All Facts Are Based in Faith

[Axe Elf]

A "fact" is not dependent on my recognizing it as a fact.

I would say that Truth (capitalized and objective) is not dependent upon the facts, but facts, by definition (remember: "a thing that is indisputably the case" from my previous post), DO require acknowledgment as being indisputably the case before they can be said to be facts.

 

[Axe Elf]

If facts are based in faith then every religious person will necessarily have two faiths - the duplicitous *7*^%*!

In all likelihood, every person harbors dozens and dozens of faiths.

 

[Axe Elf]

It depends. Whatever I can sense through personal, first-hand experience, I accept as "real" and consider it "fact." I suppose it's possible that this could all be an illusion, but it's the "reality" that I have personally experienced and accept it as it is.

Your recognition that the perceptions and sensations of first-hand, personal experience could all be just illusions is testimony to the first level of faith in which all facts are based--the faith that a "real world" exists outside of our own heads, and that at least some of our perceptions and sensations are reflective of the real world.

Then there are other facts which I may not have personal, first-hand knowledge of, but they are related to me in any number of ways and I might also accept them as true. That might require some degree of faith, along with some ability to discern between reliable and unreliable sources of information. Even if a source is reliable, language is still imperfect, and there can be miscommunications, misunderstandings, and misinterpretations. Human memory is fallible. Eyewitness testimony isn't always that reliable.

That would be the second level of the faith in which all facts are based--faith in the testimony of others beyond one's own personal experiences. One may not have seen the Leaning Tower of Pisa in person, but they could reasonably have faith in the testimony of the many people who HAVE seen it with their own eyes, faith that the various pictures of it are not "doctored," etc. So some facts are based upon the testimony of trusted sources.

The third level of faith would be faith in the axioms of formal systems of reasoning, like "If a=b and b=c, then a=c" or "two parallel lines never intersect."

I believe that all facts ultimately rely on faith in one of these three things--either faith in the real world and one's own ability to perceive it, faith in the testimony of trusted others, or faith in the axioms of a formal system of reasoning--and so all facts are based in faith.

 

[Axe Elf]

Faith doesn't require repeatable results. Fact does.

Essentially correct; facts are demonstrated by and from those things in which you have faith, but those things in which you have faith are accepted as being true without demonstration or proof.

On the other hand, if you have faith that a friend is honest, but then you find that he has lied to you three of the last four times you talked, you may lose faith in his honesty--so faith can be affected by results.

 

[Axe Elf]

Facts are obvious.

What's the faith part?

Faith is what allows us to "know" facts, by one of the following means:

1) Faith that a real world exists, and that at least some of our perceptions and sensations are representational of the real world.
2) Faith in the testimony of trusted others.
3) Faith in the axioms of formal systems of reasoning.

 

[Mock Turtle]

In all likelihood, every person harbors dozens and dozens of faiths.

Faiths/beliefs - a bit dodgy isn't it?

 

[Polymath257]

I don't necessarily distinguish between "religious faith" and "mathematical faith" or "scientific faith"; they all have to do with assuming certain things to be true without proof--faith statements.

Oh, I very much do. They are all three very different critters.

So first of all, not all facts are based on observation. Some facts are based on formal systems of reasoning, like mathematical or geometrical theorems.

And I can extend the concept of 'fact' to encompass those. But such 'facts' do not say anything about the real world simply because they are only strings of symbols in formal systems.

But even for those facts which ARE based on observation, one must have faith in one's observations--that is, one must have faith that they are not just a brain in a vat being stimulated by a mad scientist. One must have faith that such a thing as the "real world" exists, and that at least some of their perceptions and sensations are reflective of that reality. We know that not ALL of them are, but one must have faith that at least SOME of them are, if they are to trust their observations.

Starting from a position of solipsism, the option of being a brain in a vat is a non-starter: it is not possible to test it. As such, and until it *can* be tested via observation, it is literally a meaningless claim.

Mathematical 'facts' are strange beasts because they say nothing at all: they are strings in formal systems, which we often have some intuition concerning their semantics, but no such semantics is required for doing math or logic.

And so it is that all facts are based in faith--at a minimum, faith in one's ability to perceive a real world outside of oneself, and in more sophisticated settings, faith in the axioms (faith statements) that underlie formal systems of reasoning.

