Even preschoolers know that 1 + 1 = 2 is a fact:

https://www.youtube.com/watch?v=8cR_1Qi-tP4

|>ouglas

I said nature of, implying 'the nature of truth', not the truth directly. This means that I want you to analyse ourselves(human-kind; consciousness)and truth.

What do we do when we create or asess truth?

We use/sum up the fact.

In a way you are right - but fact is deriven from truth(it is non exclusive, it just is related).

When someone asks you produce fact, what do you also do?

a chair isn't a fact — Coben

My car is a fact? — Douglas Alan

One thing does not exist in abstract. This chair in its particular occurrence in relation to other things in its environment is the fact. What you say about the chair is a proposition which refers to a fact and which may be true or false. Or a pseudo-statement. Or a value judgment. To state a fact you have to establish its existence, without which there is not reference to a fact.

That a car exists and that this car is yours is a fact (or not, ça depend). "My car" doesn't say anything about facts. It is a concept not a proposition. "I have a car" does state a fact.

1 + 1 = 2 is a fact: — Douglas Alan

If you want to include numbers as ideal or abstract "facts", you can do so. But it's twisting the word out of the ordinary. In philosophy of science, a distinction is made between formal and factual sciences. Well understood, only the latter deal with facts.

(Sorry, I won't spend an hour watching the youtube you're proposing. Can you propose something more specific? Any particular time?)

What do we do when we create or asess truth?
We use/sum up the fact. — Qwex

I'm sorry, but I'm all messed. I wouldn't say that when I put a proposition I "create" a truth. I would say that truth is a quality of my proposition according to the definition of truth that we accept, which includes the criteria for knowing whether my proposition is true or false. What I create is a proposition.
It's the same as if I say my yacht is better than yours. We establish a criterion and verify whether or not my boat meets the qualities of a good yacht and yours not... or vice versa.

I wouldn't say I use facts either. Not in the sense that I use a hammer or a hat. Facts are not an instrument, but the reference for my propositions. I use words to refer to facts. Words are instruments.

How is fact not an instrument of truth? It's not merely reality, fact is a reference to reality. You would study the fact to know the truth. Maybe I'm wrong by saying it's deriven. The two however are linked. It's a fact my TV is there, therefore it's true to say it. I study what more is fact at this time

Aren't facts truth qualititive phenomena?

If you look at, collection of facts about the world and no fact. In a competition of two the collection of facts is more likely to know the truth about the world. They're at least truth-pro.

If you want to include numbers as ideal or abstract "facts", you can do so. But it's twisting the word out of the ordinary. — David Mo

I've worked with scientists my entire adult life. As far as I'm aware, they would all agree that 1 + 1 = 2 is a fact. I work with scientists right now, in fact. I could take a poll if you are interested.

(Sorry, I won't spend an hour watching the youtube you're proposing. Can you propose something more specific? Any particular time?) — David Mo

It would have taken you less time to have verified my assertion than to have typed the above sentence. The first sixty seconds.

|>ouglas

As I mentioned, some propositions, will not carry a truth value, and different logicians have different opinions about what to do about such propositions. — Douglas Alan

Hey Doug!

Okay. I was a bit confused, because I thought you said earlier that propositions were either true or false.

And other examples I alluded to earlier were relative to propositions of self reference and logical necessity, respectively:

1. This statement is false.
2. There is at least one true proposition.

And then there are statements, like Tim Wood alluded to, that are incomplete viz Godel;

1. Socrates: What Plato is about to say is false
Plato: Socrates has just spoken truly

1. Tom cannot prove this statement to be true.

As for the sentence "All events must have a cause", I can see that people may agree or disagree with this statement. Or they may feel that it doesn't have a truth value. But in terms of how logic is to deal with it, I don't see how it is different from any other proposition that might be contentious. — Douglas Alan

In Metaphysics, that's known as a Kantian synthetic a priori proposition. Something beyond pure reason or logic. Both an innate sense of wonderment, and something that can be tested a posteriori; a synthesis of both.

