What structure does time have if it's not a series of instants? — Devans99

It is a true continuum, such that an instant with no duration, or even a very small finite duration, is a strictly hypothetical discontinuity. Rather than being sharply separated, the past and future meet and overlap in the infinitesimal "now."

The analogy is with a mathematical line, which does not consist of individual dimensionless points or tiny finite segments, but instead can always be divided infinitely into shorter and shorter lines. We arbitrarily mark instants of time and measure the intervals between them, just as we arbitrarily mark points on a line and measure the distances between them.

Because space-time is a true continuum, motion/velocity is a more fundamental reality than either position or duration. Incidentally, recognizing this is the key to dissolving Zeno's famous paradoxes.

If A represents B, then B must exist prior to A otherwise there's nothing to represent. — creativesoul

What do words like "unicorn" and "phoenix" represent? If your statement is correct, how are we able to talk about things and events that are in the future - i.e., that do not (yet) exist, and may never actually exist?

Hamlet sets out a plethora of unreal states of affairs. There are true propositions about Hamlet. — creativesoul

There are true propositions about Hamlet (the play) because Hamlet (the play) exists. There are propositions about Hamlet (the character) - such as "Hamlet was the prince of Denmark" - that are true only within the universe of discourse established by the play. Shakespeare really imagined and wrote about Hamlet as the prince of Denmark; but Hamlet was not really the prince of Denmark.

Hamlet (the play) doesn't represent a man named Hamlet who was once the prince of Denmark. Rather it creates him. — creativesoul

The play itself cannot and does not create anything. Shakespeare created the idea of a man named Hamlet who was once the prince of Denmark, and then wrote about it in the play, which represents that idea. That is why Hamlet (the man) is not real - he is as he is entirely because of what Shakespeare thought (and wrote) about him, rather than being as he is regardless of what anyone thinks about him.

Then what’s the difference between that proposition and the fact that it asserts? — Michael Ossipoff

You answered your own question in how you asked it - the proposition asserts a (purported) fact, rather than being a (purported) fact. The difference is between that which represents (proposition) and that which is represented (state of affairs or relation among things) - i.e., between a sign and its object.

... that wouldn't be reasoning about hypothetical states of affairs because I don't think the idea of "fuzzy" states of affairs would be coherent in a metaphysics regarding the physical world. I'm just doing math at that point. — MindForged

That is precisely what Peirce and I mean by "hypothetical states of affairs" as the subject matter of pure mathematics - there is no connection (purported or otherwise) with reality as the subject matter of metaphysics.

Doing logic is not to pick out a type of reasoning as the correct kind. — MindForged

That depends entirely on what we mean by "doing logic."

But logic certainly isn't just normative and to think so is contrary to most of the professional work done in mathematical logic. — MindForged

I agree, but I can see how I might have given a different impression above. Charles Peirce, following his father Benjamin - one of the most accomplished American mathematicians of the 19th century - defined mathematics as the science of reasoning necessarily about hypothetical states of affairs. As such, it includes mathematical logic as distinct from and more fundamental than normative logic. However, deductively ascertaining the consequences of a particular set of postulates does not reveal anything about reality, unless those postulates turn out to be consistent with reality - something that we cannot properly investigate without normative logic.

How can one thing represent something else if that something else does not exist to begin with? There's nothing to represent. — creativesoul

This happens all the time. Shakespeare wrote a play that represents a man named Hamlet who was prince of Denmark. No such person ever actually existed. Signs can represent possibilities and necessities, not just actualities. Reality is not coextensive with existence (more below).

So you do not use this notion of 'facts obtaining'? — creativesoul

Like I said, I tend to avoid it as potentially fostering confusion.

I was confused... dialetheism... para-consistent logic... true contradictions... — creativesoul

Ah, I see. That would have made sense if I had called myself "dialetheist." :grin:

It does not follow from the fact that the same proposition can be expressed in different languages that propositions exist independently of language. — creativesoul

True, but I have not claimed otherwise. Much hinges on what we mean by "exist" in this context. Following Peirce, I define it as reacting with other things. Propositions and other signs do not exist in this sense apart from their embodiment in languages or other sign systems. However, the reality of a proposition does not depend on any (or all) of its actual embodiments - the proposition itself, as a general type rather than an individual token, is as it is regardless of what anyone thinks about it.

