If you're of a mind, and not burned out on the topic, take another swing at it. It is, after all, a philosophy forum not a math forum. Maybe if you could explain a little more clearly how your problem relates to mathematics without being a mathematical problem, we could make some progress. — Srap Tasmaner

To properly address this, I believe there first ought to be a commonly understood or accepted, philosophical (rather than one pertaining to established schools of mathematics) differentiation between types of concepts regarding the notion of infinity (again, infinity not as its is mathematically defined but as a general, sometimes philosophical, notion: commonly defined by the absence of (non-mathematically defined) “limits” to that addressed).

I don’t know. Once bitten twice shy. This thread’s issue can to my mind be easily overtaken by a broader philosophical issue and possible underlying stance. Namely, one of whether a) mathematics subsumes all reality (such as, for example, by grounding all of physics and, via further inference, thereby all of physicality … this being one example of what could be termed a “neo-Pythagorean” view) or, else, b) reality holds aspects which can be in part and imperfectly modeled by what we humans have devised - over the long course of history you address - as various schools of mathematical thought.

So, does the mathematician’s specialized definition of countability thereby take precedence over what layman understandings (such as the two Wiktionary definitions of infinity previously provided) of countability are? This on account of stance (a). Or else is the so here termed “mathematical” notion of “countability” a specialized understanding that is subsumed by commonly accepted every day notions of countability in general, namely "the capacity to count quantities"? As would naturally be the case in scenario (b).

Must I express “non-mathematical” for every term I use in attempts to define a certain species of concepts regarding infinity?

But then, what on earth would “the ‘non-mathematical’ countably of infinity” signify to a general audience?! To be countable but not mathematical is a bit of a conceptual contradiction.

Yes, I’m a little frustrated, maybe blowing off my own steam. But help me out a bit if you can.

Can we at least mutually understand a differentiation between “quantifiable infinity” which can thereby be addressed in the plural and “nonquantifiable infinity” which cannot thereby be properly addressed in the plural?

All infinities defined by mathematics would then be stereotypical examples of “quantifiable infinity”.

In contrast, the infinity of nothingness would then be one example of “nonquantifiable infinity” - such as when nothingness is conceptualized to have once “existed/been/occurred” devoid of anything. Those who claim the possibility that before the big bang was nothingness (e.g., https://en.wikipedia.org/wiki/A_Universe_from_Nothing) can be ascribed to implicitly make use of such concept of infinity.

If we can’t conceptualize - and then properly term - this differentiation between species of infinity which humans at large can historically conceive of, then I don’t see much point in further addressing the topic of the OP and, by extension, in answering your inquiry.

And this, in part, because “nonquantifiable infinity” (if this term doesn’t get lambasted as well) can only be completely non-determined and thereby completely indeterminate ontically (though, again, it will be a determinate concept). The OP’s inquiry, however, applies only to those infinities that are “quantifiable” and thereby in some way definite due to some demarcation or other occurring in that being addressed. Furthermore, to simplify the variety of such, the OP limits itself only those quantifiable infinities that are themselves made up of discrete quantities (like a geometric line being made up of discrete geometric points, or an infinite set made up of discrete numbers ).

To further complicate matters, then there needs to be a commonly held understanding of what “to determine” signifies (when the term isn’t used to address psychological processes of mind or states that thereby result). There’s again been much criticism of how I’ve attempted to define it (in short, as “to set the limits or boundaries of” - a standard dictionary definition, spelled out by me in greater explicit detail in the OP for an intended greater accuracy); none of this criticism being constructive in offering any alternative definition.

… I’m not hopeful this can work out, but I’ll check back in some time. Thanks, however, for the offer.

A mathematical infinity (in contrast to metaphysical infinity) is not limited or bounded in only certain respects and is thereby countable (metaphysical infinity is not limited or bounded in all possible respects and is thereby uncountable - and I won’t be addressing this concept). — javra

If the context is mathematics, [...] — TonesInDeepFreeze

Hey, though I hope I'm wrong, your forgone conclusions regarding me and what I was addressing, your indignation, and your seeing of red is evident to me.

But so it’s said: There are at least two distinct senses of “mathematical”.

I have nowhere stated - nor to my mind insinuated - that I am addressing infinities as they are defined by schools of mathematical thought, i.e. as they are defined by mathematics.

I have instead used “mathematical infinities” in layman’s terms from the get-go, as I initially thought (mistakenly) the OP made clear by the way terms were defined in relation to each other: in the sense of infinities that can be quantified and that furthermore pertain to quantities, and which are thereby, in this sense alone, mathematical. “Mathematical” in the sense that if a bird can count to ten, then this bird holds a respective measure of mathematical skill - despite this bird having no cognizance of any theoretical underpinnings devised by humans for the quantities it can count. In the sense that any appraisal of quantities, such as 1 + 1 = 2, is a mathematical ability that makes use of mathematical notions - irrespective of how these notions are established (hence, with or without the symbols that we humans use to express 1 + 1 = 2).

