The question is going to be ambiguous as you can talk about it either in terms of formal logic or physical causality. And then that leads to the issue of how much the two are really the same.

To jump then to what I think is the usual confusion is that most people want entailment to be a story of efficient causes. One particular thing causes that particular thing. This step dictates that step in mechanically necessary fashion.

But the larger view of deduction or causation is the holistic story where the process is one of constraints upon freedoms (or uncertainties). So the argument goes from the general to the particular, not the particular to the particular.

If Kermit is a frog, and all frogs are green, then Kermit is green by logical consequence. That is, the general constraint of "being a frog" is a limit on the colour some particular frog can be. But Kermit could be light green, forest green, aquamarine, and still meet the constraint. The actual shade of green becomes the residual freedom, the further fact about which the statements so far appear indifferent.

So reasoning deductively is about boxing in uncertainty. Information is added to limit the scope of the (Kantian) unknown. And even physical causality has this general nature - according to quantum physics now.

I have been thinking about contingency recently, how the only necessary notion is that everything is contingent. If p is given, then it must necessarily entails -p, as a contingent possibility. That's how I understand entailment.

The given always appears against a background of other possible worlds?

So reasoning deductively is about boxing in uncertainty. — apokrisis

Uncertainty on the part of whom?

What is given could have always been otherwise. What does bringing other worlds into this context add? Must the positing of an absolutely contingent world entail the possibility of an absolutely necessary world?

Uncertainty on the part of whom? — Mongrel

Depends. It could be a particular inquiring mind or it could simply be the world physically.

That would be the advantage of my semiotic approach. It applies the same way in either sphere.

You can define entailment model-theoretically. For any model, if if A is true relative to that model, then B is true relative to that model, then A entails B.

When it comes to applying logic, there is certainty by virtue of the knowledge of necessity or uncertainty by virtue of ignorance.

The world is physically ignorant? That appears to be word salad.

What is given could have always been otherwise. What does bringing other worlds into this context add? Must the positing of an absolutely contingent world entail the possibility of an absolutely necessary world? — Cavacava

I'll have to ponder this. Just as an aside.. you're sounding a little like Yoda.

You can define entailment model-theoretically. For any model, if if A is true relative to that model, then B is true relative to that model, then A entails B. — The Great Whatever

Would it be possible to model the actual world?

dun't matter what you're modeling.

You ignored that I specified ignorance due to indifference. So that is where my position is based on a full four causes analysis. Purposes are alway in play. Thus even physically, there can be differences that don't make a difference. We could call them thermal fluctuations or virtual events.

How do you understand entailment? Does it come down to necessity? Reasoning? — Mongrel

I used to puzzle over this quite a lot - assuming that what you're actually asking is about the meaning of logic. In the end I dissolved the puzzle by concluding it's just a language game. We play the game because we have found it useful in the past and we are programmed by evolution to believe that things that have been useful in the past will be useful in the future.

Under that interpretation, the statement that A entails B just means that the two events, or propositions, satisfy a certain relationship that is specified in the language game we call logic.

X entails y is the same as y is implied by x, in the sense of y validly following from x.

You need to know what validity is to understand that. Traditionally, validity obtains when it's impossible that premises are true and a conclusion false, where traditionally, "and" in that definition is parsed as "either/or," so that validity obtains when either (a) it's impossible that premises are true, or (b) it's impossible that the conclusion is false, or (c) both (a) and (b).

This is relative to the particular species of logic being employed, so that validity, and thus entailment, are going to be different in traditional, bivalent logic with excluded middle versus relevance logics, paraconsistent logic, etc.

Entailment is simply another term for 'logical necessity'.

An entailment is a deduction or implication, that is, something that follows logically from or is implied by something else. In logic, an entailment is the relationship between sentences whereby one sentence will be true if all the others are also true.

What this ought to entail is that 'entailment' is the relationship between ideas.

What is given could have always been otherwise. What does bringing other worlds into this context add? Must the positing of an absolutely contingent world entail the possibility of an absolutely necessary world? — Cavacava

Well true propositions represent aspects of the actual world.. What do false propositions represent? Some of them could be said to represent other possible worlds. Just as the actual world stands out in thought against a background of other possible words, true propositions stand out against a background of false ones.