Some states of affairs can exist independently of language. Others cannot. Relationships as well... — creativesoul

Agreed. That is basically what I mean by real states of affairs and real relations among things - they are as they are regardless of what anyone thinks (or says, or writes) about them (in a language or other sign system). Some real states/relations also exist - if they are involved in, correspond to, or govern reactions between things.

Apology accepted, although I am still curious - what did you think it meant, such that you suspected me of being comfortable with incoherence/self-contradiction?

Not all states of affairs are fact. All facts are states of affairs. — creativesoul

These two statements are not contradictory. Not all mammals are dogs. All dogs are mammals. In any case, here is what I actually said about facts.

Yes, we established earlier in the thread that facts are real states of affairs or real relations among things; i.e., they are as they are regardless of what anyone thinks about them. — aletheist

Unreal states of affairs are not facts. All facts are real states of affairs. Again, no contradiction.

And by the way, "aletheist" comes from the Greek word "aletheia," which means truth; I am someone who believes in truth.

You've arrived at incoherence(self-contradiction) — creativesoul

Please point out my self-contradiction, so that I may correct it.

Judging by your avatar name, I suspect you do not mind. — creativesoul

What do you think it means?

Not quite; more like: If an infinite community were to engage in infinite inquiry, using any and every method along the way, their ultimate consensus would be that the scientific one - retroduction, deduction, induction - is the most reliable way to arrive at true beliefs.

As should be clear from my previous comments, when discussing logic as a normative science, I mean it in the instrumental sense - we ought to think in a certain way if we want to adopt true beliefs. Going a step farther, I suggest that we ought to adopt true beliefs if we want to avoid unpleasant surprises in our future experiences.

Again, normative logic is not something that we use, it is the study of how we ought to think if we wish to acquire true beliefs - i.e., how we can deliberately improve on our instinctive reasoning habits, which is all that we have at our disposal initially. Peirce recognized four specific methods of inquiry - tenacity, authority, a priori, and science. Each can and does lead to true beliefs under the right circumstances, but only the method of science - consisting of retroduction, deduction, and induction, in that order - has self-correction built into it. It is not the only reliable way to develop true beliefs, but it is the most reliable way, given our inescapable fallibility.

Occam's Razor exhorts us not to multiply entities beyond necessity. But unless there is necessary being, there would be no being at all; this is another way of saying that it is impossible for something to come from absolutely nothing. Therefore, Occam's Razor does not apply to necessary being; i.e., God. After all, Occam himself was a devout Christian theist.

... there are no mutually-inconsistent facts. — Michael Ossipoff

Why not, if everything is hypothetical? Mere possibilities that are mutually inconsistent are not problematic at all; that is just what contingency means. What constrains facts to be consistent with each other, if nothing is real (as it is regardless of what anyone thinks about it) and nothing is actual (reacting with other things)?

A fact--a state of affairs or relation among things--is (by the definition of "proposition") a true proposition. — Michael Ossipoff

So you define a true proposition as a state of affairs or relation among things? Why not just stick with calling the latter a fact? What advantage do you gain by treating "true proposition" and "fact" as synonyms?

These intermediaries of sign, representation, etc aren't incorrect, but they're unnecessary to this topic. — Michael Ossipoff

Perhaps unnecessary, but (in my view) helpful. The benefit of defining a fact as the object of a true proposition is highlighting the representational nature of all propositions.

Why does it provide more clarity to use the term "fact" to refer to the thing which a true proposition represents? Is it better somehow to treat "a state of affairs" and "a fact" as synonyms rather than to treat "true" and "a fact" as synonyms? — Michael

Personally, I find it clearer, perhaps because I consider it important to emphasize the representational nature of a proposition. "Fact" is then a concise term for its object, if it is true.

Words can have more than one meaning. — Michael

Indeed, but in philosophy we often try to narrow down their definitions for the sake of greater conceptual clarity. That is my approach here.

“It is true that” and “it is a fact that” seem to be saying the same thing, so the thing which is true in the first case (a proposition?) is the thing which is a fact in the second case. — Michael

A proposition is true iff it represents a fact, but a fact is not something that can be true or false at all, so a proposition and a fact are not the same thing. When I say, "it is true that all dogs are mammals," I am saying that the proposition, "all dogs are mammals," is true. When I say, "it is a fact that all dogs are mammals," I am saying that the proposition, "all dogs are mammals," represents a fact.