And I disagree that this is a requirement. Even in the 'brain in a vat' scenario, I would *define* reality via the observations I make. That isn't a faith statement; it is definitional.

 

[Axe Elf]

Faiths/beliefs - a bit dodgy isn't it?

I don't know, I'm not British. Google says dodgy is "dishonest or unreliable." Are these claims you can support or should they be considered ad hominem? In what sense am I being dishonest or unreliable?

 

[Polymath257]

Faith is what allows us to "know" facts, by one of the following means:

1) Faith that a real world exists, and that at least some of our perceptions and sensations are representational of the real world.
2) Faith in the testimony of trusted others.
3) Faith in the axioms of formal systems of reasoning.

If 1) is false, then nothing about the real world is possible to know. So, it is better to simply *define* the real world via potential observations.

2) is validated via the scientific method and is certainly NOT a general claim. There are many people whom I do not rust as valid observers. To determine trustability, I use observation and testing.

Faith in the axioms is not required. All that is required to having axioms and rules of deduction. Whether those axioms *apply* to the real world is a matter of observation and testing.

 

[Axe Elf]

Oh, I very much do. They are all three very different critters.

Well, we may have to get into your differential definitions, then. If we're not talking about the same thing when we say "faith," then we probably won't get very far in this discussion.

And I can extend the concept of 'fact' to encompass those. But such 'facts' do not say anything about the real world simply because they are only strings of symbols in formal systems.

Agreed. But of course that does not mean they are USELESS facts. The formal system of logic gives us facts we can use to reason. The formal system of Mathematics gives us facts we can use to calculate. The formal system of Euclidean geometry gives us facts we can use to determine areas and spatial relationships. The formal systems of non-Euclidean geometries give us facts we can use to plot Great Circle routes on a globe or the flight paths of objects in space. But all of the "facts" (theorems) they give us are dependent upon the faith statements (axioms) from which they are derived. Facts derived from formal systems of reasoning, like facts determined from personal experience and the experience of others, are also based in faith.

Starting from a position of solipsism, the option of being a brain in a vat is a non-starter: it is not possible to test it. As such, and until it *can* be tested via observation, it is literally a meaningless claim.

That's silly. We can't test "God exists" either, but one would be mad to insist that it is "literally a meaningless claim," given the very profound meaning that it obviously has to literally billions of people around the world. But the idea that we can't test the notion that a real world actually exists outside of our own minds, or even that at least some of our perceptions and sensations actually reflect that real world, is basically my point--you can't test it, so you have to accept it on faith.

Mathematical 'facts' are strange beasts because they say nothing at all: they are strings in formal systems, which we often have some intuition concerning their semantics, but no such semantics is required for doing math or logic.

You may be meaning something different when you say "semantics," but semantics are actually VERY important in mathematical and logical expressions of fact. For instance, one must resolve terms within parentheses first, then resolve multiplication and division before finally resolving addition and subtraction. If the semantics are not followed correctly, then you will get untrue "facts." Likewise the semantics of a conditional statement in logic is important, and so on.

And I disagree that this is a requirement. Even in the 'brain in a vat' scenario, I would *define* reality via the observations I make. That isn't a faith statement; it is definitional.

Definitions, are, by definition, axioms, which are statements assumed to be true without proof--faith statements.

You can't construct a proof or a scientific test that the definition of "cat" is "a small domesticated carnivorous mammal with soft fur, a short snout, and retractile claws"; you can only point to a dictionary and say that it has to be accepted on faith, accepted as being true without proof.

 

[Polymath257]

Well, we may have to get into your differential definitions, then. If we're not talking about the same thing when we say "faith," then we probably won't get very far in this discussion.



Agreed. But of course that does not mean they are USELESS facts. The formal system of logic gives us facts we can use to reason. The formal system of Mathematics gives us facts we can use to calculate. The formal system of Euclidean geometry gives us facts we can use to determine areas and spatial relationships. The formal systems of non-Euclidean geometries give us facts we can use to plot Great Circle routes on a globe or the flight paths of objects in space. But all of the "facts" (theorems) they give us are dependent upon the faith statements (axioms) from which they are derived. Facts derived from formal systems of reasoning, like facts determined from personal experience and the experience of others, are also based in faith.

