As I see it, Potter and Holmes have not actually influenced anyone as real agents; those effects are more properly attributed to Rowling and Doyle, along with the creators of subsequent derivative works.

You said that "some x is y" is normally parsed as "there exists some x that is y". I'm saying that's an empirical claim. — Isaac

It is normally parsed that way in formal logic, both modern and Aristotelian, which is the universe of discourse for this thread. In fact, the OP explicitly stipulated modern formal logic as explicated by Bertrand Russell.

What J. K. Rowling and Arthur Conan Doyle have written about Harry Potter and Sherlock Holmes, respectively, is real--their books (and all derivative literature, movies, etc.) are as they are regardless of what anyone thinks about them. However, Harry Potter and Sherlock Holmes are not themselves real, they are fictional--they only are as they are because, and to the extent that, their creators (and others) have thought about them.

But what if the conclusion in the horsey argument isn't about existence? — S

I don't see a problem with that unless you bring existence into it. — S

In both modern and Aristotelian logic, every particular proposition (such as "Some B is C") is about existence in the universe of discourse. In Aristotelian logic, every universal proposition is also about existence in the universe of discourse, since "All A is B" is only true if "Some A is A" is true. The universe of discourse is usually understood to be the actual world, but a different one can be stipulated.

Returning to the example, "Some horses have wings" is true only if the universe of discourse is a fictional world that includes winged horses. The additional premise, "Some winged horses exist," serves the purpose of stipulating just such a universe of discourse.

The truth-maker for a conclusion is whether the conclusion follows from the premises. — Terrapin Station

Right; and in modern deductive logic, the conclusion "Some B is C" does not follow from the premises "All A is B" and "All A is C," since a universal proposition does not entail that the categories corresponding to its terms each have at least one member. An additional premise is required--"Some A is A." In Aristotelian deductive logic, that additional premise is effectively stipulated from the outset by the rule that "All A is B" is only true if "Some A is A" is also true.

More perspicuously, the conclusion "There exists an x, such that x is B and x is C" does not follow from the premises "For any x, if x is A then x is B" and "For any x, if x is A then x is C," since a hypothetical/conditional proposition does not entail the existence of anything in the universe of discourse. An additional premise is required--"There exists an x, such that x is A."

Conflating reality and existence, as usual. Cheers.

What does "continuous motion" mean other than that the intervals of time and distances are infinitely divisible? — Metaphysician Undercover

Infinite divisibility is an insufficient criterion for continuity. After all, the rational numbers are infinitely divisible--thus serving as the basis for Zeno's paradoxes--but no one takes them to be truly continuous. I now find magnification to be a more perspicuous illustration--no matter how much we were to "zoom in" on continuous space-time, we would only ever "see" continuous space-time--never discrete point-instants.

For various purposes, we arbitrarily mark points and instants, and then measure the distances and intervals of time between them by comparing them with arbitrarily established standard units. There is no unit of distance or time embedded in the universe itself, only velocity--the speed of light--consistent with my contention that continuous motion is the more fundamental reality.

Are you familiar with the analogy of the map and the terrain? Spacetime is part of the map. — Metaphysician Undercover

No, space-time itself is the terrain, and mathematical models of it are the map. The latter can be incorrect precisely because they purport to represent something real--that which is as it is regardless of what any individual mind or finite group of minds thinks about it.

However, continuity in the actual distance and time is assumed under the claim of infinite divisibility. The paradoxes are created by that assumption of continuity. — Metaphysician Undercover

We have been over all of this before. Infinite divisibility is a red herring. Continuous motion through space-time is the fundamental reality. An interval of space does not consist of infinitely many discrete positions, and an interval of time does not consist of infinitely many discrete instants.

Are you telling me that the observed behaviour of quantum particles which cannot be explained by the laws of physics, does not indicate to you that the behaviour of these discrete units is inconsistent with the continuity of space-time? — Metaphysician Undercover

I am telling you that I am not aware of any reason to interpret them as inconsistent with the continuity of space-time.

However, the assumption of continuity creates problems like Zeno's paradoxes which demonstrate that the underlying reality is likely not continuous. — Metaphysician Undercover

Huh? The assumption of discreteness is what creates problems like Zeno's paradoxes. As I have said before, recognizing that continuous motion through space-time is a more fundamental reality than discrete positions in space or discrete moments in time dissolves Zeno's paradoxes.