The thread was in part because of this placed in the category of “General Philosophy” rather than “Logic and Philosophy of Mathematics”.

Nor do I personally take established concepts in mathematics to the foundational cornerstone of what "infinity" at large can signify.

Notwithstanding, for my part, I have learned from this thread not to term quantifiable infinities that pertain to quantities “mathematical” - nor “countable” for that matter. Yes, my bad for not understanding beforehand how use of these terms would be strictly understood by those with a mindset such as your own.

I have no interest in addressing the many comments made in your many posts. And presently intend to let you have the last word, laugh, insult, or what have you.

So the cardinality of the integers is "less than" that of the reals. — jgill

This will be true only when one assumes the occurrence of actual infinities, in contrast to potential infinities. As an easy to read reference: https://en.wikipedia.org/wiki/Actual_infinity From my readings the issue is not as of yet definitively settled - or at least is relative to the mathematical school of thought.

At any rate, the issue of whether infinities (in the plural) are determinate, indeterminate, or neither has dissipated from this thread some time ago. I'm looking to follow suit. Best.

Are you talking about a single infinite line being somehow countable? Like the points on the line?

Or are you talking about the set of all infinite lines being countable?

Neither are countable. Countable means this is #1, this next is #2, the next is #3, etc. It means some sort of algorithm for actually counting.

Maybe you are using the word differently. Like "I can be counting on you to do the best you can." Rather than counting 1, 2, 3, ... — jgill

In presuming that - unlike at least the initial posts of Real Gone Cat - you’re not posting this to have “a good time” at the expense of a poster you assume to be stupid (because laughing at retards is such an admirable trait in today’s world):

I’m sincerely bewildered at the chasm of understanding (your previous unwarranted rudeness aside).

Nowhere did I state either possibility you offer.

Countable in the sense of: one infinite line and another infinite line make up two infinite lines.

Or: the infinity of real numbers and the infinity of natural numbers and the infinity of transfinite numbers make up three numerically distinct infinities. More technically, make up three numerically distinct infinite sets.

As in, the infinity of real numbers is infinity #1, the infinity of natural numbers is infinity #2, and the infinity of transfinite numbers is infinity #3. Each of these three infinities is in turn other than the infinity of surreal numbers, for example, which on this list would be infinity #4, making a total sum of four infinities that have been so far addressed.

As it is I'm wanting to bail out. But on the possibility that your latest post was sincere in its questions, I've answered.

Nothingness cannot have an ontic occurrence since it has nothing to occur, and if there were an infinite God he would be different from other objects, for example from us humans, so he would have a boundary of his identity too. — litewave

OK. So you uphold that the concept (which has been around in the history of mankind for some time) is vacuous. While neither agreeing nor disagreeing with you, I see nothing wrong with that.

Friend, as litewave pointed out, by your own argument, when you name a thing, you are placing a boundary on it. If you can, name two metaphysical identities. Now count them. Two. — Real Gone Cat

As has been typical, there's a reading comprehension problem. By my very own argument, the concept is quantifiable whereas that which the concept refers to is not.

but I think I'm out. — Real Gone Cat

That makes the two of us.

I assume you only recognize one metaphysical infinity, so haven't you counted it? One. — Real Gone Cat

Not to be rude but, in this thread, you've made it a habit to assume things I haven't expressed and most often don't believe.

Whereas metaphysical infinity would be infinite in length, in width, and in all other possible manners. — javra

But such a metaphysical infinity would still have a boundary of its identity because it would be differentiated from what it is not, for example from finiteness or from infinite lines. — litewave

This will be true when it comes to it being a concept (a map of the territory). But it cannot be true of it as an ontic occurrence (as the territory itself). The boundaries you specify would nullify the possibility of its occurrence.

Mind, I've made no claim as to whether or not metaphysical infinity can ontically occur - and am intent on leaving this issue open ended. But - as with a) the infinity of nothingness or b) the infinity of at least certain understandings of God (each being a different qualitative version of what would yet be definable as metaphysical infinity) - it is possible for certain humans to conceptualize its occurrence.

My point was and remains:

Are the infinities of natural numbers and of real numbers two different infinities? — javra

Yes. — Srap Tasmaner

By being 2 different infinities, they are thereby quantifiable as infinities wherein each individual infinity is demarcated from the other by some limits or boundaries. These infinities are thereby countable (in a non-mathematical sense): 2 infinities.