Synthetic propositions are the basis of scientific hypothesizing.

Enjoy!

It's too bad the question of the OP has been obscured by this back-and-forth over the two words "fact" and "true." But, a resolution may appear in a day or two. Because one of us has claimed repeatedly that the heavy thinkers at two of this nation's finer institutes of wa-ay higher learning use the two words interchangeably, I have emailed the linguistics department at one of them, MIT, for any comment they may care to make. We'll see how it goes.

Through all the discussions on this thread, I have managed to gather some ideas which, it seems, everyone who's participated is okay with in some way or other (according to my judgement). That is,

- a fact is the expression of state(s) of affairs.
- a truth is the principle(s) on which state(s) of affairs are established.

From the above, I've also been able to develop other definitions for information and knowledge which I think are pertinent, somewhat differentiating and still correlated. That is,

- information is a relation of fact(s).
- knowledge is the relation between fact(s) and truth(s).

Of course, there's the obvious common usage of information and knowledge, e.g. if you have information, then you know; or if you know, then you have information, etc. But, even with common usage, the test/limiting factor which, more often than not, differentiates between the two is application. Right application qualifies one as possessing knowledge in favour of those who may just possess information without the capacity to apply it. (These are just my ideas and nothing is definitive.)

To all who've participated, I would like to give my thanks. This is a very illuminating discussion.

I have emailed the linguistics department at one of them, MIT, for any comment they may care to make. We'll see how it goes. — tim wood

My boss has a PhD in Linguistics from the aforementioned Linguistics department, and I just asked him if 1 + 1 = 2 is a fact. He replied that yes it is.

|>ouglas

P.S. My SB is also from the aforementioned Linguistics (and Philosophy) dept.

If you want to include numbers as ideal or abstract "facts", you can do so. But it's twisting the word out of the ordinary. In philosophy of science, a distinction is made between formal and factual sciences. Well understood, only the latter deal with facts. — David Mo

I just went and polled four scientists, one of whom is the Director of R&D of the lab where I work, which is part of a world-famous research institute. They all said that yes, 1 + 1 = 2 is a fact when I asked them whether it is or not.

In case they were confused in some way, after asking them this question and getting their answers, I told them that the question I was really interested in is whether or not this is proper usage of the word "fact". They said that it is.

I did not lead them in any way to the answer, and I informed them that this wasn't intended to be a trick question. Just one of interest to someone who has a Philosophy degree, as I do.

|>ouglas

It's lamentable that here we waste time and effort in debate of whether two different words are different or the same, interchangeable wrt meaning, when manifestly they refer to different things. How stupid is that? And that people who ought to know better give a wrong answer is suggestive of a fault in the question.

You might go back and ask them just how it is that 1+1=2 is a fact. My guess is that in response to that you might get a more considered - and different - answer.

I will refer you again to the Stanford Encyclopedia of Philosophy:

As we pointed out above, one view about facts is that to be a fact is to be a true proposition

I have already pointed you at this, and at Wikipedia. I have told you of my education. I have talked to someone with a PhD in Linguistics and with scientists with whom I work. They all agree that 1 + 1 = 2 is a fact.

You, instead, are committed only to the echo chamber that resonates in your own empty head, while I have actually supplied real evidence.

You might go back and ask them just how it is that 1+1=2 is a fact. — tim wood

I was one step ahead of you here, and I did in fact ask them this. Or, rather I asked them why 1 + 1 = 2 isn't a "truth" rather than a "fact". They replied that these are just synonyms, as are so many other words in English.

Personally, I find saying that a proposition is a "truth" to sound a bit unidiomatic to my ears. I would typically use "true" as an adjective when talking about a proposition, or refer to it as a "fact" if I wished to use a noun.

