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L&FP, 55: Defining/Clarifying Intelligent Design as Inference, as Theory, as a Movement

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It seems, despite UD’s resources tab, some still struggle to understand ID in the three distinct senses: inference, theory/research programme, movement. Accordingly, let us headline a clarifying note from the current thread on people who doubt, for the record:

[KF, 269:] >>. . . first we must mark out a matter of inductive reasoning and epistemology. Observed tested, reliable signs such as FSCO/I [= functionally specific, complex organisation and/or associated information, “fun-skee”] beyond 500 – 1,000 bits point to design as cause for cases we have not observed. This is the design INFERENCE.

A classic example of FSCO/I, the organisation of a fishing reel
A von Neumann, kinematic Self Replicator, illustrating how an entity with
self-replication reflects considerable additional FSCO/I, where
the living cell embeds such a vNSR
The metabolic network of a cell exhibits FSCO/I in a process-flow, molecular nanotech self replicating system
Petroleum refinery block diagram illustrating FSCO/I in a process-flow system
The design inference reduced to a flowchart, the per aspect explanatory filter

Note, inference, not movement, not theory.

Following the UD Weak Argument Correctives under the Resources tab, we can identify ID Theory as a [small] research programme that explores whether there are such observable, testable, reliable signs, whether they appear in the world of life and in the cosmos, whether we may responsibly — notice, how duties of reason pop up naturally — use them to infer that cell based life, body plans, the cosmos etc are credibly the result of intelligently directed configuration . . . and that’s a definition of design. This, in a context where the proposed “scientific” alternative, blind chance and/or mechanical necessity has not been observed to actually produce things exhibiting FSCO/I etc.

Logically, this is an application of inductive reasoning, modern sense, abduction.

Which is common in science and is commonly held to ground scientific, weak philosophical sense, knowledge. Weak, it is open ended and can be defeated by further analysis and evidence, warranted, credibly true [and so reliable] belief.

Going beyond, where we have further information, evidence and argument we may explore whodunit, howtweredun, etc.

Such is after all commonplace in technical forensics, medical research, archaeology, engineering [esp. reverse engineering], code cracking etc. I guess, these can be taken as design-oriented sciences. Going back to 4th form I remember doing natural science explorations of springs. Manufactured entities. So are lenses, mirrors, glass blocks, radio systems, lasers etc.

Beyond the theory, there is a movement, comprising supporters and friendly critics as well as practitioners consciously researching design theory or extending thinking on it and applying same to society or civilisation, including history of ideas.

The first major design inference on record in our civilisation is by Plato, in The Laws, Bk X:

Ath [in The Laws, Bk X 2,360 ya]. . . .[The avant garde philosophers and poets, c. 360 BC] say that fire and water, and earth and air [i.e the classical “material” elements of the cosmos — the natural order], all exist by nature and chance, and none of them by art . . . [such that] all that is in the heaven, as well as animals and all plants, and all the seasons come from these elements, not by the action of mind, as they say, or of any God, or from art, but as I was saying, by nature and chance only [ –> that is, evolutionary materialism is ancient and would trace all things to blind chance and mechanical necessity, contrasted to “the action of mind” i.e. intelligently directed configuration] . . . .

[[T]hese people would say that the Gods exist not by nature, but by art, and by the laws of states, which are different in different places, according to the agreement of those who make them . . . .

Then, by Heaven, we have discovered the source of this vain opinion of all those physical investigators . . . . they affirm that which is the first cause of the generation and destruction of all things, to be not first, but last, and that which is last to be first, and hence they have fallen into error about the true nature of the Gods.

Cle. Still I do not understand you.

Ath. Nearly all of them, my friends, seem to be ignorant of the nature and power of the soul [[ = psuche], especially in what relates to her origin: they do not know that she is among the first of things, and before all bodies, and is the chief author of their changes and transpositions. And if this is true, and if the soul is older than the body, must not the things which are of the soul’s kindred be of necessity prior to those which appertain to the body?

Cle. Certainly.

Ath. Then thought and attention and mind and art and law will be prior to that which is hard and soft and heavy and light; and the great and primitive works and actions will be works of art; they will be the first, and after them will come nature and works of nature, which however is a wrong term for men to apply to them; these will follow, and will be under the government of art and mind.

Cle. But why is the word “nature” wrong?

Ath. Because those who use the term mean to say that nature is the first creative power; but if the soul turn out to be the primeval element, and not fire or air, then in the truest sense and beyond other things the soul may be said to exist by nature; and this would be true if you proved that the soul is older than the body, but not otherwise.

[[ . . . .]

Ath. . . . when one thing changes another, and that another, of such will there be any primary changing element? How can a thing which is moved by another ever be the beginning of change? Impossible. But when the self-moved changes other, and that again other, and thus thousands upon tens of thousands of bodies are set in motion, must not the beginning of all this motion be the change of the self-moving principle? . . . . self-motion being the origin of all motions, and the first which arises among things at rest as well as among things in motion, is the eldest and mightiest principle of change, and that which is changed by another and yet moves other is second. [–> notice, the self-moved, initiating, reflexively acting causal agent, which defines freedom as essential to our nature, and this is root of discussion on agents as first causes.]

[[ . . . .]

Ath. If we were to see this power existing in any earthy, watery, or fiery substance, simple or compound-how should we describe it?

Cle. You mean to ask whether we should call such a self-moving power life?

Ath. I do.

Cle. Certainly we should.

Ath. And when we see soul in anything, must we not do the same-must we not admit that this is life?

[[ . . . . ]

Cle. You mean to say that the essence which is defined as the self-moved is the same with that which has the name soul?

Ath. Yes; and if this is true, do we still maintain that there is anything wanting in the proof that the soul is the first origin and moving power of all that is, or has become, or will be, and their contraries, when she has been clearly shown to be the source of change and motion in all things?