So let's say I have a model M of the actual world from start to finish. Any proposition that is true of M entails ALL other propositions that are true of M.

Under that interpretation, the statement that A entails B just means that the two events, or propositions, satisfy a certain relationship that is specified in the language game we call logic. — andrewk

But rule following has to be anchored somewhere. Quine showed (in Truth by Convention) that in regard to application of logic, the anchor can't be anything external. It's apriori. Do you agree with that?

So you're echoing what TGW said.. that it's an if/then situation.

Any proposition that is true of M entails ALL other propositions that are true of M. — Mongrel

Someone might have that view, but it would be very unusual, including that it wouldn't be clear what they'd have in mind by entailment. On the surface of it, it would appear that maybe they see every fact as a necessary fact that is somehow causally connected to every other fact, and they're doing something that seems like a conflation of causality and implication (but they might have a different explanation that would make that not a conflation--again, it would partially depend on how they're thinking of entailment).

I agree with him that it's relative to something--although it's relative to the logical "system" we're employing, not (just) a(ny) "model," And I don't agree with him beyond that. Both A and B being true relative to some system or model doesn't amount to A or B entailing each other. Entailment is a matter of implication or logical following, and that's a matter of validity with respect to argumentation. A is only entailed by B if B implies A. That is, if A follows from B. Both A and B being true with respect to M isn't sufficient for B to imply A.

Say that we had a model (hopefully without needing to argue just what a model is) that encompassed mathematics. Well, that 2+2=4 doesn't imply that C=2πr, even though both are true in that model.

Do you think entailment is sense dependent or reference dependent. Sense dependent is epistemological and reference dependent is ontological. If you cannot understand a concept (A) without understanding another concept (B), then the concept (A) is sense dependent and a question of knowledge. If concept (A) cannot be without a concept (B) it is reference dependent, and a ontological issue. So, is entailment epistemological?

[as an aside, around midnight I feel like Yoda]

Not the most intelligent question ever asked — Mongrel

Clearly ;)

Do you think entailment is sense dependent or reference dependent. Sense dependent is epistemological and reference dependent is ontological. If you cannot understand a concept (A) without understanding another concept (B), then the concept (A) is sense dependent and a question of knowledge. If concept (A) cannot be without a concept (B) it is reference dependent, and a ontological issue. So, is entailment epistemological? — Cavacava

I think it's epistemological. For instance:

A: I said, "I have a dog."

If one knew everything about my dog, one would know all sorts of things about how she relates to aspects of the universe... that she likes tennis balls, that she weighs 15 lbs, how far she is from Neptune, and so on. These are truths entailed by A. Is that right?

That's sort of making use of Leibniz's complete individual concept.

I agree with him that it's relative to something--although it's relative to the logical "system" we're employing, not (just) a(ny) "model," — Terrapin Station

I think we do have to have some model because just logical possibility will become so open-ended that it's meaningless.

A: I said, "I have a dog."

All sorts of things are logically possible here.. but I don't think all those things are entailed. I think entailment is more about how any particular thing is related to everything else. Logic is on the scene, but only because models necessarily employ some sort of logic.

It's not just whether something is logically possible. Entailment is implication, or that something follows from something else.

Things follow from "I have a dog," but it's easier to understand first if you understand it in terms of an argument, so that we have a set (>1) of premises.

So, for example, "I have a dog" and "all dogs are creatures with hearts." From that, "I have a creature with a heart" is entailed--that is, it's implied by the two premises, or it follows from them.

Or, "I have a dog" and "All dogs are animals named Fido." It's entailed by that that you have an animal named Fido. Of course, the second premise in this case isn't true--not all dogs are animals named Fido, but that doesn't matter for entailment. Entailment is about what is implied by or what follows from something. "I have a dog," "All dogs are animals named Fido," "Therefore I have an animal named Fido" is a valid argument. (It's just not sound, since soundness hinges on the premises being true.) But entailment obtains when we have a valid argument. In a valid argument, the conclusion is entailed by the premises.

So it's not just any logical possibility.

Re "I have a dog," by the way, as I mentioned before, there are things that are entailed by that, but they're limited to things like "There are dogs," "There is something called 'I'," "'I''s can have possession of things," and even "I have a dog" (that's simply "If P, then P").