All propositions are language. — creativesoul

Propositions can be (and often are) expressed in language, but are not themselves language, whatever that would mean. The same proposition can be (and often is) expressed in different languages, so the proposition itself does not depend on those languages for its reality as a general sign, only for its existence in particular replicas. I already gave the example of a weathervane as the expression of a proposition without language, although it can be translated into one, such as "the wind is blowing from that direction."

Are facts states of affairs on your view? — creativesoul

Yes, we established earlier in the thread that facts are real states of affairs or real relations among things; i.e., they are as they are regardless of what anyone thinks about them.

What do false propositions represent? — creativesoul

False propositions purport to represent facts, but do not really do so; i.e., they represent unreal states of affairs or unreal relations among things.

Facts obtain if they're real? — creativesoul

All facts are real, so all facts "obtain." A state of affairs or relation among things that does not "obtain" is not a fact. I tend to avoid the use of "obtain" in this context, because in ordinary usage it carries the idea of getting something not previously possessed.

If it's (1) then how can the identification proceed without logic? How can it be determined which method is the best? — andrewk

I am talking about the study of logic, which is basically your (1), and generally agree with . We employ our instinctive reasoning habits (logica utens) all the time, with varying degrees of success. We develop our deliberate reasoning habits (logica docens) for the purpose of reducing error and ideally (but never actually) arriving at a set of beliefs that would never be confounded by subsequent experience.

If it's (2) then it is simply a declaration of faith in FOPL. — andrewk

I am talking about logic in a much broader sense than FOPL, including not only deductive reasoning, but also retroductive and inductive reasoning. It further encompasses the combination of these that serves as the scientific method - formulating explanatory hypotheses (retroduction), explicating their necessary consequences (deduction), and experimenting to ascertain whether they are falsified by experience (induction). All of this depends on the theory of signs and their relations, which also falls within my (and Peirce's) broad conception of logic.

A replica is an actual embodiment of a sign, such that it can be interpreted as such within a particular system of signs. The same word can appear many times on a page or screen, and each of these is a replica of that word. The version of this post that I typed and submitted on my computer is one replica of it; what you are reading now is another.

I never claimed that we ought to use logic if we wish to arrive at true beliefs, I defined logic as the science of how we ought to think if we wish to arrive at true beliefs. I also acknowledged that we have instinctive and uncritical habits of inference, but distinguished them from our deliberate and rigorous habits of inference. The latter are the subject matter of (normative) logic, which recognizes that there is good reasoning and there is bad reasoning.

What exactly do you mean by "existentially dependent"? Following Peirce (again), I would say that propositions - and all signs, for that matter - exist only when embodied in what he called "replicas," which include but are not limited to their expressions in various languages. The same proposition (or other sign) can (and usually does) exist in multiple replicas, which can be in different languages and even other kinds of sign systems. For example, a properly functioning weathervane is a replica of the proposition, "The wind is blowing from that direction."

The trouble with treating logic as normative is that the claim of normativity requires the use of logic, so it becomes circular. — andrewk

Please elaborate on this assessment.

Further, claiming that logic will be useful in the future, as opposed to just observing that it has been useful in the past, runs into Hume's Problem of Induction. — andrewk

Which is a myth. As Peirce observed, "The validity of Induction consists in the fact that it proceeds according to a method which, though it may give provisional results that are incorrect, will yet, if steadily pursued, eventually correct any such error."

Like Hume, I ask, 'whence comes the ought'? — andrewk

Like I already said, it comes from having the purpose of arriving at true beliefs by learning from experience.

No, I agree that the two definitions are incompatible; @andrewk seems to be saying that logic is the science of how humans do think, while I (following Peirce) hold that logic is the science of how any intelligent beings should think, if their purpose is to arrive at true beliefs by learning from experience. This is similar to the distinction that Peirce drew between logica utens, instinctive and uncritical habits of inference, and logica docens, deliberate and rigorous habits of inference. Logic has to be a normative science if there is good reasoning vs. bad reasoning, which I hope no one in this forum would deny.