Right, but the space-time continuum is understood by physicists as conceptual. — Metaphysician Undercover

I suspect that would be news to many physicists.

There is no place in the physical realm for a continuous medium, or a need to assume one. — Metaphysician Undercover

Who said anything about the physical realm? This is conflating reality and existence again.

Are you unaware of the uncertainty principle, the measurement problem, and quantum entanglement? — Metaphysician Undercover

I am not aware of any reason to interpret them as inconsistent with the continuity of space-time.

Right, the problem is the form in that the form doesn't guarantee that the conclusion is true. — Terrapin Station

But deductive validity requires that the form must guarantee deriving only true conclusions from true premises.

It is a valid argument form in Aristotelian logic because statements of the form All A is B must have one or more instances in order to be true (just as with Some A is B). — Andrew M

Right, but Aristotle stipulated that additional premise; as your Wikipedia quote states, it was "a thoughtful choice, not an inadvertent omission."

What is measured is the thing itself, and so it is said to have "extension" as extension is assigned to it through measurement. — Metaphysician Undercover

I see it the other way around--measurement is arbitrary; we impose it by comparing something to a discrete unit, but the underlying reality itself is continuous.

... relativity theory, which has a premise that denies the possibility that discrete thing exist in such a medium. — Metaphysician Undercover

I am not aware of any such premise. Relativity theory is the basis for the current scientific understanding of the space-time continuum.

Discrete things do not exist in any medium. There is nothing to warrant that assumption. — Metaphysician Undercover

There is nothing to warrant the assumption that discrete things can exist and interact without a continuous medium within which to do so.

Fundamental particles do not behave in a way consistent with the continuity of space-time. — Metaphysician Undercover

I am not aware of any such evidence. I view the Planck length and Planck time as limitations on observation and measurement, not real discrete units of space-time.

Either we're imagining As with property B in a domain, or there possibly are As in a domain, independent of our imagining. — Terrapin Station

Whether we are imagining them or not, the issue is whether there are any As at all. The proposition "All A is B," or equivalently "For all x, if x is A then x is B," takes no position on this. It simply states that if there are any As, then all of them are Bs. Hence it is not deductively valid to derive the proposition "Some A is B," or equivalently "There exists an x, such that x is A and x is B," since this entails that there is at least one A--a conclusion that was not included in the premise.

It seems quite evident that all there is around discrete things is other discrete things. — Metaphysician Undercover

It seems quite evident to me that there must be a real context within which discrete things exist and react. For example, we say that they have extension in space-time.

If there was such a medium, it would exist as an absolute, against which all the motions of things could be mapped, in an absolute way. — Metaphysician Undercover

First, I am arguing for the reality of space-time, not its existence; as I have stated repeatedly, these terms are not synonymous. Second, there is no necessity for something real to be absolute--the whole point of relativity is that space-time is really relative; as I have also stated repeatedly, continuous motion through space-time is a more fundamental reality than discrete positions in space or discrete moments in time.

No discrete things, or events, behave in a way which is consistent with continuity, that's a big problem. — Metaphysician Undercover

All discrete things and events behave in a way which is consistent with the continuity of space-time. Since you deny this, further discussion would likely be a waste of time.

No particular book recommendation, sorry. Needless to say, there is a lot of helpful material online.

The law of identity is "All A is A." We cannot derive "Some A is A" from that, either. Again, in modern deductive logic it is always a fallacy to derive a particular conclusion from universal premises; such an inference is not necessarily truth-preserving.

Correct--we can derive "It is not the case that some A is not B" from "All A is B." However, we still cannot derive "Some A is B" from either of these without the additional premise, "Some A is A."

Yes, it's an evolving concept. — Metaphysician Undercover

Of course it is a concept, but the issue is whether it is "purely conceptual," as you claim. Why did it have to evolve? Because our understanding changed. Einstein had to think differently in order to resolve observed anomalies that were inconsistent with the thinking of his predecessors. Space-time always was and always will be as it is, regardless of how we think about it; our ultimate goal in studying it is to think about it correctly.

What did you have in mind as a "medium"? — Metaphysician Undercover

A medium cannot consist of discrete things or discrete events, because it is the environment in which those things react and events occur.

Empirical evidence demonstrates to us that all which exists in the world is discrete things. — Metaphysician Undercover

I agree--but continuous space-time is the real environment in which those discrete things exist.

