How much of Peirce's metaphysics (and mathematics, and phenomenology, and logic/semeiotic) have you actually studied carefully? What fundamental distinction are you positing here between the concepts of "infinity" and "infinitesimal"?The problem with Peirce's metaphysics is that he allows that pure, absolute continuity, which can only be expressed by us human beings through the terms of infinity, to be polluted by the concept of "infinitesimal". — Metaphysician Undercover
Peirce would agree with this, although "infinitesimal point" is a contradiction in terms. There are infinitesimals, and there are points; they are two very different concepts, since infinitesimals have extension (though smaller than any assignable/measurable value), while points do not. His parallel terms when discussing time are moments, which have duration (though shorter than any assignable/measurable value), and instants, which do not.A succession of infinitesimal points does not provide the necessary conditions to fulfil the criteria of "continuity". — Metaphysician Undercover
Peirce would agree with this, as well. Infinitesimals (and moments) are indefinite, and thus cannot be individually distinguished; we can only discern differences once we have marked off specific points (or instants). In fact, one of Peirce's own definitions of a moment is "a time in which no change which can in any way be made sensible can take place." A finite lapse of time between two marked instants is required for any difference to become discernible. In his own words, "between any two instantaneous states there must be a lapse of time during which the change is continuous, not merely in that false [Cantorian] continuity which the calculus recognizes but in a much stricter sense."Positing a degree of difference as existing between the infinitesimal points, no matter how large or small that degree of difference is, necessitates the conclusion that there is something "change", which occurs between such points, rendering the supposed continuity as non-continuous. — Metaphysician Undercover
Peirce would vehemently deny both charges here--he does start with a pure and true continuity as his first principle, or at least consistently strives to do so; and he explicitly rejects materialism, calling it "quite as repugnant to scientific logic as to common sense," instead affirming objective idealism as "the one intelligible theory of the universe." It treats "the physical law as derived and special, the psychical law alone as primordial," such that "matter is effete mind, inveterate habits becoming physical laws." Accordingly, Peirce's cosmology understands the very constitution of being as true continuity underlying indefinite possibilities, some of which are actualized by the ongoing process of determination.Because Peirce proposes a polluted, and impure form of continuity, rather than starting with a pure and true continuity as his first principle, his approach to agapasm is demonstrably a materialist approach. — Metaphysician Undercover
If you can't explain something, there is still the possibility of an explanation. We just don't have it. — god must be atheist
How much of Peirce's metaphysics (and mathematics, and phenomenology, and logic/semeiotic) have you actually studied carefully? What fundamental distinction are you positing here between the concepts of "infinity" and "infinitesimal"? — aletheist
Peirce would agree with this, although "infinitesimal point" is a contradiction in terms. There are infinitesimals, and there are points; they are two very different concepts, since infinitesimals have extension (though smaller than any assignable/measurable value), while points do not. His parallel terms when discussing time are moments, which have duration (though shorter than any assignable/measurable value), and instants, which do not. — aletheist
Peirce would agree with this, as well. Infinitesimals (and moments) are indefinite, and thus cannot be individually distinguished; we can only discern differences once we have marked off specific points (or instants). — aletheist
In his own words, "between any two instantaneous states there must be a lapse of time during which the change is continuous, not merely in that false [Cantorian] continuity which the calculus recognizes but in a much stricter sense." — aletheist
Peirce would vehemently deny both charges here--he does start with a pure and true continuity as his first principle, or at least consistently strives to do so; and he explicitly rejects materialism, calling it "quite as repugnant to scientific logic as to common sense," instead affirming objective idealism as "the one intelligible theory of the universe." It treats "the physical law as derived and special, the psychical law alone as primordial," such that "matter is effete mind, inveterate habits becoming physical laws." Accordingly, Peirce's cosmology understands the very constitution of being as true continuity underlying indefinite possibilities, some of which are actualized by the ongoing process of determination. — aletheist
Peirce does not "replace" points with infinitesimals; they are two different concepts, and there is still a role for points--not as the parts of a line, but as the discrete boundaries between its continuous parts. He helpfully clarifies this in one manuscript (R 144, c. 1900) by referring to points (or instants) as limits and the line segments (or lapses of time) between them as portions. In later writings he reverts to "parts" for the latter, but suggests "connections" for the former.Let me rephrase that then, Peirce replaces the "point" with the "infinitesimal", as the point might be designated as unreal, and incapable of producing a continuity. — Metaphysician Undercover
The duration of time does not consist of infinitesimal moments, either. As with anything truly continuous, the whole is ontologically prior to any of its parts.The duration of time cannot consist of "instants", or points, which have zero duration, but it may consist of "infinitesimals", which I might have carelessly referred to as points with extension. — Metaphysician Undercover
The parts are indefinite (infinitesimals/moments) unless and until we arbitrarily mark them off (with points/instants).... I conceive that a Continuum has, IN ITSELF, no definite parts, although to endow it with definite parts of no matter what multitude, and even parts of lesser dimensionality down to absolute simplicity, it is only necessary that these should be marked off, and although even the operation of thought suffices to impart an approach to definiteness of parts of any multitude we please.*
*This indubitably proves that the possession of parts by a continuum is not a real character of it. For the real is that whose being one way or another does not depend upon how individual persons may imagine it to be. — Peirce, RS 30, 1906
No, the very nature of infinitesimals/moments is that they are not distinct from one another at all.Each infinitesimal requires a point of division, a boundary, to separate it from another infinitesimal. — Metaphysician Undercover