Cle. Certainly not; the soul as being the source of motion, has been most satisfactorily shown to be the oldest of all things.

Ath. And is not that motion which is produced in another, by reason of another, but never has any self-moving power at all, being in truth the change of an inanimate body, to be reckoned second, or by any lower number which you may prefer?

Cle. Exactly.

Ath. Then we are right, and speak the most perfect and absolute truth, when we say that the soul is prior to the body, and that the body is second and comes afterwards, and is born to obey the soul, which is the ruler?

[[ . . . . ]

Ath. If, my friend, we say that the whole path and movement of heaven, and of all that is therein, is by nature akin to the movement and revolution and calculation of mind, and proceeds by kindred laws, then, as is plain, we must say that the best soul takes care of the world and guides it along the good path. [[Plato here explicitly sets up an inference to design (by a good soul) from the intelligible order of the cosmos.

Earlier in the same Bk X, he had noted just how old and how philosophically loaded evolutionary materialism and its appeal to chance and/or necessity are, drawing out consequences for law, government and community:

Ath[enian Stranger, in The Laws, Bk X 2,360 ya]. . . .[The avant garde philosophers and poets, c. 360 BC] say that fire and water, and earth and air [i.e the classical “material” elements of the cosmos — the natural order], all exist by nature and chance, and none of them by art . . . [such that] all that is in the heaven, as well as animals and all plants, and all the seasons come from these elements, not by the action of mind, as they say, or of any God, or from art, but as I was saying, by nature and chance only [ –> that is, evolutionary materialism is ancient and would trace all things to blind chance and mechanical necessity; observe, too, the trichotomy: “nature” (here, mechanical, blind necessity), “chance” (similar to a tossed fair die), ART (the action of a mind, i.e. intelligently directed configuration)] . . . .

[Thus, they hold] that the principles of justice have no existence at all in nature, but that mankind are always disputing about them and altering them; and that the alterations which are made by art and by law have no basis in nature, but are of authority for the moment and at the time at which they are made . . .

We see the wider setting and the more specific themes.>>

U/D May 14, to promote from 470 below and onward, a summary of kernel ID theory as a cluster of postulates — based on clips from the UD Resources tab:

ID as a Postulates based Scientific Framework

The theory of intelligent design (ID) holds

[–> key, evidence backed postulate, cf those of Newtonian dynamics and special then general relativity, thermodynamics and statistical thermodynamics, postulational cores can be brief but sweeping in impact]

that

[First, Evidence-backed Programmatic Postulate:] certain features of the universe and of living things are best explained [–> explicit reference to logic of abductive reasoning] by an intelligent cause rather than an undirected process such as natural selection.

ID is thus a scientific disagreement with the core claim of evolutionary theory that the apparent design of living systems is an illusion.

In a broader sense,

[2nd, Operational Postulate:] Intelligent Design is simply the science of design detection — how to recognize patterns arranged by an intelligent cause for a purpose.

Design detection is used in a number of scientific fields, including anthropology, forensic sciences that seek to explain the cause of events such as a death or fire, cryptanalysis and the search for extraterrestrial intelligence (SETI). [–> design oriented sciences. Signal to noise ratio in telecommunications is based on a design inference.]

[3rd, Empirical Warrant/Point of test or potential falsification postulate:] An inference that certain biological information may be the product of an intelligent cause can be tested or evaluated in the same manner as scientists daily test for design in other sciences.

ID is controversial because of the implications of its evidence, rather than the significant weight of its evidence. ID proponents believe science should be conducted objectively, without regard to the implications of its findings. This is particularly necessary in origins science because of its historical (and thus very subjective) nature, and because it is a science that unavoidably impacts religion.

[Evidence Corollary:] Positive evidence of design in living systems consists of the semantic, meaningful or functional nature of biological information, the lack of any known law that can explain the sequence of symbols that carry the “messages,” and statistical and experimental evidence that tends to rule out chance as a plausible explanation. Other evidence challenges the adequacy of natural or material causes to explain both the origin and diversity of life . . . .

Intelligent design [ID] – Dr William A Dembski, a leading design theorist, has defined ID as “the science that studies signs of intelligence.” That is,

[4th, Designs and Signs Postulate:] as we ourselves instantiate [thus exemplify as opposed to “exhaust”], intelligent designers act into the world, and create artifacts. When such agents act, there are certain characteristics that commonly appear, and that – per massive experience — reliably mark such artifacts. It it therefore a reasonable and useful scientific project to study such signs and identify how we may credibly reliably infer from empirical sign to the signified causal factor: purposefully directed contingency or intelligent design. [–> definition of design, note, abductive inference from observed sign to signified cause.]

Among the signs of intelligence of current interest for research are:

[Supplement, on evidence:] [a] FSCI — function-specifying complex information [e.g. blog posts in English text that take in more than 143 ASCII characters, and/or — as was highlighted by Yockey and Wickens by the mid-1980s — as a distinguishing marker of the macromolecules in the heart of cell-based life forms], or more broadly

[b] CSI — complex, independently specified information [e.g. Mt Rushmore vs New Hampshire’s former Old Man of the mountain, or — as was highlighted by Orgel in 1973 — a distinguishing feature of the cell’s information-rich organized aperiodic macromolecules that are neither simply orderly like crystals nor random like chance-polymerized peptide chains], or

[c] IC — multi-part functionality that relies on an irreducible core of mutually co-adapted, interacting components. [e.g. the hardware parts of a PC or more simply of a mousetrap; or – as was highlighted by Behe in the mid 1990’s — the bacterial flagellum and many other cell-based bodily features and functions.], or