This cannot be so of metaphysical infinity (for reasons I've become tired of repeating).

The unit itself - which is a unit only because there are limits or boundaries which so delimit it - can however be counted. A geometric line does not have limiteless or unbounded width; its width holds a set limit or boundary, namely that of zero width. Because of this, one can quantify and thereby count geometric lines on a plane as individual units. — javra

An infinite line is a line, therefore, I suppose, a "unit". But they can't be counted since the points in the Euclidean plane cannot be counted and so pairs of these points - defining lines - cannot be counted. — jgill

In other words, “countable” can only hold the valid usage in its mathematical senses when addressing things such as lines. Therefore, the concept of there being “2 lines” is … invalid and nonsensical. — javra

You have reached an absurd conclusion. Of course there can be "two lines". Any finite collection of lines is clearly countable. And there are countable infinite collections of lines such as all lines parallel to the x-axis that pass through y= 1, 2, 3, ....

What are not countable are all lines in the plane. — jgill

All emphasis mine. Um. Okay. I certainly don't understand what your stance is on whether or not infinite lines are countable. But I'm glad others like Real Gone Cat can make sense of your writing.

So an infinite line has no ontic identity? — litewave

An infinite line is not metaphysical infinity. An infinite line is infinite only in length, not in width. Whereas metaphysical infinity would be infinite in length, in width, and in all other possible manners.

I too wonder how a continuum makes up something discrete — Gregory

Yea. That appears to roughly sum up the issue.

An infinite line is a line, therefore, I suppose, a "unit". But they can't be counted since the points in the Euclidean plane cannot be counted and so pairs of these points - defining lines - cannot be counted. — jgill

In other words, “countable” can only hold the valid usage in its mathematical senses when addressing things such as lines. Therefore, the concept of there being “2 lines” is … invalid and nonsensical. This as all mathematicians know, in contrast to the stupidity of common folk.

And I must take my own head out of my own tunnel-visioned ass in order to realize this.

Got it.

By no means in agreement, but I got it.

I warned you this would be trouble. — Srap Tasmaner

There is such a thing as equivocation between two or more meanings or usages of a term, right? I repeatedly described countability in its non-mathematical sense of “able to be counted; having a quantity”. As does the Wiktionary definitions previously posted.

(Also: Zeus could write out all the natural numbers in a finite amount of time just by doing the next one faster each step; not even Zeus could write out the real numbers in a finite amount of time. Lists are friendlier, even when they don't terminate.) — Srap Tasmaner

Are the infinities of natural numbers and of real numbers two different infinities? Or are they the same nonquantifiable infinity?

Every object is bounded in its identity, that is, it has a boundary that differentiates the object from what it is not. Does "ontically determinate" mean having such a boundary? Then it doesn't seem important whether the object is in some way infinite. — litewave

If I understand you right, yes, every individual cognition as identity is delimited from other cognitions and hence bounded. Yes, and this holds true for the concept of metaphysical infinity as well - in direct contrast with that supposedly ontic occurrence that the concept of metaphysical infinity specifies.

Ontically occurring metaphysical infinity is devoid of any ontic identity for it has no boundaries via which such an ontic identity can be established. Nothingness, for one conceivable example of such, can be identified by us on grounds of being different from somethingness, so to speak. There thereby is a conceptual boundary between nothingness and somethingness via which nothingness can be identified. But on its own, where this to be possible, nothingness would hold no ontic identity - for an identity would be something.

As to your conclusion, thanks for offering. I’ll think about it some.

Um, the points of a line may be put into one-to-one correspondence with the set of real numbers, which Cantor proved to be uncountably infinite in 1874. In fact, the points in a tiny line segment are uncountable. — Real Gone Cat

You seem to be asking me to explain a commonly established attribute. If you’d bother to check the link to “infinity” I posted you’d find the following:

1. (uncountable) endlessness, unlimitedness, absence of a beginning, end or limits to size.
2. (countable, mathematics) A number that has an infinite numerical value that cannot be counted. — https://en.wiktionary.org/wiki/infinity

The definitions can of course be questioned, but they are commonly established, at the very least as best approximations of, as Banno would say, the term’s usage.

