If we had no mathematical symbols could we have mathematical facts? — Athena

I'd like to hear what you think.

That something is what people say is a fact, but what they say is not made a fact by their saying it. — Srap Tasmaner

I'll bet you $5 that I can make something a fact just by saying it.

What is said exactly is made a fact by the saying. "I name this ship the Queen Elizabeth" can make it a fact that the ship has that name. — Banno

I'll bet you $5 that I can make something a fact just by saying it. — InPitzotl

Guys, I know what speech acts are. I even nodded at the concept by describing stipulative rules as a case of "saying it's so makes it so".

Note that the act of christening a ship is exactly that: it is, by performing that act, in the correct way in the correct circumstances, of conferring a name upon a ship by speaking certain words. That's not even in the ballpark of the words spoken at such a ceremony being a statement of fact. Not even if the particular words required for the christening to count are, "The name of this ship is the USS Banno."

If there the ceremony has gone off as it was supposed to, is it now a statement of fact to say "The name of that ship is the Banno"? I guess, kinda. On the one hand, if you take names as a sort of capsule history that reaches back to the baptism, then to claim that an object has a particular name is an historical claim about who said what about that object when, and that's obviously a factual matter. On the other hand, names are dependent on usage just like other words we can't trace to a baptism, or presume that we could. A person's legal name may require particular procedures to change, but otherwise names can come and go. (Here, I've looked up one: the Flatiron Building was originally the Fuller Building and nicknamed "Eno's flatiron", then widely called "the Flatiron", and eventually officially (I don't know how) named "the Flatiron Building". Persons tend to have even more say in what their name is than buildings.)

So, there as well, insofar as we're talking about the facts of the moment, how people use some word as a name to refer to some object, sure, and nothing I said contradicts that. But those are facts that are very much in play and that we might even participate in changing, precisely because they are facts about how we use particular words. ("You always call him 'Butthead'." "Yeah, I used to but then I felt bad, so I haven't called him that in weeks.") I'd be reluctant to say that everything we express in words is just a statement about how we use words.

Unless names are not facts. — Banno

I suppose I'm okay with names counting as facts, for the reasons given above, but I'm not enthusiastic about it. Fact and stipulation -- baptism being a kind of stipulation, right? -- just shouldn't end up together. Talking classification with @Athena, I think I can distinguish everything I want to: that we call animals like this "dogs" is a fact; that that animal there is a dog, is a fact, given our criteria; that what we call "dogs" are dogs -- no, not a fact, just an explanation of what we mean by "dog"; that all dogs are dogs -- not a fact, just a tautology. Names are a little trickier to get around in the same way, aren't they?

Maybe you could persuade me that stipulations and tautologies should count as facts, but for now they feel way different to me. I suspect we talk about them differently too, but I'm not going to get into that unless we have to.

A question - is that the area of a circle is given by   π r² a fact? — Banno

So you'd rather not call this formula a fact?

Maybe you could persuade me that stipulations and tautologies should count as facts — Srap Tasmaner

I'm positing that post facto, it is a fact that the bishop moves diagonally. The point being to show that facts are not solely the result of observation.

The act of naming brings about the fact of the name referring.

Fact and stipulation -- baptism being a kind of stipulation, right? -- just shouldn't end up together. — Srap Tasmaner

If a ship is christened, the name is a kind of stipulation. That the ship henceforward becomes known by the name it was christened with (if it does) is a fact. I see no problem here.

A question - is that the area of a circle is given by π r² a fact? — Banno


So you'd rather not call this formula a fact? — Banno

I'm not much invested either way. Whether you throw mathematical theorems into the fact box or not, you're still going to end up talking about them differently. The procedure for verifying a "mathematical fact" bears no resemblance at all to the procedure for verifying any kind of empirical fact. If we use "fact" because it's handy and gets the point across, especially with children or the math-challenged, I won't squawk. But it would be nice to get them to the point where they can just say "theorem".

How do you feel about this formula?

$C = \pi d$

Is that a fact?

The act of naming brings about the fact of the name referring. — Banno

In which case, "name" is there used as a success verb, right? Otherwise, no reference. So what you're saying is that naming is naming. Yeah, I'm okay with that.

I'm positing that post facto, it is a fact that the bishop moves diagonally. The point being to show that facts are not solely the result of observation.

The act of naming brings about the fact of the name referring. — Banno

It is a fact that when people play chess the bishop is always moved diagonally, and this fact is not a result of observation (unless you mean 'observing the rule'). But this fact is determined by observation.