[d] “Oracular” active information – in some cases, e.g. many Genetic Algorithms, successful performance of a system traces to built-in information or organisation that guides algorithmicsearch processes and/or performance so that the system significantly outperforms random search. Such guidance may include oracles that, step by step, inform a search process that the iterations are “warmer/ colder” relative to a performance target zone. (A classic example is the Weasel phrase search program.) Also,

[e] Complex, algorithmically active, coded information – the complex information used in systems and processes is symbolically coded in ways that are not preset by underlying physical or chemical forces, but by encoding and decoding dynamically inert but algorithmically active information that guides step by step execution sequences, i.e. algorithms. (For instance, in hard disk drives, the stored information in bits is coded based a conventional, symbolic assignment of the N/S poles, forces and fields involved, and is impressed and used algorithmically. The physics of forces and fields does not determine or control the bit-pattern of the information – or, the drive would be useless. Similarly, in DNA, the polymer chaining chemistry is effectively unrelated to the information stored in the sequence and reading frames of the A/ G/ C/ T side-groups. It is the coded genetic information in the successive three-letter D/RNA codons that is used by the cell’s molecular nano- machines in the step by step creation of proteins. Such DNA sets from observed living organisms starts at 100,000 – 500,000 four-state elements [200 k – 1 M bits], abundantly meriting the description: function- specifying, complex information, or FSCI.)

[(f) evidence of the fine tuned cosmos.] . . . .

Thus, ID can be framed on postulates, and we may draw forth from such that cells using memory structures storing coded algorithms and associated execution machinery are strong evidence of the design of cell based life. With Drexler, we are looking a bit at nanotech issues.>>

Food for thought and for clarification. END

U/D May 8th, to allow another thread to return to its focus:

>>THE FOLLOWING COME FROM THE LEAK CASE THREAD:

F/N May 7: As tangential objections to the design inference have been taken up (in obvious subject switching) I pose p. 5 from Sir Francis Crick’s March 19, 1953 letter to his son:

Crick’s letter

And, here is the protein synthesis process in outline:

Protein Synthesis (HT: Wiki Media)

Together with a summary of the information communication system involved, as outlined by Yockey:

Yockey’s analysis of protein synthesis as a code-based communication process

F/N, May 8: As the tangent continues, it seems a further illustration is advisable:

It seems more is needed, so here is how this fits into protein synthesis and the metabolic network and how we see prong height coding:

In for a penny, in for a pound, here is a video:

Notice, we are actually dealing with a storage register. Say, each shaft with pins is set for five positions, four elevated, one on the ledge. This is directly comparable to GCAT, and as the video shows there are five digits:

| X1 | X2 | X3 | X4 | X5 |

The key is encoded to the correct string of digits that in combination will open the lock, say 13213. The resting fully locked position is of course 00000.>>

U/D May 14: As a side chain appeared in another thread that is more appropriate here, I cross post a footnote added there:

It being now an obvious tactic to sidetrack non technical UD threads into ID debates (even where there is a thread that is live on the topic with relevant information, graphics and video) I will augment basic correction below by adding here a chart showing tRNA as a Drexler style molecular nanotech position-arm device:

We may expand our view of the Ribosome’s action:

The Ribosome, assembling a protein step by step based on the instructions in the mRNA “control tape”

As a comparison, here is punched paper tape used formerly to store digital information:

Punch Tape

We should tabulate”

The Genetic code uses three-letter codons to specify the sequence of AA’s in proteins and specifying start/stop, and using six bits per AA

In Yockey’s communication system framework, we now can see the loading [blue dotted box] and how tRNA is involved in translation, as the AA chain towards protein formation is created, step by step — algorithm — under control of the mRNA chain of three base codons that match successive tRNA anticodons, the matching, of course is by key-lock fitting of G-C or C-G and A-T or T-A, a 4-state, prong height digital code:

Yockey’s analysis of protein synthesis as a code-based communication process

Further to this, DNA has been extended with other similar monomers, and DNA has been used as a general purpose information storage medium for digital codes, apparently even including for movie files.

The point of this is, for record, to expose and correct how hyperskeptical objectors have inappropriately tried to deny that D/RNA acts as a string based digital information storage unit, that it holds algorithmic code used in protein synthesis, and latterly that tRNA acts in this process in the role of a position-arm nanotech robot device with a CCA tool tip, CCA being a universal joint that attaches to the COOH end of an AA.

Speaking of which, AA structure, with side branches [R] and chaining links, i.e. NH2-alpha Carbon + R – COOH:

F/N, May 14, it is worth the while to add, regarding layer cake communication architectures and protocols:

Where, underlying this is the Shannon model, here bent into a U to show how layers fit in, this also ties to Yockey:

A communication system

We may then extend to Gitt’s broader framework:

Gitt’s Layer-cake communications model

As an illustration, the ISO model:

OSI Network “layer-cake” model

Similarly, here is a layer cake view of a computer (network ports can be added):

These layers, of course, are abstract, only the physical layer is hardware we can see directly. Even for that, we cannot easily see all the design details for compatibility and function.

These may be compared to Yockey, to draw out the framework of codes, protocols and communication requisites.