I’ll again try to explain. A metaphysical infinity has absolutely no limits or boundaries. Due to this, it cannot be discerned as a unit: it is immeasurable in all senses and respects and hence, when ontically addressed (rather than addressed in terms of being a concept) it is nonquantifiable. As a thought experiment, try to imagine two ontically occurring metaphysical infinities side by side; since neither holds any delimitations (be these spatial, temporal, or any other) how would you either empirically or rationally discern one from the other so as to establish that there are two metaphysical infinities? In wordplay games, we can of course state, “two metaphysical infinities side by side” but the statement is nonsensical. More concretely, ontic nothingness, i.e. indefinite nonoccurrence - were it to occur (but see the paradox in this very affirmation: the occurrence of nonoccurrence, else the being (is-ness) of nonbeing) - is one possible to conceive example of metaphysical infinity. Can one have 1, 2, 3, etc., ontic nothingnesses in any conceivable relation to each other? (My answer will be “no” for the reasons just provided regarding metaphysical infinity. However, if you believe this possible, please explain on what empirical or rational grounds.)

With that distinction hopefully out of the way, you can then have limitlessness or unboundedness that applies to a certain aspect of what nevertheless remains a unit. That which is limitless or unbounded about the unit cannot be measured of counted to completion - this as I've previously mentioned. The unit itself - which is a unit only because there are limits or boundaries which so delimit it - can however be counted. A geometric line does not have limiteless or unbounded width; its width holds a set limit or boundary, namely that of zero width. Because of this, one can quantify and thereby count geometric lines on a plane as individual units.

It bears note that I’m not arguing for a novel concept here. As I pointed out to jgill, these are established notions: you have dictionary definitions such as those provided by Wiktionary and SEP entries on infinity in reference to this.

I'm unsure why you're hung up on causal determinism. — Real Gone Cat

It was given as one possible concrete example of ontic determinacy, primarily on account of all-knowing people such as Banno not getting the context of the usage of the term "determinacy". But no, causal determinism does not hold the only conceivable type of determincay: there can be already established notions of non-causal determinacies, this as @Srap Tasmaner illustrated in this post.

You seem genuinely interested in the topic. — Real Gone Cat

Yea, I am. And as opposed to what? (a rhetorical question)

agreed
this is what I'm questioning.

In attempts to simplify the reason for this thread:

We have two well-established concepts: that of determinacy (such as can be found in the notion of causal determinism), on one hand, and that of “non-metaphysical" (aka, countable, mathematical) infinity (such as can be found in a geometric line of infinite length), on the other. On their own, both concepts are cogent (to most folks, at least). However, when attempting to define infinity (which describes a certain state of affairs) via determinacy (which describes how a certain state of affairs comes to be), inconsistencies emerge.

(Non-metaphysical) Infinity can thus either be:

a) determined, hence determinate
b) undetermined, hence indeterminate
c) neither (a) nor (b)

If determinate, then you run into problems such as given by

If indeterminate, then this directly contradicts the fact that, for example, a geometric line can be determined by geometric points … as well as having properties specified by once so determined

---------

Seeing how I’m having a hard time in even getting people to understand the problem, my only current conclusion regarding this problem is that it’s so dense that I needn’t concern myself with it when specifying metaphysical possibilities of determinacy.

Thanks for the input.

Is this what you're looking for? — Real Gone Cat

Thanks for the offer.

Unfortunately, not to my satisfaction as expressed, no.

Can not two points in a plane (with the plane itself determined by a multitude of points) determine a unique line, this as offered? In which case, the line here then has determinants and is thereby not indeterminate (i.e., undetermined). An indeterminate line so far makes little sense to me, as it would not be determined by determinants (here, namely, by points).

... as it is, been sitting on my own ass a little too long today. Going to take a break.

I don't know what you're talking about. — jgill

Nor I. — Banno

and ...

I don't have an opinion [on what determinacy is]. — Banno

I can only interpret this as implying that to you causal determinism is meaningless or nonsensical, as is its notion of determinacy.

But you're still butting in as the measure of all that can be understood.

OK, then.

It has a bunch of uses, which we might set out one by one, but which change and evolve over time - like all such words. — Banno

Aright. What use do you take it to presently hold in the notion of causal determinism in particular? If you find that it holds different uses in this context, I'm more than happy to listen.

If a line (not a line segment) is ontically determinate, I assume you can draw it in its entirety. No?

I can't. Can you? — Real Gone Cat

OK, I get that. Tis why I've started the thread. But then, would you say that it is instead indeterminate? Neither determinate nor indeterminate?

Should we go into it in more detail? — Banno

Please do. Answer this question:

What would you say "to be determined" is? This in the ontological sense rather than the psychological. — javra

...with the supposition that any of this makes sense. — Banno

OK Banno. What would you say "to be determined" is? This in the ontological sense rather than the psychological.