We conceive of continuities and continuums, but we never ever encounter such in the empirical world. So the evidence indicates that continuities and continuums are conceptual whereas the physical world consists of discrete things. — Metaphysician Undercover

What is the warrant for holding that whatever does not exist is necessarily conceptual, rather than real but in a different mode of being? If the discrete things and events that we can and do observe behave in ways that are consistent with continuity, why would we rule out its reality?

What makes the claim the case that if x is A then x is B? — Terrapin Station

I still do not understand the question. We are discussing formal logic, what true conclusions we can--or rather, cannot--derive from that proposition, assuming that it is true.

For all x, if x is A then x is B by virtue of? — Terrapin Station

Sorry, I do not understand this question.

No, a universal proposition does not establish the universe of discourse all by itself. I provided a link, so if you want to disagree with modern categorical logic, I suppose that is your prerogative.

Again, the error is more apparent if we make the quantifications explicit. "All A is B" is equivalent to "For all x, if x is A then x is B"; and "Some A is B" is equivalent to "There exists an x, such that x is A and x is B." Since the former is a hypothetical proposition, a second premise is required in order to derive the latter conclusion; namely, "There exists an x, such that x is A."

I guess you missed my second sentence.

Note that in this context, "existence" pertains to the universe of discourse, which is not necessarily the actual universe. — aletheist

I am not sure why we are having this debate at all; it is an uncontroversial principle of modern deductive logic that deriving "Some A is B" from "All A is B" is a fallacy, unless the universe of discourse is specified separately as including at least one member of A. In other words, it requires the additional premise, "Some A is A."

That's your opinion. Got any support for that opinion? — Metaphysician Undercover

Can you (or anyone else) establish or change the properties of space-time just by thinking differently about them? Or is space-time something that we must investigate in order to ascertain what its properties are, regardless of what we think about it?

Things themselves are the medium of separation between you and I. — Metaphysician Undercover

Sorry, that is not what it means to be a medium.

The continuum is purely conceptual, it's our tool for measuring the discrete things which form the medium. — Metaphysician Undercover

That's your opinion. Got any support for that opinion?

"All A is B" does not entail the existence of any A, but "Some A is B" does; so it is not deductively valid to derive the latter from the former. Note that in this context, "existence" pertains to the universe of discourse, which is not necessarily the actual universe.

Right, and it is not logically valid to derive an existential proposition directly from a universal proposition with the same terms. "All A is B" does not entail "Some A is B."

Correct.

But it's wrong, the argument says "some B are C", not "all B are C". — Nicholas Ferreira

Your statement was, "But can't we imply "some B are C" from "all B are C"?" So the premise was "All B are C," which is equivalent to "For all x, if x is B then x is C"; and the conclusion was "Some B are C," which is equivalent to "There exists an x, such that x is B and x is C"; but this does not follow. An existential quantification cannot be derived from a universal quantification. "If something is a unicorn, then it is a horse with a single horn" is true, but does not entail "Something exists that is a unicorn."

That's because "space-time" is purely conceptual. — Metaphysician Undercover

No, space-time is real--it is as it is regardless of what any individual mind or finite group of minds thinks about it.

What is modeled is the way things behave, the way events occur. There's nothing about the model which says that space-time is something real. — Metaphysician Undercover

On the contrary, space-time is the continuous medium (reality) within which discrete things react and discrete events occur (existence).

If we were to try that with a real line, we'd see discrete atoms. — Devans99

You mean a physical line, which is not the same thing. If you were to "zoom in" on space-time itself--not any physical object within space-time--you would never "see" anything other than continuous space-time.

Continua are illogical, reality is logical, hence continua don't exist in reality. — Devans99

Continua are perfectly logical, just not in strict accordance with the logic of discrete quantity. It straightforwardly begs the question to insist that the latter is the only version of logic that corresponds to reality.

But can't we imply "some B are C" from "all B are C"? — Nicholas Ferreira

No, that is invalid. It becomes more obvious if we reformulate the two propositions as follows.

• For all x, if x is B, then x is C.
• There exists an x, such that x is B and x is C.

The first proposition clearly does not entail the second.

Do you have good reason to believe the theory that predicts the existence of Neptune to be true? — Inis

I stand by my previous answers. Perhaps you should clarify exactly what you mean by "the theory that predicts the existence of Neptune"; or better yet, just spell out whatever point you apparently want to make.

Otherwise, the answer will always be 42. — Banno

When is the answer ever not 42?