The act of naming does not bring about the fact of the name referring, but rather it is the fact that people use the name to refer that establishes the fact of its referring.

How do you feel about this formula?

C=πd

Is that a fact? — Srap Tasmaner

No, it's a formula. It's a fact that people use it to determine the circumference of circles, though. Does it represent a fact? If it is a fact that the circumference if any circle is equal to pi multiplied by the diameter then yes.

If a ship is christened, the name is a kind of stipulation. That the ship henceforward becomes known by the name it was christened with (if it does) is a fact. I see no problem here. — Janus

I really thought that's what I said, but said it acknowledging that names are a little weird.

Why does everyone go straight for names and math, areas that are notoriously odd, with generations-long debates over how to deal with them? Hard cases make bad law.

That response was more for Banno's benefit than yours...in case stipulation and fact were ending up together in his mind. :wink:

No, it's a formula. It's a fact that people use it to determine the circumference of circles, though. Does it represent a fact? If it is a fact that the circumference is equal to pi multiplied by the diameter then yes. — Janus

I was thinking of it as the definition of $\pi$ most people learn first. They may learn other identities later, and thus other ways of deriving $\pi$, but something somewhere has to count as a definition of the symbol.

I'm fine with saying it's a fact that we use the symbol the way we do, but that doesn't make the definition itself a fact, does it?

Not "a statement of fact", if that's any clearer.

Pretty much agree. I wasn't expecting anything controversial.

I'm fine with saying it's a fact that we use the symbol the way we do, but that doesn't make the definition itself a fact, does it? — Srap Tasmaner

I guess it kind of does, but like all tautologies it's empty and doesn't seem to deserve the status of fact. Like saying it's a fact that all bachelors are unmarried, or that something is identical to itself.

I share that intuition that tautologies shouldn't count. Either because they carry no information, or the information they carry is only the indirect sort that almost all statements carry, indicating something of how we use symbols.

If it's helpful to call them "facts" because it gets the point across, cool. It is also odd but a known fact that making a tautologous statement to someone can count as communication, even when it's not a matter of explaining our use of symbols. People also say, "It is what it is," and others nod in solemn agreement. Language is some weird shit.

All of this by way of showing that using "fact" to talk only about observations is obtuse. — Banno

Last day or so I've trying half-heartedly to form a thought about this, and maybe you have something to add.

Let's say we have reason to think disentangling theory from observation is a non-starter. (I was thinking this might be congenial to you for Davidsonian reasons, death to "conceptual schemes" and all that.)

We might, in addition, have reason to think that theories, even if we have some way of defining them -- which might happen in a moment, or might not -- aren't themselves bedrock, but are always embedded in a natural language. (I floated part of this idea in the discussion of Curry's paradox, when I was talking about the role of "Let P = the statement ...") Historically, this is just obviously true. But maybe it's also necessarily true, or necessary enough for our needs.

With those two points, I've been thinking maybe facts are exactly the right battle-line for theories, if we take "theory" to mean something like a set of statements you treat as factual (whether true or false) or simply as a set of facts (factual statements you count as true), though both looks the most promising. The idea is that maybe natural language is all you need to have such a fight, and you pass right by both incommensurability and the abyss of the Quine-Duhem thesis. We get to ignore the latter because if you count the same statements as factual and the same statements as facts, you're the same theory, end of story. Anything else would be, for us, a difference that makes no difference.

And as it happens, this gets us pretty close to the ground again, because ordinary people do fight over facts and over what's factual. Having tried for a while to have a theory of theories, we could give it up for a bad job and go back to fighting over facts like everyone else.

People also say, "It is what it is," and others nod in solemn agreement. Language is some weird shit. — Srap Tasmaner

Translation: "Shit happens". :wink:

Maybe you could persuade me that stipulations and tautologies should count as facts, but for now they feel way different to me. — Srap Tasmaner

You didn't really discuss my bet at all. I didn't name anything; I "made a bet".

