tastes better than earwax." Even if every single person on earth agrees with that statement, it is still an opinion. We don't have a term for 'a claim of opinion' because opinions are not disputable. There is no objective test we can apply to determine whether one thing tastes better than another.

Back to the real question: what is a 'fact', then. I think the obvious first answer to that is: facts are factual claims that are actually true. But there's a problem with this idea, what is true? The flat earth believer is sure that it is true that the earth is flat. They are not stating an opinion when they make that claim. In their mind, it is a fact. If a 'round-earther' calls that claim an opinion, it's fair for the flat-earther to assert that the claim the earth is round is also an opinion. That would make facts ... subjective? To avoid this absurd conclusion, we must accept that a fact need not be correct.

But, the round-earther says "wait, I can prove the earth is not flat!" and the flat-earther says "and I can prove the earth is not round!" This, I think gets to an answer: a fact is a statement that can be falsified. If you think my argument sounds Popperian, you are spot on. An opinion is a statement that inherently cannot be disproven. Facts are disprovable.

It can be hard to accept that a 'fact' can be false. If I say something is a fact (and I am not intentionally lying or using words improperly) it's because I believe it is substantially true. There's a sort of cognitive dissonance when considering the idea of a false fact. I think it's easier to comprehend from a 3rd-person perspective.

Consider the example of the Aristotelian 'fact' that air is entirely weightless. For centuries, this was accepted as truth of reality. It's not too hard to imagine why someone might think that even though we now know that air does have weight. The idea that light travels through an invisible medium called the luminiferous aether was generally considered a fact until much more recently. But it really makes no sense to look back and think that these were opinions. The people who believed these 'facts' did not consider them to be opinions.

In a strict sense a fact is simply a statement about reality that can be shown to be false or (in a weaker sense) true.

Statements about someone's state of mind are also usually considered 'facts' but they don't fit neatly into the above. "I like chocolate" is a claim of fact. It's difficult to disprove but still an objective statement. I think this is a confusing aspect of the term as it is an objective statement about a subjective assessment. And given that we don't (yet) have a way to observe what someone else is thinking (despite many people seeming to believe they can) it seems weird to call these types of statements factual, but I argue that they are.

Another complication is that we can make factual claims about unprovable statements. When an ancient Romans asserted that Zeus (or Jupiter) was angry with someone who was struck by lightning, this wasn't an opinion. They were stating that as a fact. But no one can disprove that Zeus disfavored that person, so it doesn't fit neatly into my previous definition. I think the way out of this is to say that person has a belief. They may think it is a fact and state that it is a fact. It's not an opinion because it lacks subjectivity and it's not really a fact because it lacks falsifiability.

Answer 6

What are some necessary and sufficient conditions for a true or false statement to be a "fact" and not an “opinion"?

Here are my thoughts:

1.The statement must describe some act, event, or object external to every human being. This quality precludes the possibility that the object is nothing more than a figment of someone's imagination or a collective delusion.

2.The thing described must be perceptible by every human being. This quality assures that the statement can always be tested.

3. The statement must not contradict any other statement of fact. This precludes the possibility that two mutually contradictory statements about the world will not cause an “explosion” where all of logic, or physics, or history, must unravel in order for the new statement to be true.

4. Into the future, the statement must not be contradicted by any further development which might show that the original statement, in whole or in part, is false; this last quality gives the statement its uncertainty. This quality keeps the statement as part of the world. Without it, the statement becomes nominally true forever, and thus more doctrine than a representation of reality.

At the moment, scientists are uncertain about the existence of Planet 9, a large object which might orbit the sun outside the distant orbit of the dwarf planet Pluto. When can someone say, as fact, “Planet 9 exists”?

This new planet is easily outside the experience of every human being. But every human can see and understand the data concerning this planet; at least, given the right instruments, it is perceptible. The data about the planet does not, and cannot interfere with what is already known about the solar system; knowledge of the current solar system is one of the primary ways of identifying anomalies which might be the mystery planet.