So, is the theory, that predicted Neptune true or not? — Inis

I currently have no good reason to doubt that Neptune exists; that is, I believe that the proposition "Neptune exists" is true, where "Neptune" designates a gas giant planet with an orbit outside that of Uranus. As Peirce once put it, "Let us not pretend to doubt in philosophy what we do not doubt in our hearts" (1868).

So you retrodict/deduce/induce that the theory that predicts Neptune is true? — Inis

Again, we adopt the belief that Neptune exists, because the hypothesis that Neptune exists not only explained our initial anomalous observations, but also resulted in predictions that were corroborated by subsequent observations. We then maintain that belief unless and until we have good reason to doubt that Neptune exists.

You retrodict Neptune/Vulcan. — Inis

"Retrodict" is not a word. We hypothesize the existence of Neptune/Vulcan.

You induce corroborations or falsification. — Inis

"Induce" usually means "cause." We conduct experiments and/or make additional observations to evaluate whether the necessary consequences of the hypothesis actually come about. If so, then the hypothesis is corroborated; if not, then it is falsified.

What do we do next? — Inis

We continue evaluating the hypotheses, eventually adopting the corroborated one (e.g., Neptune) as a belief and abandoning the falsified one (e.g., Vulcan).

Geometry reflects reality. If we can't construct it geometrically, its probably does not exist. — Devans99

"Construct" implies building something up from discrete constituents, which cannot be done in the case of a true continuum. I have never claimed that true continua exist, only that they are real. I have already given a specific example of a true continuum in geometry--a line.

If you sub-divide a continuum you get two continua identical to the one you started with - the parts are equal to the whole. Thats a unique and illogical property of continua. — Devans99

Who (besides you) has attributed any such property to a continuum? What I said was that if we were to "zoom in" on a continuous line, we would never "see" anything other than a continuous line.

The anomalous orbit of Uranus/Mercury becomes normal when the statement "Neptune/Vulcan exists" is true, which gives us the good reason to believe that "Neptune/Vulcan exists" is true. — Inis

The existence of Neptune/Vulcan was a valid retroduction--a plausible explanatory hypothesis for the observed (and surprising) anomalies in Uranus's/Mercury's orbit--but again, that is only the first step in any scientific inquiry. The second step was deduction, deriving other necessary consequences of the hypothesis. The third step was induction, making additional observations to ascertain whether those predictions were corroborated or falsified. In the case of Neptune, they were corroborated (repeatedly). In the case of Vulcan, they were falsified, resulting in abandonment of that particular hypothesis.

And by the same logic, we have reason to believe the statement "Vulcan exists", is true? — Inis

What is the observed surprising fact that would be a matter of course if Vulcan exists?

What do you mean by continuous? — Devans99

Exactly what I said before--not composed of discrete parts. If we were to "zoom in" on a continuous line, we would never "see" anything other than a continuous line.

How on earth would you ever construct a continuum? — Devans99

Who said anything about "constructing" a continuum? It is the more fundamental reality.

By what magic processes do you construct something with the property 'each part is equal to its whole'? — Devans99

Who said anything about such an alleged property?

How do we describe time then? The only models of a continua I've seen have used points or line segments to model it. In both cases its valid to discuss the length of the point or line segment representing 'now'. — Devans99

We describe time as continuous--it is not composed of discrete instants or very short durations. Likewise, we describe a line as continuous--it is not composed of discrete dimensionless points or very short line segments. "Now" is an arbitrary human construct that separates what we call "the past" from what we call "the future," but time itself does not really include any such discontinuity.

You can say time is a human construct ... — Devans99

But that is not what I am saying. Time is real and continuous; a durationless instant is an arbitrary human construct.

There was ‘then’ and there is ‘now’ and there is a non-zero distance between them measured in units of what we call time. — Devans99

Measurement is a human construct. We indeed mark two instants as "then" and "now," and measure the non-zero interval of time between them by comparing it to an arbitrary unit--e.g., one second as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom."

Is that a fair representation of Pierce's method? — Inis

Yes, the hypothesis that Neptune exists (A) would make the surprising anomalies in the orbit of Uranus (C) a matter of course; therefore, we have reason to suspect that Neptune exists.

Rather, 'plausibility' looks more like high conditional probability ... — fdrake

Immediately after what I quoted previously, Peirce added that "this acceptance ranges in different cases--and reasonably so--from a mere expression of it in the interrogative mood, as a question meriting attention and reply, up through all appraisals of Plausibility, to uncontrollable inclination to believe."