ETA:

Maybe you could persuade me that stipulations and tautologies should count as facts, but for now they feel way different to me. — Srap Tasmaner

Might I suggest there are different "kinds" of facts, and they feel different because they're doing different things? But along those lines, "water molecules are composed of two hydrogen atoms and one oxygen atom", "bishops always stay on their own color", and "Joe is married to Sue" all feel different to me... IOW, perhaps a taxonomy of facts would be preferred to a refinement of the concept?

the abyss of the Quine-Duhem thesis. — Srap Tasmaner

A bit of a dramatic way to put it... Duhem-Quine is but a rehash of Francis Bacon's "we need to put nature to the question". As Collingwood observes, Bacon was a lawyer and knew that this meant: "we need to put nature to torture in order to get answers". Hence the modern form of scientific experiments, in highly artificialized settings. There never was a scientific experimentation without a theoretical framework underpinning the "question being put", at least since Bacon. All knowledge proceeds through questions and answers. You can't have answers if you don't ask questions first, and questions proceed from a "line of questioning", i.e. from some framework. I wouldn't worry about that too much.

Is what not a fact? That animals we've classified as canines are what we've classified them as? That they share certain characteristics we used to define the box we put them in?

Call it a fact if you like. I wouldn't. I'd agree that it's a fact this is how zoologists classify animals. It's a fact that I have to work today. It's a fact that men landed on the moon in 1969. It's a fact that Joe Biden won the 2020 election. — Srap Tasmaner

Yeap, I think what you said is a fact. I think you are working really hard to have an argument. :lol: Isn't that a little uptight? Maybe the main cause of the violence in our society is people taking themselves way too seriously and believing they have something to fight about. You might try some peaceful music and chill out.

Yes, the same facts can be expressed in different languages. There are facts of conformation and characteristic that have been criteria for classification of animals, plants and other natural kinds; that seems to be what you are getting at, and I agree. — Janus

Well, it was not my intention to make that point, but it seems to come out of the discussion. I have not given the subject a lot of thought before but through the discussion, I am realizing an appreciation for why we have the word "spell" which means the letters we use for a word and also the power of the word to affect what is so. There is something magical about the word. Like there is something magical about math. This is beyond accepted materialistic thinking and I am not sure if anyone wants to go that far?

My reason for starting this thread is we argue so much about theoretical things that can not be validated and many of our arguments are opinions and not facts. Clear thinking seems to depend on our awareness of the category of our arguments. As I tell the kids arguing in the back seat of my car- stop arguing, we can check the facts, and then we will know who is correct. I love arguing points because you all open my mind and expand my consciousness, but I really hate it when the arguing gets unpleasant and has nothing to do with facts!

I'd like to hear what you think. — Banno

Oh my, as I just said about words and math, I am not sure of this metaphysical reality. It is not 3-dimensional physical reality. Pi is mind-blowing with some definite mystical qualities. We can not even think of it without a word to name it or a symbol to represent it, but as we have explored pi we have discovered it has profound consequences in our lives.

We can not even think of it without a word to name it or a symbol to represent it, but as we have explored pi we have discovered it has profound consequences in our lives. — Athena

Which are these profound consequences? We can easily set pi to one. But what will be become of one in this case?

I'll bet you $5 that I can make something a fact just by saying it. — InPitzotl

Hum, what mystical power do you have that you can make something a fact? Any of us can state a fact but how can we make one?

Everyone may know what a fact is but I am not sure what everyone thinks a fact is. I have a second question to ask when there is an answer to what a fact is. — Athena

I'm not so sure everyone knows what a fact is.

I like Banno's reply for starters.

There's a couple of uses for the word.

A fact is a statement that is true.

It is also the state of affairs set out by a true statement. — Banno

These exemplify the two sorts of use of the term I'm most accustomed to encounter in philosophical conversations. I believe I tend to favor the second sort of use in my own speech, though it's often hard to tell the difference.

How do you know it's true? — tim wood

aaha, you asked the second question. — Athena

Was that really the second question? (Or how else might you express the "second question" you had in mind?)

It's a good question. I don't think it supports an objection to Banno's rather standard definitions, though I have the impression Tim may have intended it that way.

My reason for starting this thread is we argue so much about theoretical things that can not be validated and many of our arguments are opinions and not facts. — Athena

I strongly agree that too much time is squandered in philosophical disputes in which it seems there is no objective standard or criterion available to settle the matter. I suggest it's one of the more important tasks of the philosopher to identify such controversies and put them to rest.

So you'd rather not call this formula a fact? — Banno

It is a fact. But we constructed it. In nature this does not exist. It's projected by means of a mathematical net. Thrown over the physical universe. There are no inherent areas of circles. After the orojection only.

Hum, what mystical power do you have that you can make something a fact? Any of us can state a fact but how can we make one? — Athena

Well for one, the power to make a bet by stating that I'm making one. It's a fact that I made that bet; a fact made true by the fact that I stated that I made it (is that not how bets are made?)