Finally, should Planet 9 exist, it will only take its place as one more bit of data, waiting to be dethroned by a wandering Planet 10. Planet 9 will not contradict existing knowledge about the solar system, nor will Planet 10 interrupt what we have learned about new neighbor Nine.

Answer 7

An opinion can never be said to be "true", on an objective basis, i.e. outside the individual who holds it, since it is of a subjective nature. It can only be true to that individual.

From Dictionary.com:

Opinion: 1. A belief or judgment that rests on grounds insufficient to produce complete certainty. 2. A personal view, attitude, or appraisal.

Fact: 1. That which actually exists or is the case; reality or truth 2. Something known to exist or to have happened

So, a statement that refers to an opinion can never be a fact, by definition.

Now, if you are asking how can a statement be recognized as being an opinion and not a fact, I believe there are various ways, depending on its form and content, most of which are quite evident but other can be questionable. It is impossible to cover all the cases with single formula, rule or condition. The closest to it that I can think of is that a statement is an opinion if its truth or validity cannot proved or verified. If it can, then it can be consirdered a fact. The best way though is to examine the form and content of the statements. Examples of obvious ones are when the statement is explicitly based on a belief or opinion: "It believe/think/guess etc. that ..." or "It is believed that ..." and so on. A less obvious case would be when the statement is too general or refers to something abstract, like a concept. E.g. "God is good", "democracy is the best political system". And a questionable case would be e.g. "Love makes people happy". Beside this being something personal, it can be also considered a fact if one makes a survey in which people are asked if they are/were happy when they are/were in love and the answer from the vast is "Yes". Although this is a collection of opinions, their commonness makes them a "fact", a "reality". Now, what cannot be considered an opinion, but rather a fact, is something of a physical nature, which can be proved to be true. E.g. "The sun shines in a clear sky", "today is Tuesday (locally)", "This mother has just delivered a baby", and so on.

Finally, there is another category of statements that cannot be considered either opinions or facts. These are lies. And they can be judged as such based on the rule I stated earlier, i.e. if something can be proved to be false, it's a lie.

To summarize, the main element that separates an opinion from a fact regarding a statement is evidence proving that it is true or it has happened. Yet, as I said regarding the general rule, it is the closest one can get to their differentiation. There are no absolute or objective facts. As there is no absolute or objective reality.

Answer 8

Necessary Condition:

A statement must not be falsifiable within its applicable range. Example: Newtonian physics is true within the limits of classical mechanics (low speeds and weak gravitational fields).

Sufficient Condition:

A statement must not be superseded by a more fundamental truth. Example: Newtonian physics was later found to be an approximation of a deeper reality described by relativity and quantum mechanics. Since scientific knowledge evolves, what we consider "true" is subject to refinement.

Key Takeaway:

In science, "facts" are provisional truths based on current knowledge, while "opinions" are subjective interpretations. The distinction depends on the ability to test, falsify, and refine knowledge over time.

Answer 9

Match it with reality dude.

A fact is what is real, as in non-imaginary. Does not exist only in somebody's head.

You can imagine that its raining. Is it really raining? Look outside. If you cannot look outside - you dont have working eyes or its too dark - then go outside and if you can feel the droplets falling on you, then its raining or may be someone at upper floor is urinating or somebody's pipe is leaking or somebody is watering his lawn.

The point is, the best you can do is match with reality. Ofcourse this dont always work. You for example dont know whats going on in other people's minds.

You cannot say what a person is telling you is his opinion or not, even if you know it dont match with reality. If it dont match with reality then its sure is imaginary. But you dont know that the person knows its imaginary or not.

If the person knows its imaginary then its not even his opinion. He is just (knowingly) lieing to you.

If the person thinks its not imaginary then its that person's opinion. It can also be at the same time a fact. To be a fact it just has to match with reality.