U/D May 21, on illustrating one aspect of cosmological fine tuning:

Barnes: “What if we tweaked just two of the fundamental constants? This figure shows what the universe would look like if the strength of the strong nuclear force (which holds atoms together) and the value of the fine-structure constant (which represents the strength of the electromagnetic force between elementary particles) were higher or lower than they are in this universe. The small, white sliver represents where life can use all the complexity of chemistry and the energy of stars. Within that region, the small “x” marks the spot where those constants are set in our own universe.” (HT: New Atlantis)
Comments
Kairosfocus VL, objective warrant is not to be equated with willingness to agree. KF
...or with willingness to appear more mannered , courteous and considerate than those unrespectful Christians . "Peace worth 4 times more than justice"(a saint ) ...except peace in falsehood worth nothing, it's hypocrisy . If you say to a man that he is a woman if he thinks so this is not respect ,you hurt even more his already damaged mental health. Same thing with saying that all religions are the same , playing a false reconciliatory agent.Lieutenant Commander Data
April 26, 2022
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And who is to judge that your idea of what is objectively warranted is correct and mine isn't, or vice versa. You don't just get to declare this issue settled because you think you have provided "objective warrant" and someone else hasn't. I've provided mathematically true statements that provide "objective warrant" for the distinctions that I've made. I think my objective warrant is valid, and yours isn't. Therefore, there is disagreement, as there was in the thread from 2019.Viola Lee
April 26, 2022
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VL, objective warrant is not to be equated with willingness to agree. KFkairosfocus
April 26, 2022
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No, I'm sure this was not "settled years ago". I seriously doubt that the people you were discussing with then went away saying, "Oh, KF is right!" In fact, from a very quick scroll through the thread you posted I see much that is similar to this thread: lots of tangents and lack of agreement about what is being discussed, including some frustration about not being able to focus on narrowing down the actual topic. So, no, the subject was not settled years ago.Viola Lee
April 26, 2022
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VL, inference is personal, implication is objective. The description of a beginningless succession of years maps to the pattern of negative integers, which is transfinite of order type w. Beyond any k' = [k+0]' , we have [k+1]' [k+2]' and so forth without limit; to see Z- simply set k' = 0. That precisely maps. At this point, it is clear where the weight on merits is, once the no beginning, plus year by year or stage by stage succession to today claim is made; where kindly note the metric, the same as in our calendar, which is an ordinal succession with zero point at approximate time of Jesus' birth . . . notice how years BC descend to the zero point then ascend to now the twenty-FIRST century. Thus, my, go look at the calendar. As for setting zero at the singularity, much the same . . . except the onward is speculative not observational. A beginningless past of years etc, therefore implies exhaustion of Z-, and transfinite succession of order w, which is infeasible . . . to make it explicit. As I said, this was settled years ago. KFkairosfocus
April 26, 2022
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How many angels can dance on the point of a pin?
Quantum Gravity Treatment of the Angel Density Problem We derive upper bounds for the density of angels dancing on the point of a pin. It is dependent on the assumed mass of the angels, with a maximum number of 8.6766*10exp49 angels at the critical angel mass (3.8807*10exp-34 kg). If the angels dance very quickly and in the same direction, then the angular momentum could lead to a situation like the extremal Kerr metric, where no event horizon forms (this could also be achieved by charging the angels). Hence the number of dancing angels that can crowd together is likely much higher than the number of stationary angels.
https://improbable.com/airchives/paperair/volume7/v7i3/angels-7-3.htm Let the debate begin! jerry
April 26, 2022
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KF writes, "VL, first, as I just noted, the beginningless past succession of stages clearly implies traversal of a transfinite in finite steps." It "clearly implies" that to you, but that's because you find what you're looking for rather than paying attention to what is actually said by someone else. I’ve made a clear distinction between the potential infinity produced by the negative numbers continuing indefinitely, with no beginning, and the incapability of that process to produce an actual, completed infinity. I took a very quick look at the old thread you posted, and saw this exchange early in the comments:
ET: But please do tell how we can reach the present from an infinite past. DaveS: I didn’t claim to have such an argument. Let’s have no burden-shifting in this thread, please.
That's what's going on here. I say one thing, and you say I implied something else. Well, I'm not obligated to accept what you think I implied, or suggested, or invited the supposition of or enabled the claim of or whatever vague terms you use to "burden-shift" the discussion. I'm only obligated to take responsibility for what I am actually saying, not for your Quixotic suppositions that what I am saying actually implies the opposite of what I say. Here’s another example: you write, “Therefore, to claim that past finite stages of time that cumulate to now are without beginning, thus can be mapped to the set of the negative integers exhaustively.” No. I have clearly said, and it is mathematically true, that the process of continuing indefinitely DOES NOT and CANNOT exhaust the entire set of negative integers. That’s mathematically true, and you know it.Viola Lee
April 26, 2022
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PPS: I find from the thread of three years ago this month: >>48 kairosfocus April 18, 2019 at 1:11 am (Edit) F/N: The core issue being raised to WLC, which he is answering: (P) IF (i) the temporal series of all past events is actually infinite in its duration (as measured by equal temporal intervals), THEN (ii) there COULD be some mind/clock/counting machine/computer/angel/god which would SUCCESSIVELY pair all the past equal intervals (say, seconds) to all negative whole numbers in the corresponding order. Notice, this would imply that the past countable stages are of order w, where any particular definite stage -k will be a corresponding count of magnitude k in the past. Where of course, { . . . -k, . . . -2, -1, 0} is transfinite leftwards. Consequently, it is implied that at any -k finitely removed from us, the transfinite causal-temporal succession of stages up to -k in the past has already happened; as can be seen by taking a leftward mirror of the pink vs blue ribbon tapes in the OP. Craig goes on to summarise: The only hope for proponents of the infinite past is to insist that the series of past events has the order type ?