But hey, I looked up "truth" in the dictionary, just for you, and this is what it said:

a fact or belief that is accepted as true

But it appears that in Tim Wood's echo chamber head, there are no synonyms. In fact, only those who are stupid and ignorant believe that synonyms exist.

If I had asked the scientists, literally, "Just how is it that 1+1=2 is a fact?" they would have no doubt replied something along the lines of, "It's a mathematical fact. Math tells us that it is true." Or somesuch. They aren't philosophers; they are scientists. They aren't going to provide us with a philosophical answer to this question. They are only going to affirm that they consider 1 + 1 = 2 to be a fact because anyone who knows any math knows that it is true.

|>ouglas

P.S. As I have said many times so far, I am not committed to there being only one correct usage of the word "fact". As with many English words, it can mean different things in different contexts, and different people can use the same word differently.

My only claim has been that identifying facts with true propositions is a common usage of the word "fact". Sure there are other uses. Feel free to use an alternate meaning, so long as you are clear as to which sense of "fact" you are using in your exposition and why.

Okay. I was a bit confused, because I thought you said earlier that propositions were either true or false. — 3017amen

Well, it's complicated. In some accounts they are. In others, they aren't. I'm no expert on the history, but my understanding is that the contemporary concept of propositions didn't really come into heavy use until Frege and Russell. Since they were logicians, they wanted propositions to always have truth values. Or at least one of them did. It's been a long time. I spent half a semester in a Philosophy of Language class going over Russel's theory about how to turn all propositions into formal logic. (I.e., predicate calculus.) In predicate calculus, every expression has a definite truth value.

This program of trying to transform all propositions into formal logic was quite problematic, and I'm pretty sure that this goal has largely been abandoned by philosophers. (Though I don't know for sure, since that was the end of my studies in Philosophy of Language.)

But in my philosophical education, even in moral theory, we were encouraged to practice converting every philosophical argument that we might find into a logically deductive argument. In the process of doing so, I might end up writing down something like

Premise 1: Boiling live babies to death is very bad.
Premise 2: People who wish to do very bad things are bad people.
Premise 3: Cannibals wish to boil live babies to death.
Conclusion 1 (from Premises 1 & 3): Cannibals wish to do things that are very bad.
Conclusion 2 (from Conclusion 1 and Premise 2): Cannibals are bad people.

Note that even if we believe that moral propositions have no truth values, we can kind of pretend that they do for the sake of evaluating this argument. E.g., even if we think that moral propositions fail to have truth values, this logically deductive argument shows us that if we agree with the premises, then we are forced to agree with the conclusions.

As for logical paradoxes, such as "This sentence is false", Tarski tried to resolve these sorts of things. IIRC, he argued that "This sentence is false" fails to be a proposition and hence the fact that it can't have a truth value doesn't allow us to conclude that there are propositions without truth values.

But forgive me if I am butchering Tarski. Or I am just completely wrong. This was a long time ago, and his argument gave me a huge migraine.

In Metaphysics, that's known as a Kantian synthetic a priori proposition. Something beyond pure reason or logic. Both an innate sense of wonderment, and something that can be tested a posteriori; a synthesis of both.

Synthetic propositions are the basis of scientific hypothesizing. — 3017amen

Such propositions would have truth values, though, would they not? So they are not problematic for those who hold that propositions always have truth values.

|>ouglas

They replied that these are just synonyms, as are so many other words in English. — Douglas Alan

And precisely there you have it. No point in looking further because this is it, that we can drill into. And this is to say that there is no difference between the two words. But consider: if it is accurate to call X true, and if true then a fact - which it seems you must grant as they're the same - then X is as well a fact. (X is true)=(X is a fact). That's your position.

And really this has ceased to be about two words, but about two meanings - what it means to be true and what it means to be a fact: and you must hold these too to be the same thing. Mine, of course, is that facts are about historical matters, in the sense they cannot be about future things. And that truth applies to things that by some unequivocal standard are universally and necessarily and always so - by which I mean that if it's true then it's provable under those criteria. Facts on the other hand are never so provable, though evidence may support the conclusion that the fact in question is highly likely.