It's a fact that I made that bet; a fact made true by the fact that I stated that I made it (is that not how bets are made?) — InPitzotl

For the record, no, that's not how bets are made. Like the christening of a ship or any other speech act, it requires specific circumstances and the cooperation of others. People also use the language of wagers to indicate firm belief ("I'll bet a million bucks Jerry's gonna be late today"). We use the same language to challenge each other to contests: "Bet I can beat you to the mailbox" might be met with "You're on!" and the kids race, or with "Loser takes out the trash?" in which case there's now an actual wager being offered, but it's still not a wager until the other says "Deal!"

The whole reason Austin developed the theory of performative utterance was to point out that not every utterance is a factual statement. "Bet I can beat you to the mailbox" might be a challenge, might be the first step in negotiating a wager, but it is still not itself a factual statement. Everytime you speak someone -- you included -- could make factual statements about you having spoken and what you said. Same here for issuing a challenge or making a wager.

Facts are like truths in that they come in degrees. The relationship between some statement and some state-of-affairs is a fact/fiction or a truth/falsehood. The more some statement accurately describes some state-of-affairs, the more factual/truthful it is, and vice versa for fictions and falsehoods. The boundary one decides on where some statement is more factual than fictional can depend on what is being talked about and how detailed you need to be.

For the record, no, that's not how bets are made. — Srap Tasmaner

You have failed to make your case.

Like the christening of a ship or any other speech act, it requires specific circumstances — Srap Tasmaner

"I'll bet a million bucks Jerry's gonna be late today" — Srap Tasmaner

You're over-interpreting here. A claim that x is how y happens (in this context) is a claim about means, not sufficiency. That the speaker can use the language of making a bet without really making one does not refute that this is how bets are made.

For example, we propel bicycles by pushing on their pedals, but that requires specific circumstances (wheels on the ground, you on the seat, chain hooked up, etc). Nevertheless, that is indeed how we propel bicycles. To say that this isn't how we propel bicycles because if the chain weren't there it wouldn't work would just be silly; there's nothing in the claim that this is how we propel bicycles that purports this to be sufficient.

Arguably, the speaker's probably (but not necessarily) making a bet anyway; they're just being satirical about the wager. (A case where the speaker might not be making a bet may be if the speaker is teasing; e.g., using that language to suggest Jerry may have had lots of fun last night).

and the cooperation of others. — Srap Tasmaner

"Bet I can beat you to the mailbox" might be met with "You're on!" and the kids race, — Srap Tasmaner

Let's call the person who said "Bet I can beat you to the mailbox" Jack, and "You're on!" Joe.

In natural English, Joe may say "Jack bet me that he could beat me to the mailbox; naturally, I accepted".

Let's say, instead, that Joe said "No way!". In natural English, Joe may say "Jack bet me that he could beat me to the mailbox, but I didn't feel like a race so I refused the bet."

What you seem to be doing here is considering a bet only having been made when it is accepted. But this does not match the language usage above, where bets are made when they are offered.

or with "Loser takes out the trash?" in which case there's now an actual wager being offered, but it's still not a wager until the other says "Deal!"

...this is just negotiating a wager.

So to summarize, you're suggesting that I'm wrong by misinterpreting a claim of means as a claim of sufficiency. Next you're suggesting I'm wrong by misinterpreting "to make a bet" as applying to acceptance as opposed to offer. And finally, there's that wager negotiation part, but I'm not sure what to make of it because prior to the negotiation your example explicitly uses the term "bet" (I'm not sure you're even suggesting it's not a bet until it has a negotiated wager?)

To say that this isn't how we propel bicycles because if the chain weren't there it wouldn't work would just be silly; there's nothing in the claim that this is how we propel bicycles that purports this to be sufficient. — InPitzotl

Perhaps I misunderstood you. I thought you had claimed that because you had said something like "I bet $5 I can make a fact by saying something" you must have made a bet; I don't think that's true. Consider your example here: if I had just reassembled the crankset after repacking it with grease, and were now turning the crank to see if it spins smoothly, I would not be propelling a bicycle, I would not even intend to be propelling a bicycle. Fine, you say, it's necessary but not sufficient; but it's not necessary either, because you can also walk alongside it pushing the handlebars or run along behind someone pushing on the seat while they steer. Just so, given the right circumstances you can place a bet just by sliding some chips across a table or buying a ticket from some guy sitting behind a little window. The words "I bet ..." are neither necessary nor sufficient to create the fact of a bet having been made.