We can only introduce points/instants as the boundaries between adjacent segments/lapses that have finite length/duration.Another plain deliverance of the percipuum is that moment melts into moment. That is to say, moments may be so related as not to be entirely separate and yet not be the same. Obviously, this would be so according to our interpretation. But if time consists of instants, each instant is exactly what it is and is absolutely not any other. In particular, any two real quantities differ by a finite amount. — Peirce, CP 7.656, 1903
If we have good reason from our phenomenal experience to posit that continuity is real, and the hypothesis of infinitesimals "provides the logical foundation for the reality of continuity," then we have good reason to conclude that infinitesimals are likewise real.If infinitesimals are real, this provides the logical foundation for the reality of continuity. But the only thing which supports the reality of the infinitesimals is the "need" to support the continuity. — Metaphysician Undercover
What is the argument for denying the reality of infinitesimals?Now a fact that goes to show that time is continuous is that our consciousness seems to flow in time. If we suppose that we are immediately sensible of time, the origin of the idea is explained; but if not, then we must cast about for some other way of accounting for our having the idea. Now there are great difficulties in the way of supposing that we are immediately conscious of time, and therefore of the past and future, unless we suppose it to possess the third property of continuity [infinitesimals], so that we can be immediately conscious of all that is within an infinitesimal interval from any instant of which we are immediately conscious, without its thereby following that we are immediately conscious of all instants. — Peirce, R 257, c. 1894
That is not a problem at all, it is precisely Peirce's view.See, the problem here is that the "two instantaneous states" are not real. — Metaphysician Undercover
Instantaneous states are creations of thought for describing real events in time. We arbitrarily mark them at finite intervals, but the reality is continuous motion/change.... it is strictly correct to say that nobody is ever in an exact Position (except instantaneously, and an Instant is a fiction, or ens rationis), but Positions are either vaguely described states of motion of small range, or else (what is the better view), are entia rationis (i.e. fictions recognized to be fictions, and thus no longer fictions) invented for the purposes of closer descriptions of states of motion ... — Peirce, R 295, 1906
Nonsense, Peirce consistently affirms that time is (potentially, not actually) infinitely divisible, and that this is always necessary (but insufficient) for true continuity. In fact, he asserts repeatedly that instants of any multitude, or even exceeding all multitude, may be inserted within any lapse of time--even an infinitesimal moment.But if divisions in time are created artificially by positing such points, then there is no principle to deny dividing time infinitely. So the infinitesimals are posited solely for the purpose of denying infinite division, without any real substance. — Metaphysician Undercover
This is a confusion of reality and existence. Indefinite infinitesimals/moments are real, but do not exist; distinct points/instants exist, but only by virtue of being marked off by an act of someone's will.In order to have real existence, the infinitesimals require real boundaries. So if the infinitesimals are real, then the continuity is not, due to the existence of the boundaries. — Metaphysician Undercover
‘Miracles are not against nature, only what we know about nature’ ~ St. Augustine. — Wayfarer
Which means, in effect, that nothing happens that science cannot explain in principle. That's how it works out. — Wayfarer
St. Augustine also believed that having slaves was a good thing, and having those who refused to convert to Christianity spiked on a stake or burnt alive underwater was a good thing. — god must be atheist
But scientists and atheists are on the opinion that miracles don't ever happen. — god must be atheist
They might, though. To say ‘miracles can’t happen’ as matter of principle verges on superstition of another kind, as it put scientific orthodoxy in a role previously assigned to religious authority. — Wayfarer
I commit to science. It appears, you commit to the power of the supernatural. — god must be atheist
Peirce does not "replace" points with infinitesimals; they are two different concepts, and there is still a role for points--not as the parts of a line, but as the discrete boundaries between its continuous parts. — aletheist
He helpfully clarifies this in one manuscript (R 144, c. 1900) by referring to points (or instants) as limits and the line segments (or lapses of time) between them as portions. In later writings he reverts to "parts" for the latter, but suggests "connections" for the former. — aletheist
No, the very nature of infinitesimals/moments is that they are not distinct from one another at all. — aletheist
f we have good reason from our phenomenal experience to posit that continuity is real, and the hypothesis of infinitesimals "provides the logical foundation for the reality of continuity," then we have good reason to conclude that infinitesimals are likewise real. — aletheist
What is the argument for denying the reality of infinitesimals? — aletheist
Instantaneous states are creations of thought for describing real events in time. We arbitrarily mark them at finite intervals, but the reality is continuous motion/change. — aletheist
Nonsense, Peirce consistently affirms that time is (potentially, not actually) infinitely divisible, and that this is always necessary (but insufficient) for true continuity. In fact, he asserts repeatedly that instants of any multitude, or even exceeding all multitude, may be inserted within any lapse of time--even an infinitesimal moment. — aletheist
With all due respect, this sweeping generalization is rather misleading. Peirce described his own view as "extreme scholastic realism" (CP 8.208; c. 1905), calling himself "an Aristotelian of the scholastic wing, approaching Scotism, but going much farther in the direction of scholastic realism" (CP 5.77n; 1903) and "a scholastic realist of a somewhat extreme stripe" (CP 5.470; 1907). It is not much of a stretch to say that his entire philosophy is the result of a lifelong crusade against nominalism, and there was no more disparaging statement from his pen than the charge that someone else was a nominalist.The nominalists gleened from Scotus what would fit their stance, and the realists gleened from Scotus what would fit their stance. They have also done this with Peirce's work. The nominalists and realists were and are both misguided. — Mapping the Medium
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