Some examples: if they stand - you cannot fault them as examples - then you're forced to acknowledge that true and fact are not the same.

a) That Shakespeare wrote Hamlet is a fact.
b) That Homer wrote the Iliad and the Odyssey is a fact.
c) That the battleship Massachusetts cannot possibly disappear from its Fall River mooring and instantly reappear moored to the Harvard (a/k/a Mass. Ave.) bridge is true.
d) that a) and b) are facts is true.
e) c) is false, though a fact.

Neither a) nor b) is provable, hence not true in the sense above. d) the proposition that they're facts is true because it's generally accepted that what they state is supported by enough evidence to compel the assent of reasonable people. That is, true in the sense of true above.

c) is false. There is such a chance, but it's just not a very big chance, and not likely to occur this week or any time soon. And it's a fact because while it could happen, it definitely ain't gonna happen.

None of this gainsays that informally the distinction is sometimes neglected or ignored - or even isn't recognized at all. But in any case that is not been what this is about.

Feel free to use "fact" however you want. As Humpty Dumpty said, "When I use a word, it means just what I choose it to mean—neither more nor less."

But Mr. Humpty Dumpty, I haven't seen many, if any, contemporary philosophers–or scientists, or linguists, or average Joe's–using the word as you are.

That being said, I've read plenty of philosophical arguments where jargon is introduced, explained, and then used, and I have had no problem with this. As long as the jargon is introduced to elucidate rather than obfuscate.

As for your putative proof that being a fact and being true cannot be synonymous, your proof doesn't fly with me. Furthermore, you make a grievous error when you say that things that are true must be provable. Have you never heard of Kurt Gödel?

I agree that if I use your definitions of "fact" and "true", then "fact" and true" are not synonyms. But that was obvious before you even provided your proof, so what's the point of your proof? You've just conducted a somewhat long and textbook exercise of begging the question!

If I use my preferred definitions for "true" and "fact", then your proof does not work at all. I.e., I will agree that a, b, and d are probably true, but I will assert that c and e are false.

And now we are back where we started, with me preferring the definitions that I am used to, and you preferring the ones that you are apparently used to. Though where you conduct philosophy in which the words are used in this manner, I can't quite imagine, since I was made to read quite a lot of philosophy, and most of it with not published in Cambridge, MA. If philosophers in all of these books and papers were using the words "fact" and "true" in the manner in which you prefer, I somehow failed to notice and yet still managed to get straight A's.

Well, I guess that just goes to show that any ol' ignorant and stupid person can get straight A's at even the fourth best Philosophy department in the world. What a sorry state of affairs for the world that we find ourselves in! I think that you have proved Leibnitz wrong since clearly this is far from the best of all possible worlds!

|>ouglas

How is fact not an instrument of truth? It's not merely reality, fact is a reference to reality. You would study the fact to know the truth. — Qwex

I observe Mars with a telescope. Mars is the reality, the object. The telescope is the instrument. And "Mars is a red planet" is a statement of facts. And the fact that I have enunciated is true. To speak of facts only has sense in the context of a proposition that refers reality. But fact is not an instrument of truth. It is the reference of a proposition and truth is a property of this proposition.

"Go to facts in order to find the truth" is an abbreviated way to say the same.

I've worked with scientists my entire adult life. — Douglas Alan

And I have lived and worked with scientists and philosophers all my life (since my first day of life). In addition I have read some books on the subject written by scientists or philosophers. Now that we've strutted around a bit, we can talk about things. Don't you think so?

In the first sixteen seconds of the YouTube you linked there is no more that a child choir that shout about "math facts". It is not too much to begin.
Do you have something less childish that this?

My boss has a PhD in Linguistics from the aforementioned Linguistics department, and I just asked him if 1 + 1 = 2 is a fact. He replied that yes it is. — Douglas Alan

Ask him for the difference between applied and pure maths and what is the fact behind the irrational numbers and Riemann axioms.