* so that every event lies at only a finite distance from the present. In that way, forming an infinite past by successive addition doesn’t involve, they claim, traversing an infinite distance. Now, let us note his comment on a related question: https://www.reasonablefaith.org/writings/question-answer/is-a-beginningless-past-actually-infinite/ . . . It might be said that at least there have been past events, and so they can be numbered. But by the same token there will be future events, so why can they not be numbered? Accordingly, one might be tempted to say that in an endless future there will be an actually infinite number of events, just as in a beginningless past there have been an actually infinite number of events. But in a sense that assertion is false; for there never will be an actually infinite number of events, since it is impossible to count to infinity. The only sense in which there will be an infinite number of events is that the series of events will go toward infinity as a limit. But that is the concept of a potential infinite, not an actual infinite. Here the objectivity of temporal becoming makes itself felt. For as a result of the arrow of time, the series of events later than any arbitrarily selected past event is properly to be regarded as potentially infinite, that is to say, finite but indefinitely increasing toward infinity as a limit. The situation, significantly, is not symmetrical: as we have seen, the series of events earlier than any arbitrarily selected future event cannot properly be regarded as potentially infinite. So when we say that the number of past events is infinite, we mean that prior to today ?0 events have elapsed. But when we say that the number of future events is infinite, we do not mean that ?0 events will elapse, for that is false. [emphasis mine] Similarly, another question poses: https://www.reasonablefaith.org/writings/question-answer/forming-an-actual-infinite-by-successive-addition/ . . . I have a question concerning one of the philosophical arguments you offer in support of the view that the universe began to exist, namely the argument from the impossibility of forming an actual infinite by successive addition. You set up the argument as follows: 1. A collection formed by successive addition cannot be actually infinite. 2. The temporal series of past events is a collection formed by successive addition. 3. Therefore, the temporal series of past events cannot be actually infinite. This argument exposes a feature in the notion of an infinite series of events that I find bewildering. To set the situation up, we’ll assume the past is infinite. By virtue of a tensed conception of time, every event in the infinite past up to the present was a real event that had to be “lived” through. But, if that’s the case, how could all those events have been lived through, one by one, up till now? Just how, exactly, could we reach the end of that beginningless series? How could the present event arrive if, before it could arrive, an infinite number of previous events had to arrive first? Like I said, this seems very puzzling. But I can’t quite put my finger on why. Is it simply that, on an intuitive level, I find the idea of traversing a beginningless series absurd? As you wrote in your reply to John Taylor, “The question is whether an infinite series of events, having no beginning and having an ending in the present, is metaphysically possible given a tensed view of time. Intuitively, this does not seem possible, for it seems that the present event could not arrive if its arrival had to be preceded by the successive arrival of an infinite number of prior events.” [“A Swift and Simple Refutation of the Kalam Cosmological Argument?” Religious Studies 35 (1999): 57-72. Footnote 26] This is exactly what impels me to accept the argument. But is there a way to analyze our intuition more deeply to find out exactly why such a traversal is impossible? Or is it somehow non-analyzable? The “traditional objection” to this argument is that it is only impossible to traverse infinity if one begins at some point. But, whatever this reply manages to do, it doesn’t seem to rebut our intuition or reduce the apparent absurdity engendered by the situation; after considering the objection, I’m still genuinely perplexed as to how such a traversal could happen. In his answer we find: . . . In the case of beginning with some finite quantity and adding finite quantities to it we can pinpoint the problem clearly: since any finite quantity plus another finite quantity is always a finite quantity, we shall never arrive at infinity even if we keep on adding forever. Infinity in this case serves merely as a limit which we never attain. What becomes truly puzzling, even mind-boggling, is the suggestion that we can, by adding only finite quantities, form an infinite quantity or collection–say, a certain collection of baseball cards–by never beginning but ending at some time! Here the impossibility cannot be analyzed as due to the impossibility of adding finite quantities to finite quantities and getting an infinite quantity, for in this case the quantity to which finite additions are being made is always and already infinite. We are successively adding finite quantities to an already infinite quantity, so of course the sum is an infinite quantity. Here infinity is not functioning as a mere limit but as a collection of concrete elements. Now notice that one still hasn’t explained how we are able to form our infinite collection of baseball cards by successive addition. For at any time in the past the collection is already infinite, and yet the total collection has not yet been formed . . . . Here’s the problem, it seems to me: in order for the collection [of an infinite number of successively added baseball cards] to be completed, we must have already enumerated, one at a time, an infinite number of previous cards. But before the final card could be added, the card immediately prior to it would have to be added; and before that card could be added, the card immediately prior to it would have to be added; and so on ad infinitum. So one gets driven back and back into the infinite past, making it impossible for any card to be added to the collection . . . . About the best that the critic of the argument can do at this point, I think, is to say that if one adds cards at a rate of, say, one card per second, then the collection can be completed because there has been an infinite number of seconds in the beginningless past. But clearly this response only pushes the problem back a notch: for the question then is, how can the infinite collection of past seconds be formed by successive addition? For before the present second could elapse, the one before it would have to elapse, and so on, as before. Because the problem is applicable to time itself, it cannot be resolved by appealing to infinite past time. Of course, proponents of a static or tenseless theory of time will deny that moments of time really do elapse, but then their objection is actually to premiss (2), not premiss (1). If one is not yet convinced by this argument, then I would offer a further defense of premiss (1) by arguing that if an actual infinite could be formed by succesive addition, then various absurditites would result . . . . Suppose we meet a man who claims to have been counting down from infinity and who is now finishing: . . ., -3, -2, -1, 0. We could ask, why didn’t he finish counting yesterday or the day before or the year before? By then an infinite time had already elapsed, so that he should already have finished. Thus, at no point in the infinite past could we ever find the man finishing his countdown, for by that point