No, those are results of formal systems that are *applied* to aspects of the real world. Whether the formal system is actually applicable is solely determined by observation and testing. So, the computation of area using Euclidean geometry is NOT always a valid use: in particular because the Earth is not flat. That is a matter of observation. The use of Great Circles to determine routes on a globe is also NOT always valid because the Earth is NOT a perfect sphere. That is also a matter of observation.

In every case, whether the formal system *applies* is a matter of observation. The 'factas' of the mathematics do not, in and of themselves, say anything about the real world.

That's silly. We can't test "God exists" either, but one would be mad to insist that it is "literally a meaningless claim," given the very profound meaning that it obviously has to literally billions of people around the world. But the idea that we can't test the notion that a real world actually exists outside of our own minds, or even that at least some of our perceptions and sensations actually reflect that real world, is basically my point--you can't test it, so you have to accept it on faith.

Actually, given the lack of a consistent definition of the noun 'God' and the lack of any observational test for such, I *would* say that most statements about God are literally meaningless.

You may be meaning something different when you say "semantics," but semantics are actually VERY important in mathematical and logical expressions of fact. For instance, one must resolve terms within parentheses first, then resolve multiplication and division before finally resolving addition and subtraction. If the semantics are not followed correctly, then you will get untrue "facts." Likewise the semantics of a conditional statement in logic is important, and so on.

Actually, that isn't semantics. It is syntactics. Syntax has to do with manipulation of formal symbols. Semantics has to do with the meaning of such symbols. For mal systems are syntactical constructs. Whether the formal system applies to the real world is a semantical one and is determined through observation and testing.

Definitions, are, by definition, axioms, which are statements assumed to be true without proof--faith statements.

Um no. Definitions are abbreviations. They are true by decree, if you will. We don't *assume* definitions to be true. We make definitions as abbreviations and they are true *by definition*.

You can't construct a proof or a scientific test that the definition of "cat" is "a small domesticated carnivorous mammal with soft fur, a short snout, and retractile claws"; you can only point to a dictionary and say that it has to be accepted on faith, accepted as being true without proof.

That isn't faith. That is simply definition. I am not claiming a truth: I am stating how I am using the language.

 

[Axe Elf]

If 1) is false, then nothing about the real world is possible to know. So, it is better to simply *define* the real world via potential observations.

Yes, you can do that, once you have decided to have faith that the real world does indeed exist outside of your own head, and that at least some of your perceptions and sensations reflect that reality.

2) is validated via the scientific method and is certainly NOT a general claim. There are many people whom I do not rust as valid observers. To determine trustability, I use observation and testing.

To perform observation and testing, you are back to #1--having faith in the accuracy of your first-person observations. When the scientific method gets to replication and peer review, then you are at #2--having faith in the testimony of others about their own observations. But for the vast majority of "facts" in most people's lives ("She's getting married in December," "They have three kids," "Your report is due on Friday," etc.), the testimony of trusted others is sufficient to establish fact.

Note that I am not saying this is the best or most conclusive way to establish fact, but merely that many "facts" are indeed based on faith in the second-person testimony of trusted others, just as first-person (personal) experience is based on faith in the real world and our ability to apprehend it.

Faith in the axioms is not required. All that is required to having axioms and rules of deduction. Whether those axioms *apply* to the real world is a matter of observation and testing.

Faith in the axioms IS required if you are to have faith in the theorems as "facts." If I don't have faith in the transitive property, for instance, then I cannot accept that a=c, even knowing that a=b and b=c.

1) All men are mortal.
2) Socrates is a man.
A) Socrates is mortal.

You may accept that 1 and 2 are true, but unless you also accept (let's call it 3) "if 1 and 2 are true, then A must be true," then you are not constrained to recognize the truth of A.

1) All men are mortal.
2) Socrates is a man.
3) If 1 and 2 are true, then A must be true.
A) Socrates is mortal.

But again, you may still accept that 1, 2 and 3 are true, but unless you also accept (let's call it 4) "If 1, 2 and 3 are true, then A must be true," then you are still not constrained to accept that A is true.