In the first sixteen seconds of the YouTube you linked there is no more that a child choir that shout about "math facts". It is not too much to begin.
Do you have something less childish that this? — David Mo

My point is that in "ordinary language" mathematical truths are typically considered to be facts. Nothing more. I have shown this by talking to someone with a PhD in Linguistics, to a small room full of scientists, and by evidence of how we train our children about math.

I have never claimed that there are no philosophers who use the word "fact" in a jargony manner that differs from this. But, as I have proven by citing the Stanford Encyclopedia of Philosophy on the issue, there are philosophers who use the word "fact" just to mean "true proposition".

|>ouglas

Ask him for the difference between applied and pure maths and what is the fact behind the irrational numbers and Riemann axioms. — David Mo

If you want to, I can ask my friend who has a PhD in number theory and is a professor at UPenn if he thinks that mathematical truths are facts or not. Would you like to wager on what his answer will be?

|>ouglas

That "a fact is a true propostion" is a useful stipulation, the one I prefer, and to the best of my knowledge is the most common usage among philosophers. But let's bear in mind that we don't have access to the truth value of most propostions. This is the problem of knowledge: knowing a proposition is true means believing it with a justification that establishes it as true and avoids Gettier problems. We cannot know that Shakespeare wrote Hamlet, but we can treat is as a "fact" (different sense of the word) - there is reasonable justification for believing it and it is commonly accepted as true. I don't think there's an alternative term to "fact" when discussing history or literature - but there's rarely any confusion about what is meant.

This program of trying to transform all propositions into formal logic was quite problematic, and I'm pretty sure that this goal has largely been abandoned by philosophers. (Though I don't know for sure, since that was the end of my studies in Philosophy of Language.) — Douglas Alan

I think basically you're referring to Logical Positivism. And as such, it denies propositions that relate to sentient Beings (Ontology, Metaphysics, Cosmology).

Examples that LP's or analytical philosopher's , for whatever reason (psychologically that is), find no truth value in:

1. All events must have a cause (synthetic a priori)
2. All bachelors are happy (Ontological proposition)
3. The color red is an exciting color
4. Truth is beautiful; that car is beautiful, he is angry, why do I wonder about things, I feel happy/sad, etc.. etc..

As for logical paradoxes, such as "This sentence is false", Tarski tried to resolve these sorts of things. IIRC, he argued that "This sentence is false" fails to be a proposition and hence the fact that it can't have a truth value doesn't allow us to conclude that there are propositions without truth values. — Douglas Alan

The liars paradox basically proves that Omega is unknowable.

Such propositions would have truth values, though, would they not? So they are not problematic for those who hold that propositions always have truth values. — Douglas Alan

In reference to your question about synthetic propositions, again, the analytical philosopher or the LP would deny/consider such a statement as nonsensical, which is one reason why LP (has limitations) is not used in say cognitive science/psychology or theoretical physics, etc. etc..

The irony seems to be that although the LP recognizes the empirical method for discovering/uncovering its truth value, for whatever reason they deny the aforementioned propositions relating to existential phenomenlogy... .

I think basically you're referring to Logical Positivism. — 3017amen

No, that's not right. The project of reducing all propositions to formal logic is orthogonal to logical positivism, which is the thesis that only propositions that can be verified (either via irrefutable reasoning or via empirical observation) have meaning.

Just because you've reduced a proposition to logic does not entail that you can verify it. And even if you can't reduce propositions to logic doesn't mean that you can't verify them.

Whether Russel was in fact a logical positivist is a matter of debate, as far as I'm aware. He definitely wasn't part of the movement.

|>ouglas

Whether Russel was in fact a logical positivist is a matter of debate, as far as I'm aware. He definitely wasn't part of the movement. — Douglas Alan

I think he was at one time, then basically discovered it's limitations. Perhaps another one who awoke from his dogmatic slumber's :brow:

No, that's not right. The project of reducing all propositions to formal logic is orthogonal to logical positivism, which is the thesis that only propositions that can be verified (either via irrefutable reasoning or via empirical observation) have meaning. — Douglas Alan

That's not right either Douglas. Formal logic is a priori.