So width is length? — Real Gone Cat

no

And what is "uncurved" length? — Real Gone Cat

a straight extension in space

I would like a better definition of determinacy. — Real Gone Cat

see my latest post for the definition also mentioned in the OP

You seem to be implying that the line is determinate because the line exists in its entirety in the plane. Is this correct? — Real Gone Cat

no

Oh, Banno. You're ruining our fun. — Real Gone Cat

Let him play! As an self proclaimed anti-philosophy philosopher enamored with Witt, he's into games. :wink:

Just an example. Mathematics does sometimes directly address how determinate its objects are, at least in this sort of sense, whether there's a unique solution, finitely many, infinitely many, etc.

Is this sort of determinateness any use to you? — Srap Tasmaner

So far I don't find it being of use to alleviate the issue. Thanks for the input, though. What you say addresses determinacy in the sense of "that determined has its limits or boundaries set by one or more determinants". I'm so for robustly in favor of this definition.

Yet the same issue results: if a unique line is so determined by any two points on a plane (in the sense just provided above) how does one then commingle this same stipulation with the fact that that which is being so determined is - at the same time and in some respect - infinite and, hence, does not have some limits or boundaries in any way set by its determinants. Here, the two point on a plane do not set the limits or boundaries of the line's length - despite setting the limits or boundaries of the unique line's figure and orientation on the plane. Again, once the line is so determined by the two points on a plane, it is fully fixed or fully set; hence, fully determined in this sense. But going back to the offered definition above, this would imply that "the line, aka that determined, has it limits or boundaries fully set by one or more determinants" - which it does not on account of being of infinite length.

So, if I have a countable collection of lines, they are countable? I suppose that's a step in the right direction. — jgill

What makes them countable if they are completely devoid of any boundaries? So might staying on topic be another step in the right direction.

That's where I'm currently stuck. It feels like I'd equivocating between apples and oranges. Yet both determinacy/indeterminacy and finitude/infinitude are defined by the ontic presence or absence of limits/boundaries.

So, a geometric line for example, once its placed on a geometric plane it is - in one sense - fully determinate. Its direction and figure are fully fixed in place. No variance; no vagueness. It is not as though the geometric line is semi-fixed or semi-vague. Yet in a different sense, it is only semi-limited or semi-bounded: being infinite only in length (but not in figure or, as a one-dimensional object, in width).

Yet this doesn't make it semi-determinate in the sense of being only partially fixed, or set.

-------

BTW, not naval gazing. I'm trying to address three metaphysical possibilities in regard to determinacy - namely, that of being a) completely determinate, b) completely nondeterminate, or the possibility of c) being only partly determined by determinants (i.e., of being semi-determinate). And my stumbling block is that by defining determinacy as I did in the OP (i.e., having limits or boundaries set by one or more determinants), I run into this stubborn paradox of having to differentate semi-determinacy from what I've so far termed "mathematical infinities" ... which are, again, only partly infinite in some respect while yet being finite in others.

I'm assuming this is somewhat dense, but there's the background to the OP and an answer to your question.

Ah, I see, you meant countable as a unit, as a line. — Srap Tasmaner

Right, and its countable as a unit on account of having some limits or boundaries via which it can be so distinguished.

If we're in agreement on this, cool. :smile:

Set theorists and foundations people might be interested in such distinctions, but for me infinity simply means unbounded. — jgill

Is a geometric line - a maths concept - to you unbounded in all possible respects?

Besides, again, the issue is one of whether such unbounded things that we discern via definite demarcations are determinate, indeterminate, or neither.

and the length of a line is not countable in that sense. — Srap Tasmaner

I specifically said the length is immeasurable. If one can discern the quantity of lines specified, then lines as a whole are indeed countable. Or would you disagree with what I actually said?

Mea, in terms of what you've quoted, here's some reference: https://plato.stanford.edu/entries/infinity/#InfiPhilSomeHistRema

OP's question is one of whether mathematical infinity - your field I take it - is determinate, indeterminate, or neither?

Yet the infinite length of a geometric line is definite, — javra

Can you elaborate? Do you mean that the line is measurable?

I know so little about math, but I'm always eager to learn. — Real Gone Cat

I'm in no way a mathematician; not my personal forte. Wanted to be forthright about that. But sure on elaboration of my philosophical reasoning regarding the matter:

As I tried to point out in the OP: a geometric line is defined by an uncurved infinite length of zero width. Its length's expansion in both directions is not limited or bounded, yes. Its length is then of itself immeasurable. But its width and shape is subject to fully set limits or boundaries, thereby endowing the geometric line with a definite uncurved length. Devoid of this definite state of being brought about by fully set limits or boundaries - namely, of having zero width and a straight length - we wouldn't be able to discern it as a geometric line. Hence, as with all other mathematical infinities I currently know of, a geometric line is not perfectly infinite in all respects but only infinite in some respects while being finite in others. Due to its finite aspects, we hold a definite idea of what a geometric line is (it then becomes measurable in this sense; else expressed, it becomes countable).