1) All men are mortal.
2) Socrates is a man.
3) If 1 and 2 are true, then A must be true.
4) If 1, 2 and 3 are true, then A must be true.
A) Socrates is mortal.

And so on. So yes, you very much have to have faith in the axioms of the system you are using--accept them as being true without proof--before you can do anything useful with the system at all.

 

[Polymath257]

Yes, you can do that, once you have decided to have faith that the real world does indeed exist outside of your own head, and that at least some of your perceptions and sensations reflect that reality.

To perform observation and testing, you are back to #1--having faith in the accuracy of your first-person observations. When the scientific method gets to replication and peer review, then you are at #2--having faith in the testimony of others about their own observations. But for the vast majority of "facts" in most people's lives ("She's getting married in December," "They have three kids," "Your report is due on Friday," etc.), the testimony of trusted others is sufficient to establish fact.

Note that I am not saying this is the best or most conclusive way to establish fact, but merely that many "facts" are indeed based on faith in the second-person testimony of trusted others, just as first-person (personal) experience is based on faith in the real world and our ability to apprehend it.

Of course. And for the vast majority of such claims, there is 1) no reason to lie, and 2) sufficient authority to make the claim. So, in the case of the wedding, the authority for the statement came from a decision the couple made to get married in December and then communicated that decision to others.

This is so completely different than religious faith that I am surprised you can't see the difference. In religious faith, there is not any actual ability to be an authority. So no claims can be supported. No observation can show the claims to be valid nor are they simply a matter of decision.

Faith in the axioms IS required if you are to have faith in the theorems as "facts." If I don't have faith in the transitive property, for instance, then I cannot accept that a=c, even knowing that a=b and b=c.

Again, this is not the same as faith. It is an *assumption* in a formal system. Whether that assumption is useful or not depends on the assumption and the applicability to observation and testing.

1) All men are mortal.
2) Socrates is a man.
A) Socrates is mortal.

You may accept that 1 and 2 are true, but unless you also accept (let's call it 3) "if 1 and 2 are true, then A must be true," then you are not constrained to recognize the truth of A.

Exactly. it is called a rule of inference. That isn't faith. It is simply an assumption for that formal system.

1) All men are mortal.
2) Socrates is a man.
3) If 1 and 2 are true, then A must be true.
A) Socrates is mortal.

But again, you may still accept that 1, 2 and 3 are true, but unless you also accept (let's call it 4) "If 1, 2 and 3 are true, then A must be true," then you are still not constrained to accept that A is true.

1) All men are mortal.
2) Socrates is a man.
3) If 1 and 2 are true, then A must be true.
4) If 1, 2 and 3 are true, then A must be true.
A) Socrates is mortal.

And so on. So yes, you very much have to have faith in the axioms of the system you are using--accept them as being true without proof--before you can do anything useful with the system at all.

Lewis Carroll would be proud.

And again, that is NOT what faith means. In a formal system, there are rules of construction for valid strings (syntax) and rules of inference (proofs). Nobody needs to assume any of these are actually true to do things in the formal system. So no faith is required.

An example: chess is a formal system. it has rules for the initial position (axioms) and rules of inference (moves of the pieces and alteration of moves). I don't have to have faith in chess to play chess. I simply obey the rules.

The exact same happens in *any* formal system, including logic and math.

 

[Axe Elf]

No, those are results of formal systems that are *applied* to aspects of the real world. Whether the formal system is actually applicable is solely determined by observation and testing. So, the computation of area using Euclidean geometry is NOT always a valid use: in particular because the Earth is not flat. That is a matter of observation. The use of Great Circles to determine routes on a globe is also NOT always valid because the Earth is NOT a perfect sphere. That is also a matter of observation.

In every case, whether the formal system *applies* is a matter of observation. The 'factas' of the mathematics do not, in and of themselves, say anything about the real world.

You are splitting irrelevant hairs. Facts (theorems) derived from faith statements (axioms) in formal systems of reasoning do not HAVE to say anything about the real world. Most often, facts about the real world are determined through personal experience and the experiences of others (observation and the scientific process), which, as I have demonstrated, are based in faith as well. But we're talking about abstract facts here, like, "If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other as well." For that fact to be true, you have to have faith in Euclid's definition of parallel lines. The fact (theorem) is based in faith (axioms).