he should already be done! In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will already have finished. But if at no point in the past do we find him counting, this contradicts the hypothesis that he has been counting from eternity. This shows again that the formation of an actual infinite by never beginning but reaching an end is as impossible as beginning at a point and trying to reach infinity. Thus, we see in effect a begging of the question by inferring that at any -k prior no now (set that n = 0), the succession involving the transfinite has already occurred. But, that was the problem, how is that so, how could it be feasible without a duration between some past actual stage Q and n being itself transfinite thus IMPLICITLY — as opposed to explicitly — requiring traversing a transfinite in successive steps? Saying that there is an infinity of finite succession, with the duration between any two events or stages t1 and t2 being finite only, seems to be dubious, even contradictory. I think instead, it is first reasonable to argue that we have no warrant to claim a transfinite actual past that would not involve an actually transfinite duration to now. Where, that would imply precisely the spanning the transfinite duration in successive stages that is a supertask. Instead, it seems to me, we are only warranted to speak of a finite span of succession between any two stages t1 and t2. This, implying that we are warranted only to speak of a finite actual past, and of course of a potentially infinite future (ignoring for the moment the heat death issue).>>kairosfocus
April 25, 2022
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VL, first, as I just noted, the beginningless past succession of stages clearly implies traversal of a transfinite in finite steps, of order type omega. I again point to 221. This was hammered out across three years. Your repeated claims notwithstanding, the matter was settled years ago now, was it 2019. Above at 221 I have taken time to explicitly show how the claimed or suggested traversal of Z- is necessarily a claim to traversal of a transfinite span of order type w:
let us do a comma separated value construction of a wx3 matrix, pardon limitations of Word Press: {0: , 0 –>1 , 1 –> -1 1: , 2 –> 2 , 3 –> -2 2: , 4 –> 4, 5 –> -3 . . . , . . . , . . . w: , w , w’} Where clearly w + w’ = 0, as can be seen by decimation of the rows. We here see next, that the naturals, the integers, the evens and the odds as well as the negatives all have order type w. Where, a basic definition of a transfinite set is that a proper subset can be placed in 1:1 correspondence with the whole. Thus, the integers and particularly the negative integers can be seen to be transfinite, with the counting numbers as a metric. Therefore, to claim that past finite stages of time that cumulate to now are without beginning, thus can be mapped to the set of the negative integers exhaustively, is to imply that the traverse from the remote pass to now is transfinite. Implicitly, transfinite. That such a span cannot be traversed in cumulative, finite stage steps should be obvious and should be acknowledged. However, given the open or veiled acerbity that has generated a toxic climate surrounding origins in general and UD in particular, let us note for the simple case of counting onward from some k and its complement k’, again using a matrix: 0: , k+0 , k’-0 1: , k+1 , k’-1 2: , k+2 , k’-2 . . . , . . ., . . . w: , k+w , k’ – w} That is, counting on beyond any k we state or represent in N, with k’ in Z-, will continue transfinitely of order type w, just as for the col 1 case k = 0. This of course reflects the same transfiniteness. It also means that at any finite stage k, or k’ we may go on from there as though we had just begun. A labour of Sisyphus. This is how the futile supertask I have often spoken of arises.
Following up, once one claims, suggests or implies or just invites the supposition that for any past year [for convenience] k' that has a negative value, e.g. effectively years BC or we could set singularity as zero point, that beyond k' there are any number of further past actual years, one may properly be taken as proposing that the deep past of origins is transfinite, maps to Z- exhaustively, is of order type w. So, with years count as relevant metric, implicitly transfinite. It is therefore, again, a warranted conclusion, that proponents or enablers of claims of a beginningless past are advocating or enabling the claim, that a transfinite traversal of order type w has occurred as our actual past. But such traversal is an infeasible supertask so we may freely infer it never happened. That is, the causal temporal thermodynamic domain we inhabit and/or antecedents such as a q-foam with fluctuations, etc, had a definite beginning. This, even without being able to put a particular value now that q-foams etc have been used to inject a non-empirical extension of the claimed past beyond the singularity. That's philosophy dressed up in a lab coat and it is in order to apply logic of being considerations. KF PS, the dragging continues. I am not going to let a mischaracterisation stand without at least making a statement for record.kairosfocus
April 25, 2022
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And, KF, I simply stated that your summary was inaccurate, in one short sentence. See 131. And nobody has "dragged you through" anything. You've chosen to respond. If you want to keep the discussion going, keep posting. If you don't want to keep it going, quit posting. You're in charge of yourself, so don't keep blaming/accusing other people as if we were responsible for your behavior.Viola Lee
April 25, 2022
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If we consider the integers, the negative integers are just like the positive ones: they extend indefinitely (that is, accumulate without limit) although in doing so neither the positive nor the negative integers can accumulate to an actualized infinity. The positive integers are a potential infinity without an end and the negative integers are a potential infinity without a beginning. The issue here is an old one, going back to Aristotle: a potential vs an actualized infinity. An actualized infinity can only be considered as existing, in whatever way it might be said to exist, as a complete whole: you can't build an actualized infinity through any type of accumulation, such as by adding elements one-by-one in stepwise fashion. That's just mathematics.Viola Lee
April 25, 2022
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VL, kindly note 247 to SA at 243, and onward 221 https://uncommondescent.com/intelligent-design/lfp-55-defining-clarifying-intelligent-design-as-inference-as-theory-as-a-movement/#comment-752456 KF PS, summarising accurately the result of a debate as warranted on substance is not re opening debate. I simply stated what was established and have again needlessly been dragged through outlining why it is established.kairosfocus
April 25, 2022