Maybe mathematical infinities only make sense in relation to the metaphysically infinite — Gregory

How so? As background: I've read a little on Cantor's "Absolute Infinity" and find it to be a nice poetic conception. But I don't see any relevant connection between, for example, a geometric line and the attributes which Cantor said of God - aka of Absolute Infinity - e.g., that of being "the supreme perfection".

More to the point: how would this in any way clarify whether mathematical infinities are determinate, indeterminate, or neither?

To be more explicit on this matter, metaphysical infinity, in being perfectly devoid of all possible limits and boundaries (as defined in the OP), would then be perfectly undetermined in all respects. As such, it would then be perfect indeterminate (aka, nondeterminate). Yet the infinite length of a geometric line is definite, and so I take it in at least some meaningful way determinate; but, then, if it is determinate this brings back the issue addressed in the OP of apparent contradiction in regard to limits (contradictions which don't occur for metaphysical infinity on account of it being perfectly indeterminate).

[BTW, to my way of thinking, one can conceptualize metaphysical infinity as perfect being (i.e., God) just as readily as perfect nonbeing (i.e., nothingness ... as in, "why is there something rather than nothing") - this though the two are polar opposites. And neither have been either empirically or rationally evidenced to be to the satisfaction of most. Whereas at least some mathematical infinities - like the irrational number pi (whose decimal expansion is infinite despite the sequence of its decimals being, by all apparent accounts, determinate) - do occur in nature, or at least can influence our reality as though they do. But discussion of metaphysical infinity to me appears to enter a whole different ballpark than what the OP is asking.]

It's very hard for me to sustain his though experiment, that once we stop perceiving an object, we don't have many good reasons (although something must be there, in the world) to suppose it continues to exist. For as he says (I know I'm re-quoting him, but, he articulates it so well): — Manuel

But it is very, very clear, that Hume was what is now called a "mysterian", which should be the common- sense view that we are natural creatures, and hence some things are beyond our capacities, as some things are beyond the capacities of dogs or birds. — Manuel

For whatever reason, his allusions to instincts always resonated with me and quenched the otherwise potential difficulty in not having conscious reasons for an external world. Myself, I can fall back to the notion of the moon being there when no one is looking precisely on grounds of causal reasoning (riptides and such), and believe this can be extended to all external objects. But yes, Hume presented more problems than he resolved.

As to the title of "mysterian," I agree. From what I recall, maybe most notably, he was a kind of mysterian compatibalist who upheld both metaphysical free will and causal determinacy co-occurring; a very different species of compatibalism than what we have today wherein the notion of "freedom" is modified in any number of ways so as to suit a fixed stance on causal determinism (determinism being a term that wasn't coined yet in his day).

like an instinct, a phrase he doesn't appear to use in this chapter. — Manuel

That's exactly right, or at least, that's how it looks like to me as well. — Manuel

I’ve found another supporting quote from within the chapter (Part IV Section II, page 214). This is in introduction to the notion of double existence: to roughly paraphrase, here he articulates the opinion that our instinctive awareness of resembling perceptions being continued, identical, and independent is indicative of the external existence of objects in the world whereas our reasoned awareness that our perceptions are all dependent, interrupted, and different is indicative of our minds’ internal existence. (Emphasis on the former external existence being inferred by us on account of what our instinctive awareness informs us of – this in contrast to our internal existence which is inferred from reasoning regarding our perceptions.)

“There is a great difference betwixt such opinions as we form after a calm and profound reflection, and such as we embrace by a kind of instinct or natural impulse, on account of their suitableness and conformity to the mind. […] Thus tho’ we clearly perceive the dependence and interruption of our perceptions, we stop short in our career, and never upon that account reject the notion of an independent and continu’d existence. […]”

boldface mine.

This is somewhat paradoxical, given his reputation and thrust of his thought, an argument for innate faculties, — Manuel

Yes, maybe. Still, what I’ve read about Hume is often quite different than what I gathered from directly reading Hume. For one example, to me, Kant borrowed from Hume rather than debunking him. Hence, imo, Kant’s categories are a subset of Hume’s natural impulses (instincts) which Kant worked out to far greater extents - and to which Hume's epistemology of causation still applies. Likewise, Kant’s noumena are Hume’s objects of external existence which, again to paraphrase Hume, resemble internal perceptions due only to fancy but not due to any reason to so infer. (see page 216, for example). Had to throw this in. :smile:

The word might be in there somewhere, but there doesn't seem to be much use made of the idea; the whole flavor of the account is causal, mechanical. — Srap Tasmaner