Actually, given the lack of a consistent definition of the noun 'God' and the lack of any observational test for such, I *would* say that most statements about God are literally meaningless.

Well fine, I guess you can say that, but any reasonable person can look around and see that claims of God's existence are profoundly meaningful to a vast majority of Earth's inhabitants. Now, that meaning doesn't imply that God actually EXISTS, mind you--but it does pretty soundly defeat the claim of meaninglessness.

Actually, that isn't semantics. It is syntactics. Syntax has to do with manipulation of formal symbols. Semantics has to do with the meaning of such symbols. For mal systems are syntactical constructs. Whether the formal system applies to the real world is a semantical one and is determined through observation and testing.

Fair enough. So replace "semantics" with "syntax" in my paragraph, and it still stands. Again, you want to appeal to observation and testing, but again, those don't really matter, they just rely on different faith statements. We are still forced to accept that ALL facts are based in faith--faith in personal experience at the most basic level, faith in the testimony of others at the level of second-hand experience, and faith in the axioms of formal systems of reasoning at the most abstract level.

Um no. Definitions are abbreviations. They are true by decree, if you will. We don't *assume* definitions to be true. We make definitions as abbreviations and they are true *by definition*.

Now you're just being silly, right? Definitions are abbreviations? Then why are they usually longer than the word that they define? They ARE true by decree, so long as you have faith in that decree. To say that definitions are true by definition is begging the question. The dictionary definition can't be true just because the dictionary says it is--otherwise everything in the Bible would be true because the Word of God says that it is. The definition of a "cat" is assumed to be true without proof when one wants to talk about cats, just as the definition of parallel lines is assumed to be true without proof when one wants to do Euclidean geometry.

A definition is an axiom is a faith statement.

That isn't faith. That is simply definition. I am not claiming a truth: I am stating how I am using the language.

You can tapdance as quickly as you like, but by defining a word, you are indeed claiming that the definition is true--and that you can offer no proof of its truth, the fact must simply be accepted on faith.

 

[Axe Elf]

Of course. And for the vast majority of such claims, there is 1) no reason to lie, and 2) sufficient authority to make the claim. So, in the case of the wedding, the authority for the statement came from a decision the couple made to get married in December and then communicated that decision to others.

This is so completely different than religious faith that I am surprised you can't see the difference. In religious faith, there is not any actual ability to be an authority. So no claims can be supported. No observation can show the claims to be valid nor are they simply a matter of decision.



Again, this is not the same as faith. It is an *assumption* in a formal system. Whether that assumption is useful or not depends on the assumption and the applicability to observation and testing.



Exactly. it is called a rule of inference. That isn't faith. It is simply an assumption for that formal system.



Lewis Carroll would be proud.

And again, that is NOT what faith means. In a formal system, there are rules of construction for valid strings (syntax) and rules of inference (proofs). Nobody needs to assume any of these are actually true to do things in the formal system. So no faith is required.

An example: chess is a formal system. it has rules for the initial position (axioms) and rules of inference (moves of the pieces and alteration of moves). I don't have to have faith in chess to play chess. I simply obey the rules.

The exact same happens in *any* formal system, including logic and math.

All right, I can see that this is simply beyond your grasp. You keep saying the same things over and over in protest, and I keep having to explain where you are missing the point over and over. I'm sorry that I'm not a better teacher, so that I could find a different way of explaining it to you, in a way that you would understand, but for now... I guess you'll just have to take it on faith that all facts are based in faith.

 

[Polymath257]

You are splitting irrelevant hairs. Facts (theorems) derived from faith statements (axioms) in formal systems of reasoning do not HAVE to say anything about the real world. Most often, facts about the real world are determined through personal experience and the experiences of others (observation and the scientific process), which, as I have demonstrated, are based in faith as well.

And, as per my claim, are derived from observation.

But we're talking about abstract facts here, like, "If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other as well." For that fact to be true, you have to have faith in Euclid's definition of parallel lines. The fact (theorem) is based in faith (axioms).