The suggestion that the physical world consists of the hypothetical setting of a hypothetical experience-story, consisting of a complex system of inter-referring abstract implications about hypothetical propositions about hypothetical things is entirely consistent with our experience of the things and events of our physical surroundings. — Michael Ossipoff

You evidently have a very different definition of "hypothetical" than I and most others do. If everything is hypothetical, then nothing is actual.

No, I defined a fact as a state-of-affairs or a relation among things, and I defined “proposition” in terms of fact. — Michael Ossipoff

So did I - a proposition is a sign that purports to represent a fact, which is a real state of affairs or a real relation among things. A state of affairs or a relation among things cannot be true or false, only a sign can - specifically, a proposition. There are no "true facts" or "false facts," only true propositions (representing facts) and false propositions (not representing facts).

One thing I like about 2c is that it doesn’t need to bring in additional entities such as signs and interpretants. — Michael Ossipoff

What you see as a benefit, I see as a mistake. Again, I think that distinguishing signs from their objects (and their interpretants) is very important in this context. YMMV.

You are basically defining a fact as a true proposition, rather than as the object of a true proposition. This is inconsistent with defining a fact as a real state of affairs or a real relation among things. There is an important distinction between a sign (such as a proposition) and its object (such as a state of affairs); i.e., that which represents vs. that which is represented. There is also a third aspect, the sign's interpretant, which is the effect that it has on an interpreter.

I propose that the facts of the physical world are, ultimately, just abstract facts, like the other abstract facts. ...and that the describable realm (including the physical universes) consists of nothing other than abstract implications about hypothetical propositions about hypothetical things. — Michael Ossipoff

This is what Peirce identified as the subject matter of mathematics - drawing necessary conclusions about hypothetical states of affairs, the universe of pure possibility. The problem with trying to extend it to the actual universe is what he called "the outward clash" - we constantly encounter resistance as we interact with other things; only some of our hypotheses turn out to be consistent with our experience. Inquiry is the process by which we distinguish truth from error - retroduction generates hypotheses, deduction explicates them, and induction evaluates them.

A fact is a state of affairs or a relation among things — Michael Ossipoff

This definition is fine, but a proposition is not itself a state of affairs or a relation among things, so a proposition cannot be a fact. Instead, a proposition represents a state of affairs or a relation among things; i.e., a true proposition represents a fact. In other words, 2c is correct (assuming bivalence) once modified to read as follows: A proposition is a sign that purports to represent a fact, and has a truth-value of "True" or "False," and does represent a fact if and only if its truth-value is "True."

I don't know of any problem that results by letting a kitchen-table be called a false proposition — Michael Ossipoff

A kitchen table is not a proposition at all, because it does not purport to represent a state of affairs or a relation among things, and does not have a truth-value. Even the English expression, "kitchen table," is not a proposition, but a term; it represents a certain general class of things, rather than a state of affairs or a relation among things. However, every proposition involves terms; for example, "some kitchen tables have four legs" is a (true) proposition.

A proposition is or might be a state of affairs or a relation among things? — creativesoul

No, again, a proposition represents a purported state of affairs or a purported relation among things. A true proposition represents a real state of affairs or a real relation among things.

Why "like" being used here? Like denotes that nothing in the real world is representative of something idealized, like Superman? — Posty McPostface

As far as we know, nothing really flies the way that Superman is imagined to do in comic books, television shows, movies, etc. By all appearances, he simply wills himself to fly without activating any particular mechanism for physically doing so. I seem to recall that in the earliest comic books, he was portrayed more as jumping than flying - "leaping over tall buildings in a single bound" - which is perhaps more plausible.

However, Superman is an actuality here. — Posty McPostface

Where? "Flying like Superman" is shorthand for "flying like Superman is imagined to do in comic books, television shows, movies, etc."

So, in your example, Superman is not analytic, yet, we talk about him as a synthetic a priori sense. So, is he a synthetic a priori conception of the human mind, only? I mean, he could exist in a possible world, no? Therefore has he become analytic? — Posty McPostface

As above, and as in the case of Hamlet, we would have to specify the universe of discourse.

So, how is it so obvious that a proposition represents states of affairs? — Posty McPostface

It is obvious that we use language to express propositions. It may not be obvious that propositions represent states of affairs. It should be obvious that words represent all kinds of objects.