Yes. I think he has in mind something like mechanical, but also something like an instinct, a phrase he doesn't appear to use in this chapter. Perceiving is like breathing or seeing, we can't not have perceptions. — Manuel

we need principles that will relate certain perceptions to each other. — Srap Tasmaner

VERY perceptive. This is one of the reasons he gives in the Appendix for, essentially stating that his system fails, or as he puts it "my hopes vanish". This is one of the things he cannot account for, how perceptions relate to each other. The other being that we really do perceive continuity in the objects. In other words, he has used these two principles: the uniting principle and the continuity principle (my terminology, not his), without being able to justify them, but he isn't able to renounce either of them. — Manuel

I agree that he had instincts in mind. My interpretation of his thought: though to a far smaller (else, more generalized) extent than lesser animals, humans are nevertheless inescapably driven by instincts - including those of what you’ve termed the unifying principle and the continuity principle of perceptions, both to my mind being subsumed by reasoning in general.

To my reading he briefly addresses our faculties of reasoning being instinctive at the very end of a previous chapter, Part III Section XVI (Of the reason of animals), starting at the bottom of page 179 [boldface mine ... as well as any potential typos]:

“Nothing shews more the force of habit in reconciling us to any phenomenon, than this, that men are not astonish’d at the operations of their own reason, at the same time, that they admire the instinct of animals, and find a difficulty in explaining it, merely because it cannot be reduc’d to the very same principles. To consider the matter aright, reason is nothing but a wonderful and unintelligible instinct in our souls, which carries us along a certain train of ideas, and endows them with particular qualities, according to their particular situations and relations. This instinct, ‘tis true, arises from past observation and experience; but can any one give the ultimate reason, why past experience and observation produces such an effect, any more than why nature alone shou’d produce it? Nature may certainly produce whatever can arise from habit: Nay, habit is nothing but one of the principles of nature, and derives all its force from that origin.”

Very many humans are very off-put today when told that we humans are to significant extents instinctively driven - and this is well after our knowledge of evolution. I can easily envision that Hume didn't greatly dwell on this notion in his writings due to the audience of his time.

To put it another way, I don't see it as having anything to do with "reality"; I think that term is altogether too overblown. "The most plausible" is just what seems to be the best explanation; the one that fits best within a general network of perspectives that I find explanatorily workable. — Janus

Best explanation for what if not for what is real or else what is really the case? But if you think the notion of reality is too overblown, even though I disagree, I won’t argue with you.

I guess the example is unclear because it lacks specificity. The unknown critter is referred to as both an experience-based prediction and also an inference. — praxis

There were two competing alternatives rather than the one scenario of an unknown critter. Then again, I don’t get how experience-based predictions can be anything other than inferences based on some experience.


Maybe it’s just me not being up to par. All the same, I’m going to likely call it a day.

Believing something is "holding it to be true". That is not what I'm talking about; I'm talking about entertaining the idea that seem most plausible, not holding ideas to be true. — Janus

“Most plausible” to me signifies “most likely to be real or conformant to reality”; to deem X most plausible is hence to provisionally accept X’s reality, thereby constituting a belief.

How can S deem X plausible without deeming X to be likely real or else likely conformant to what is real? Thereby in some way attributing reality to X, which would then be an act of believing.

For instance, to believe that extraterrestrial intelligence occurs and that humans therefore are not the only sapient species in the universe is neither a) to know that extraterrestrial intelligence occurs nor b) to be uncertain and fully agnostic about the matter but, rather, c) to deem its occurrence most plausible - hence most likely real.

In short, how else should I understand “plausible” in the contexts we’re using?

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To address a previous notion, a justified and true idea that one cognizes but does not hold to be true is not a personal instance of knowledge. As one example, a theist may hold the idea of atheism, may be aware of the justifications for it, and it might in fact be the case that atheism conforms to what is real; still, if this theist doesn’t hold the idea of atheism to be true, this justified and true idea of atheism which the theist holds awareness of will not be an instance of the theist’s knowledge. On second thought, if you deem that it is not possible to either know that there is no divinity or else that there is divinity, the same argument can be presented of numerous other propositions, such as that of “the house is over the hill”: the idea might be justified and true, but if one doesn’t hold it to be true then it cannot be something which one knows.

Tangentially, to clarify something on my part in case this does need clarifying:

Beliefs - at least as I’ve so far tentatively defined and understood them - which will never waiver irrespective of evidence or reasoning will presume an unwarranted infallibility. And I again fully agree with @Ken Edwards that such a species of belief is most often, if not always, detrimental to at the very least an accurate understanding of reality. But the observation of this species of belief sometimes occurring in others does not signify that all beliefs are thereby just such a species of belief. Hence my disagreements in this thread.