And I disagree. For one, it is *only* a 'fact' in Euclidean geometry. And it is only a fact in Euclidean geometry because of the axioms and rules of inference of Euclidean geometry. I don't have to assume those axioms and rules of inference are *true* in order to use them to deduce theorems in Euclidean geometry. So it is NOT a matter of faith (assuming them to be true).

Well fine, I guess you can say that, but any reasonable person can look around and see that claims of God's existence are profoundly meaningful to a vast majority of Earth's inhabitants. Now, that meaning doesn't imply that God actually EXISTS, mind you--but it does pretty soundly defeat the claim of meaninglessness.

Fair enough. So replace "semantics" with "syntax" in my paragraph, and it still stands. Again, you want to appeal to observation and testing, but again, those don't really matter, they just rely on different faith statements. We are still forced to accept that ALL facts are based in faith--faith in personal experience at the most basic level, faith in the testimony of others at the level of second-hand experience, and faith in the axioms of formal systems of reasoning at the most abstract level.

No, all *facts* depend on observation and testing. Math and logic are not facts in the sense you are talking about. They do not need to be true since they are simply aspects of a formal system.

Now you're just being silly, right? Definitions are abbreviations? Then why are they usually longer than the word that they define? They ARE true by decree, so long as you have faith in that decree.

A definition states how we abbreviate a longer phrase by a shorter one. So of course the definition is longer than the word defined. That is the whole point.

To say that definitions are true by definition is begging the question. The dictionary definition can't be true just because the dictionary says it is--otherwise everything in the Bible would be true because the Word of God says that it is. The definition of a "cat" is assumed to be true without proof when one wants to talk about cats, just as the definition of parallel lines is assumed to be true without proof when one wants to do Euclidean geometry.

A definition is an axiom is a faith statement.

OK, I completely disagree here. A definition is NOT an axiom. It is an abbreviation. The definitions in a dictionary show how we use language. Nothing else. So the word 'cat' is used to describe a certain type of small mammal. There is nothing at all about that word that *requires* it to be about a small mammal: it is simply a matter of convention. This is easily seen since the words 'chat' and 'gato' can also refer to such small mammals.

You can tapdance as quickly as you like, but by defining a word, you are indeed claiming that the definition is true--and that you can offer no proof of its truth, the fact must simply be accepted on faith.

No, that is simply not how definitions work: we define a concept by stating how we intend to use the language from that point on. It isn't a matter of faith or even truth. It is simply a matter of convention and abbreviation for convenience. So a bachelor is an unmarried man *because* we defined the term 'bachelor' to mean 'unmarried man'. It is a matter of usage of language and nothing else.

 

[Mock Turtle]

I don't know, I'm not British. Google says dodgy is "dishonest or unreliable." Are these claims you can support or should they be considered ad hominem? In what sense am I being dishonest or unreliable?

It's dodgy trying to equate the two. Faith usually doesn't require any concrete evidence - belief does. How much testing of science do you need to test your beliefs? Where would I look to test any faith? As in results obtained.

 

[Polymath257]

All right, I can see that this is simply beyond your grasp. You keep saying the same things over and over in protest, and I keep having to explain where you are missing the point over and over. I'm sorry that I'm not a better teacher, so that I could find a different way of explaining it to you, in a way that you would understand, but for now... I guess you'll just have to take it on faith that all facts are based in faith.

No, I grasp your point. I just disagree with it. Facts are based on observation and testing. Even the applicability of logic and math are determined by observation and testing. Faith, especially in the religious sense, isn't what is going on. If any statement is challenged, there is a set way to resolve the dispute.

 

[Axe Elf]

No, I grasp your point. I just disagree with it. Facts are based on observation and testing. Even the applicability of logic and math are determined by observation and testing. Faith, especially in the religious sense, isn't what is going on. If any statement is challenged, there is a set way to resolve the dispute.

Facts about the "real world" are based on observation and testing. Observation and testing are based in faith--faith in personal experiences and the experiences of others. Ergo, facts about the real world are based in faith. Now if you keep insisting that they are not, that they are in fact based on observation and testing, then I'm really going to have to question my faith in making one last attempt here.

 

[ImmortalFlame]

Google says "complete trust or confidence in someone or something."

By that definition, yes. But there are other definitions of "faith" and it is worth noting that not all of them fit the assertion in the OP.