What do you mean by "actually" here? — Posty McPostface

Actuality is existence, which is the reaction of things upon one another. If I were to jump off the roof and start flying like Superman, that would be actually flying like Superman. Dreaming about flying like Superman, or imagining that I am flying like Superman, is not actually flying like Superman.

So, what happens to the Principle of Bipolarity? — Posty McPostface

I am not familiar enough with it to say for sure. Why should we rule out propositions that are necessarily true or necessarily false? What kind of necessity is relevant? Does this alleged principle only exclude analytic propositions, such as "all bachelors are unmarried" (necessarily true) and "some bachelors are married" (necessarily false)? My example is not in that category.

States of affairs sounds right. So, what I said was true? — Posty McPostface

To which specific statement are you referring? Obviously we use language to express propositions, which represent states of affairs.

Not true, In the dream, you were flying like superman... — Posty McPostface

Yes, it would be a fact that I was flying like Superman in the dream, but not that I was actually flying like Superman.

True propositions really do represent the actual state of affairs? Is that more succinct? — Posty McPostface

True propositions really do represent real states of affairs. Reality is not limited to the actual; there are also possible and necessary states of affairs that are as they are regardless of what anyone thinks about them, even if they never actually come about. For example, this is a true proposition: If I were to drop a stone while standing on the earth, it would fall to the ground.

Representation of what, then? — Posty McPostface

Whatever you like - states of affairs, qualities, things, habits, etc.

Again, you use 'real' here again. Why is that? — Posty McPostface

A state of affairs that is not real is not a fact. If I were to have a dream in which I was flying like Superman, it would be a fact that I had the dream, but not that I was flying like Superman.

Facts represent things in the world. — Posty McPostface

No, facts are real states of affairs in the world and do not represent anything else. Propositions purport to represent facts. True propositions really do represent facts. Other kinds of signs represent other aspects of the world, including qualities, things, and habits.

What's this "representation" thing doing here in language? — Posty McPostface

I do not understand this question. Language itself is a system of signs, a means of representation.

Hence, what do facts represent? — Posty McPostface

I do not understand this question. Facts are not signs that represent something else; as we established previously, they are real states of affairs. Propositions purport to represent facts, and true propositions really do represent facts.

So, facts are independent of the Principle of Bipolarity? — Posty McPostface

The Principle of Bipolarity has to do with propositions, not facts.

So facts are mind-independent? I thought they were mind-dependent... — Posty McPostface

Facts are independent of any individual mind or finite collection of minds. This does not entail that they are independent of mind in general. If an infinite community were to carry out infinite inquiry, facts are what would be represented in all propositions constituting their consensus beliefs - i.e., the absolute truth.

The present King of France is bald, is a fact that doesn't correspond to reality. What can you say about that? — Posty McPostface

It is not a fact, it is a proposition; and it is not a true proposition, since it does not refer to a real object - there is no present King of France - so it does not even represent a fact. It merely purports to represent a fact, as all propositions do.

What's a "real state of affairs'? — Posty McPostface

The real is that which is as it is regardless of what anyone thinks about it. Consider these three propositions.

• Shakespeare wrote a play called "Hamlet."
• Hamlet was the prince of Denmark within that play.
• Hamlet was actually the prince of Denmark.

The first two are true, and thus represent facts. The third one is false, and thus does not represent a fact, even though it purports to do so.

A fact represents a state of affairs, no? — Posty McPostface

No, a fact is a real state of affairs, which a true proposition represents.

Alright, but isn't a sign a thing? I define things are what are describable and can be referred to. — Michael Ossipoff

By that definition, I suppose so. I was mostly emphasizing that a proposition purports to represent a fact, rather than to be a fact.

What about a false proposition? Is that possible for a fact to represent a false proposition? — Posty McPostface

This is backwards; a fact does not represent anything. A true proposition represents a fact; a false proposition purports to represent a fact, but does not really do so.

A false proposition is still a thing that purports to be a fact. — Michael Ossipoff

No, a proposition is a sign that purports to represent a fact.

I prefer to say that a fact is a state of affairs or a relation among things. — Michael Ossipoff

I agree. A proposition is a sign that purports to represent a fact. A fact is that which is represented by a true proposition.