That's not right either Douglas. Formal logic is a priori. — 3017amen

Russel's project was to convert propositions into formal logic. One cannot determine the truth of a statement expressed in formal logic a priori when it is not a logically valid statement.

E.g., if we convert the sentence "Santa Claus exists" into formal logic, we get something like:

There exists an x such that S(x)

where S is a predicate that is true for Santa Claus and false for everything else.

We cannot a priori determine the truth value of this statement just because it has been expressed in formal logic.

|>ouglas

http://www.importanceofphilosophy.com

*The above site is not the definitive on philosophical terms and meanings. It has a disclaimer at the bottom which reads,

The content of this website is primarily based on Ayn Rand's philosophy, Objectivism.

And, because of that, it will be readily evident what its shortcomings are. However, it presents a very good (workable) relation between the meanings of various philosophical expressions.

Some of the expressions and meanings are:

- An axiom is an irreducible primary. It doesn't rest upon anything in order to be valid, and it cannot be proven by any "more basic" premises. A true axiom can not be refuted because the act of trying to refute it requires that very axiom as a premise. An attempt to contradict an axiom can only end in a contradiction.
The term "axiom" has been abused in many different ways, so it is important to distinguish the proper definition from the others. The other definitions amount to calling any arbitrary postulate an 'axiom'.

- Words are symbols of concepts. They act as the means of making concepts into mental concretes. They allow the storage of a conceptual integration that can be recalled on demand. Words are references to a concept. They are mental entities which trigger the contents of the concept. By making the concepts into concretes that can be easily maintained and used, we are able to use concepts as particulars, allowing further integration.
Words in themselves are meaningless and mostly arbitrary. They are auditory or visual symbols of concepts, which contains the meaning. A definition applies to a concept, not a word. A word is a name given to a concept. It isn't the concept itself. A word is only meaningful if it has a concept, which in turn, has a definition. Without these, a word is just a noise.

- A definition describes the basis of integration of a specific concept. It describes the essential nature of the concept. It differentiates all other particulars from those included under the concept.
A concept has a genus and a differentia. The role of the definition is to describe both.

- Knowledge is the mental grasp of the facts of reality. It is the awareness of the identity of particular aspects of reality. It is not just an awareness of reality, but an understanding of it. It is a successfully formed conclusion about some aspect of reality. An example of knowledge is the identification of the law of gravity. It is a characteristic of reality that is identified and understood.
Knowledge is gained through a successful evaluation of one's perceptions. It is through the use of reason that man draws conclusions about the world. It is through objectivity that man identifies the validity of those conclusions. Knowledge is the clear, lucid information gained through the process of reason applied to reality.

We cannot a priori determine the truth value of this statement just because it has been expressed in formal logic — Douglas Alan

Indeed. And so would Kant, I think. Accordingly, I believe he would say existence is not a real predicate, in that existence in itself by definition, does not describe its properties. And so S (x) would be a synthetic statement v. a more obvious analytic/a priori/ tautological statement.

Of course, the ontological argument for God's existence is the contextual framework for all that. To this end, a priori formal logico-deductive reasoning would not be the exclusive means or tool to use in trying to determine causation, Being, so on and so forth [for a Deity's existence]. Instead, most would agree (theoretical physicists) that synthetic judgements and inductive reasoning is the more appropriate method when making statements and/or discovering properties about same.

In Cosmology/Metaphysics it therefore makes the "search for a Deity" more bottom-up, versus the traditional approach for most creationist's who seem to prefer top-down-logic. Personally, I like both.

The phenomena of living this life is much more than simple a priori/ tautological statements... .