(To my fallibilist mind, the alternative is to hold all beliefs to at the end of the day be fallible, and thereby remain open to revising them if evidence or reasoning gives warrant to so doing.)

You asked: “If one then moves away from one’s position so as to avoid the possibility of contact with a small animal, how can this activity be accounted for in the absence of belief (to whatever extent conscious and/or subconscious) that the movement was likely produced by a small animal (rather than, for example, by wind-blown leaves)?”

If a mind accurately predicts the presence of a rat then moving away from it, assuming the rat is rabid or whatever, is a good and adaptive prediction. Otherwise it’s a prediction error. — praxis

While it may not have been the best example I could have offered, you’re still overlooking a key ingredient that was stipulated from the beginning: lack of knowledge. You do not know what caused the movement in the dark corner. You haven’t clearly seen anything but a movement; you haven’t seen a small animal, never mind seeing a rat. But you’re mind inferentially predicts that the movement might either have been caused by wind-blown leaves or by a small animal (but not both). Which one is real is to you not known, and hence not a psychological certainty.

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BTW, I’ll ask that you also comment on the working definitions I’ve provided of belief in my previous post – which culminate in stipulating that all forms of belief in one way or another consist of “the attribution of reality to”. This so as to arrive at a common understanding of terms.

Going by what was so far offered, if one attributes reality to the contents of a prediction, then the given prediction will by default be believed - thereby constituting one form of belief. Otherwise one deems the prediction fallacious and, by the same count, does not believe - i.e., does not attribute reality to - it.

Then, going back to the example of the two alternative predictions - that of either wind-blown leaves or of a small animal (to make this explicit, which are to be understood as mutually exclusive) - it's to be understood that they cannot both be real. And again, one does not know which one is real. If one acts accordant to one of the two predictions - thereby evidencing via action that one attributes reality to the prediction’s contents and, hence, believes the prediction’s contents - then one at the same time dispels the other prediction's validity (here, at least momentarily disbelieving the other prediction’s contents).

… I'm thinking this holds unless you find the offered definitions of belief to be fallacious. In which case, what do you instead recommend?

(Note: “X is held by S to be true” is equivalent to “X is held by S to be conformant to what is real” which to my mind in turn is equivalent to “S attributes reality to the contents of X" - this example being just one of many variant forms of belief.)

Prediction, to put it succinctly. This happens whether we like it or not. Our minds are constantly looking for patterns and making predictions. — praxis

In the example provided, the mind predicts two conflicting alternatives are possible: wind-blown leaves or a small animal. Also given is that you do not consciously know which alternative is real. To consciously act on either is not prediction: the predictions of if-then are already embedded in each alternative. So prediction as stipulated does not account for why one chooses to act on one alternative but not the other.



Prior to addressing what you’ve stated, I think it's best that we agree upon what terms signify. I’ll start by providing some working definitions of what I understand by “belief”:

-- a belief (a noun) is an instantiation of the activity of believing (a verb)
-- believing can occur in the form of “believing that [the given clause]” or “believing in [the given noun]” or else “believing [the given agent(s)]
-- to believe that [the given clause] is to trust (i.e., hold confidence) that [the given clause] is real and, hence, is to attribute reality to [the given clause] (e.g., I believe that tomorrow will be like today)
-- to believe in [the given noun] is to attribute reality to [the given noun] (e.g., he believes in UFOs), else to [the given noun]’s moral standing or preferability (e.g., she believes in not burning flags), or else to [the given noun]’s ability to accomplish (e.g., I believe in Bill (e.g., in Bill’s ability to finish the marathon)).
-- to believe [the given agent(s)] is to attribute truthfulness to [the given agent(s)]’s claims and, hence, to attribute reality to what [the given agent(s)] claim (e.g., he believed her).
-- hence, common to all three types of belief is some variant of “the attribution of reality to”.

Do you disagree with these definitions, and, if you do disagree, what do you instead recommend?

You say:" I do get the often grave problem of unjustified belief treated as incontrovertible knowledge. But I so far take it that such isn’t equivalent to belief per se.)

I think that beleif per se would also apply to Justified belief. — Ken Edwards

Sure. Belief, in and of itself, would also apply to "justified true belief", which is the commonly accepted definition of descriptive knowledge. Which in turn would make belief and indispensable aspect of, at the very least, descriptive knowledge.

This, however, for example does not make "knowledge" equivalent to "unjustified belief treated as incontrovertible knowledge" - even though both make use of belief.

Still, you might have a definition of knowledge in mind which does not make use of belief. In which case, the just mentioned wouldn't apply, granted.