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SA, Integers are vectors, as are reals and signed rationals. That is they express size and direction. This is part of the logic of structure and quantity of any possible world. Ten miles North is not equivalent to ten miles South, and this is as embedded into reality as anything else. A gallon of gas as physical quantity has size but not direction but transactions where one owes $21.25 EC for having just bought but not yet paid for a gallon do have a financial analogue of direction. I have already shown at 221 that the negative integers are transfinite of order type w, cardinality aleph null, and so any suggested model of the past which tries to represent that at any k' there are any number of onward finite stages, years for convenience, is an attempt to model and map the claimed beginningless past to a transfinite set. Thus, the challenge of infeasibility of stepwise, cumulative, finite stage traversal of the traversal of the transfinite applies. See https://uncommondescent.com/intelligent-design/lfp-55-defining-clarifying-intelligent-design-as-inference-as-theory-as-a-movement/#comment-752456 That is, on logic of being considerations tied to structure and quantity, aka mathematics, the past of our causal temporal thermodynamic domain is inherently finite even as in principle its future may accumulate without limit but at any particular stage cumulative time would be finite. Potential as opposed to actualised transfinite. Where the metric is the count of stages as we see from a calendar. KFkairosfocus
April 25, 2022
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Querius Exactly! It's been a game where the rules are changed as it is played.Silver Asiatic
April 25, 2022
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And I agree with Q 100% on that in respect to applying math to reality. There is lots of math that has value and interest for its own sake, but if we want to apply it we create and test models that we have mapped to reality.Viola Lee
April 25, 2022
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Silver Asiatic @243, Haha! Maybe we should just cut to the chase with minimalist statements. Q: But we choose what math models reality sufficiently for our purposes. -QQuerius
April 25, 2022
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KF
an objector tried to re open the debates across three years on inherent finitude of the past
The debate was reopened with the discussion of negative numbers which are proposed as a model of a beginningless sequence where any two numbers selected have a finite distance between them, and this is a placeholder for the traversal of an infinite sequence. Otherwise, why is the math discussion relevant to anything. A: Negative numbers do not represent reality. B: Yes, true, but negative numbers are a sequence with no beginning and we can select a number .... A: But negative numbers do not represent reality. B: Of course, but they are a sequence with no beginning. A: But they cannot represent what is real B: I'm not interested in reality, only mathSilver Asiatic
April 25, 2022
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KF writes, "we are on a tangent as an objector tried to re open the debates across three years on inherent finitude of the past." No, KF, you "opened the debate" at 129 when you wrote, " Traversal of the transfinite in finite steps is an infeasible supertask, a matter we hammered out here over three years." I responded because of your mischaracterization: at 131 I replied, "KF, no one ever said that you could “traverse the transfinite in finite steps.” That didn’t need to “get hammered out.” That’s obvious." Then at 148, 149, and 150 you made more comments addressed to me. So don't blame me for "opening the debate."Viola Lee
April 25, 2022
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F/N3, 211 is updated fixing what WP cannot read. long minuses and less than equals. KFkairosfocus
April 24, 2022
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F/N2, mapping where we are, we are on a tangent as an objector tried to re open the debates across three years on inherent finitude of the past. This connects to the issue of a beginning. We see that both thermodynamically and structurally, a finitely remote beginning stage is well warranted not only from the singularity but even on a speculative quasi physical extension such as a quantum foam with cosmi as fluctuation bubbles. Of course, that is philosophy there is no actual empirical evidence of such a multiverse. But, the urge to get rid of a credible beginning has been there ever since Einstein's surprise that General Relativity expects an expanding cosmos. KFkairosfocus
April 24, 2022
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F/N: I tried to add a comment on the number line, refused. I reconstruct. In effect when our HS teachers draw number lines with arrows pointing to infinity, it is better to see them as implying R* not R, embracing transfinite hyperreals and Robinson's tamed infinitesimals. Where, any vector 0 --> r can become infinitesimally altered by shifting the infinitesimals cloud *0* to the tip, by 1-d vector addition. Thus r + dr, beloved from Calculus is in the infinitesimally altered r zone. Yes, I am highlighting that reals, like integers, are vectors with size and direction. Once we embrace R* we see that R is structurally locked in as expressing finite values within a fuzzy macro border zone beyond which lie the transfinites. Positive hyperreals: 0* -------->*r* ------- . . . ---H ------> Where H beyond the ellipsis is the transfinite zone and 0* embraces the infinitesimals. The other side L-ward is just a mirror image. KFkairosfocus
April 24, 2022
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VL, I of course, point to my 221, just above, and on points from your 209" >>KF writes, “No beginning implies a transfinite past, a beginning implies a finite past.”>> 1: This means, an ACTUAL past without a beginning will have cumulative finite stages to now constituting a mapping to the negative integers [and of course some positive ones, e.g. the singularity is an apt zero] and no finite actual past stage -- year for convenience -- k' swill not be exceeded by onward stages without further limit by any finite value. 2: This is the precise required character. >>No.>> 3: This fails to agree with the relevant reason. >>1. The distance from every integer to any other integer is finite.>> 4: I could quibble that first hyperintegers are valid, but that is just to emphasize that you are identifying integers that are specifically at finite remove. 5: This is a quarter story, any two finite integers we may describe or represent, z1 and z2, can and will be exceeded on the relevant side going away from zero without definable finite limit. 6: This is why it is important to reckon with the ellipses and what they mean, they bind us to finitude of particular cases we map, but also to onward cases without limit. 7: Where, the metric involved is precisely numbers of years, so finitude of spans between z1 and z2 also comes with there are onward cases without limit. 8: That is part of why attempts to assert a past without a beginning constitute such an extraordinary, bizarre claim that implies traversal of a transfinite span, not due to particular identified cases but due to the inherent onwardness. >>2. There is no smallest integer: the integers have no beginning.>> 9: Which leads to what I just pointed out and the relevant metric is years count, where the required count is of years past without a beginning up to now >>Therefore, the integers having no beginning does not imply that there is ever an infinite distance between two integers.>> 10: This comes down to, what is the implied metric? The answer is P, years count from the total past to now, which is being claimed as without a beginning. 11: Where, in 221 above I showed that the negative integers are of order type w, thus cardinality aleph null. Thus, we have a metric for infinite past that reckons with the key structural element, the transfinite ellipsis. 12: In short the proper metric is P, years to date including the ellipses beyond any particular z1 and z2. >>You are correct that an actual infinite set of integers can not be exhausted, in your words, by any accumulative process.>> 13: In short, traversal of a transfinite span cannot be effected by cumulative finite stage steps. Where the ellipsis is there to tell us that the Integers have that character. >> But having no beginning is different than saying the entire infinite set has been instantiated.>> 14: Nope, the character of years is that they are countable and cumulative to date. As integers, discrete, so count by comparison to N is an appropriate metric and clipping from 221 we see:
w [omega] is the order type of the naturals constructed as ordinals, and N has cardinality, aleph-null. Now, let us do a comma separated value construction of a wx3 matrix, pardon limitations of Word Press: {0: , 0 –>1 , 1 –> -1 1: , 2 –> 2 , 3 –> -2 2: , 4 –> 4, 5 –> -3 . . . , . . . , . . . w: , w , w’} Where clearly w + w’ = 0, as can be seen by decimation of the rows. We here see next, that the naturals, the integers, the evens and the odds as well as the negatives all have order type w. Where, a basic definition of a transfinite set is that a proper subset can be placed in 1:1 correspondence with the whole. Thus, the integers and particularly the negative integers can be seen to be transfinite, with the counting numbers as a metric. Therefore, to claim that past finite stages of time that cumulate to now are without beginning, thus can be mapped to the set of the negative integers exhaustively, is to imply that the traverse from the remote pass to now is transfinite. Implicitly, transfinite. That such a span cannot be traversed in cumulative, finite stage steps should be obvious and should be acknowledged.
15: Y, years to date with 0 at singularity, on assertion that it is without beginning would have, say 13.8 BY R-ward of 0, and an unlimited number L-ward. That is, the L-ward part maps Z- and the metrics apply. 16: Again, the transfinite continuation ellipses count. 17: Wolfram Alpha: https://www.wolframalpha.com/input?i=order+type
Every totally ordered set (A, LTE) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski 1997, p. 38; Dauben 1990, pp. 184 and 199; Moore 1982, p. 52; Suppes 1972, pp. 127-129). Thus, an order type categorizes totally ordered sets in the same way that a cardinal number categorizes sets. The term is due to Georg Cantor, and the definition works equally well on partially ordered sets. The order type of the negative integers is called * ?, although Suppes calls it ?*. The order type of the rationals is called eta. Some sources call the order type of the reals theta, while others call it lambda.
Where toohttps://www.wolframalpha.com/input?i=transfinite+induction
Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to the natural numbers Z, which are precisely the finite ordinal numbers. The normal inductive step of deriving P(n + 1) from P(n) can fail due to limit ordinals. Let A be a well ordered set and let P(x) be a proposition with domain A. A proof by transfinite induction uses the following steps: 1. Demonstrate P(0) is true. 2. Assume P(b) is true for all bLTa. 3. Prove P(a), using the assumption in (2). 4. Then P(a) is true for all a element A. To prove various results in point-set topology, Cantor developed the first transfinite induction methods in the 1880s. Zermelo extended Cantor's method with a "proof that every set can be well-ordered, " which became the axiom of choice or Zorn's Lemma. Transfinite induction and Zorn's lemma are often used interchangeably, or are strongly linked. Hausdorff was the first to explicitly name transfinite induction.
18: See 221 for the relevant order types. KFkairosfocus
April 24, 2022
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Jerry, complex numbers and integers are cases of vectors, quantities where size and direction are relevant. Ten miles north is not as ten miles south, indeed the second can reverse the effect of the first displacement. Similarly, having $25,000 credit in your account is very different from having that much in overdraft; an economic and financial reality. Indeed that much would be required to get to zero balance and another like sum to get back to that balance. KFkairosfocus
April 24, 2022
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Jerry, Please. Just look at the definition of the word integer: https://www.mathsisfun.com/definitions/integer.html The thermometer I'm looking at is marked in degrees Fahrenheit and certainly not in Kelvin or Rankin. Fortunately, the current air temperature is not below zero! -QQuerius
April 24, 2022
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I see negative integers and zero on it.
Great! Is that Celsius, Fahrenheit or Kelvin? What you are looking at is a symbol for vibration of matter. The negative integers you see just represent a positive number that’s lower than another positive number. I can write -2 on a piece of paper. Does not point to anything real. Aside: I have been down this road hundreds of times. I have logic on my side. At no time do I disparage the use of these concepts as extremely advantageous to a better life. It’s just that something that extremely useful gets turned into something that does not exist in the real world.jerry
April 24, 2022
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Jerry, I'm looking at the markings of my thermometer on the outside wall of my house. I see negative integers and zero on it. Please check out the definition of integer: https://www.mathsisfun.com/definitions/integer.html -QQuerius
April 24, 2022
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I’m sure this is beside the point, but you’re probably thinking of counting numbers
You mean integers When you can point to -2 anywhere, I would love to see it. Zero is all around, zero of a gazillion things. It’s amazing how they all can fit into my hand. Then I go into the next room and there are a gazillion more zeros of things. They’re everywhere. But no -2s or even a -1.jerry
April 24, 2022
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VL, smallest has two senses. In magnitude the smallest integer is zero, algebraically, there is no definable most negative integer, that is finite. Which goes back to traversing in finite steps issues as I drew out earlier this afternoon. I am now back from an afternoon presentation. KFkairosfocus
April 24, 2022
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Q, imaginary numbers with reals allow us to represent 2-d vectors, integers are already 1-d vectors.[+/- gives directionality] . . . that then leads to rotation, oscillations and waves, all very real phenomena. KFkairosfocus
April 24, 2022
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Jerry @226,
I believe 1 is the smallest integer.
I'm sure this is beside the point, but you're probably thinking of counting numbers. Integers are positive, negative and 0. Rounded-off distances, velocities (not speed), accelerations, temperatures (C or F), and balances in overdrawn checkbooks can all be represented by integers: positive, negative, or zero. Please look up the definition of integer. In addition, so-called imaginary numbers can play an important role in electrical engineering and physics. -QQuerius
April 24, 2022
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1 8 9 10 11 12 18

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