I don't know if I agree with it in general. I am dubious about words like 'anchoring'. But in this case it seems an OK question, the answer to which, I think, is that it is anchored in our nature: we are programmed by evolution to be inclined to follow the rules of the logic game.

I think the ability to see what is entailed by propositions and situations must be an intuitive capacity; entailment is simply knowable a priori and cannot be analyzed further.

A: I said, "I have a dog."

If one knew everything about my dog, one would know all sorts of things about how she relates to aspects of the universe... that she likes tennis balls, that she weighs 15 lbs, how far she is from Neptune, and so on. These are truths entailed by A. Is that right? — Mongrel

Things follow from "I have a dog," but it's easier to understand first if you understand it in terms of an argument, so that we have a set (>1) of premises. — Terrapin Station

This illustrates how entailment is "mechanical". It claims states of constraint that are absolute. And speaks to the way such states can be constructed.

So as I say, the physical reality is different. Constraints can never be absolute. Freedoms - either as ontic material entropy or epistemic informational uncertainty - can only be minimised, not eliminated. It is an important discovered fact of nature that it is indeterministic in the final analysis.

Also, constraints in nature tend to be contextual or holistic. A mountain or an earthquake are events produced by circumstances not of their own making. It is the accidents of plate tectonics and other geomorphic forces that entail the building of a mountain, the fissuring of a fault-line.

So there is a way that nature is.

Then life and mind come along and can play logical (or semiotic) tricks. They are modellers in a modelling relation with the world (a model being a formal system of entailment connected to the world by "acts of measurement").

So a modeller seeks to impose constraints on freedoms (ontic or epistemic, material or informational) in pursuit of some overarching purpose. There has to be a reason for being reasonable. And while it is still impossible for such constraints on nature to be absolute, it is not that hard for constraints to be "good enough" to achieve a purpose. A model can be indifferent to any difference which doesn't make a difference (to it).

And where a modeller really wins out over nature is the ability to construct states of constraint. A modeller can stick bits of an argument together to form some strait-jacket arrangement which forces nature into some tight corner.

That is the basis of the mechanistic view of reality. Petrol vapour explodes given a spark. But if you wrap that explosion around with pistons, cylinders, crankshafts and all the other bits of an engine - plus have control over the timing of the vapour puffed into a cavity, and the spark that ignites it - you are in business. You can drive right over nature in your SUV.

All life constructs these kinds of mechanisms. A bird makes a nest to protect its eggs. A spider spins a web to trap flies. At work is a mind that can build something that serves a purpose in mechanical step by step fashion.

So if we are looking for the origins of logic, for the reasons why it might be an abstraction that works, it is easy enough to see those origins in the rise of life and mind as a semiotic modelling relation.

First comes the ability to impose some state of constraint on nature (one that serves a purpose and is not merely an accident). And then comes the ability to assemble systems of constraint, step by step.

Thus entailment is indeed all about implication. It is about constructing states of constraint (material or informational) that restrict nature to such a degree it has no choice but to behave in a desired way. The rules of logic are all about encoding that biological imperative - the modelling relation - in the most abstract and universal set of rules we can imagine.

Again, the fact that nature is at base indeteministic - incapable of being completely constrained, is something that is left out of normal discussions of logic and thus results in great confusion when it comes to non-pragmatic "theories of truth".

But pragmatically, it's not a big deal as naturally all the attention of logic-users goes to what logical thinking can achieve. So it is the ability to construct arguments - formal systems of entailment - that gets celebrated. It is a remarkable fact that modellers can regulate the world to the degree that their desires can be reliably cashed out in systems of logical necessitation.

We can just get in our cars and ... drive.

This illustrates how entailment is "mechanical". It claims states of constraint that are absolute. And speaks to the way such states can be constructed.

So as I say, the physical reality is different. Constraints can never be absolute. Freedoms - either as ontic material entropy or epistemic informational uncertainty - can only be minimised, not eliminated. It is an important discovered fact of nature that it is indeterministic in the final analysis . . . — apokrisis

Like usual, I haven't the faintest idea what you're talking about. Even things that seem to me should be simple I don't get. For example, "It claims states of constraint"--I'm not sure what "It" is given the way you've constructed your sentences. I just can't follow you most of the time.