Comments

  • Platonic Realism & Scientific Method
    Fictional characters are known as subjects, not objects. — Metaphysician Undercover
    Again, in semeiotic a subject is a term within a proposition that denotes one of its objects. "Hamlet" is a sign, a subject of a proposition such as "Hamlet killed Claudius." The fictional character in Shakespeare's play is its object. Other subjects of that proposition are "killing" and "Claudius," which denote a relation and another fictional character in Shakespeare's play as their objects. The predicate is signified by the syntax, conveying that something called "Hamlet" stood in the relation of "killing" to something called "Claudius" within the universe of discourse, which in this case is Shakespeare's fictional play--not the real universe.

    Your claim that "Hamlet" refers to an object is unsupported by any conventional grammar. — Metaphysician Undercover
    It is firmly supported by what is known as speculative (theoretical) grammar within semeiotic, the science of all signs.

    Even if I grant you that fictional, imaginary things may be called objects, my point was that some form of Platonism, as an ontology is required to support the claimed reality of such objects. — Metaphysician Undercover
    No one is claiming that fictional, imaginary things are real. In fact, being fictional is precisely the opposite of being real. That which is fictional is such as it is only because someone thinks about it that way; Hamlet was the prince of Denmark only because Shakespeare created a story in which that was the case. By contrast, that which is real is such as it is regardless of what anyone thinks about it; Platonism is one form of mathematical realism in this sense, but not the only one.

    Trying to establish a separation between "real" and "existent" just muddies the water by creating ambiguity, and is counterproductive toward understanding. — Metaphysician Undercover
    On the contrary, I have found that carefully drawing the proper distinction between reality (whatever is such as it is regardless of what anyone thinks about it) and existence (whatever reacts with other like things in the environment) is extremely clarifying and helpful. Treating them as synonymous is what muddies the water by imposing nominalism, effectively begging the question against realism.

    As well as being "real", ideas, concepts and abstractions are obviously "existent". They have a significant effect on the physical world as clearly demonstrated by engineering. — Metaphysician Undercover
    The first sentence is false, but the second is true. The kind of effects that ideas, concepts, and abstractions have on the physical world is obviously very different from the kind of effects that physical things have on the physical world. The former are not like things in the (physical) environment, so they do not exist in that sense. Nevertheless, some of them are real--they are such as they are regardless of what anyone thinks about them--but this does not require them to be "located" in a Platonic realm.
  • Have we really proved the existence of irrational numbers?
    I might know who Henry Fonda is, but I might not know he's Peter Fonda's father. — fishfry
    Again, what anyone knows or does not know is beside the point. Since it is fact that Henry Fonda is the father of Peter Fonda, by definition (in semeiotic) the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object.

    I can see Meta's point that the "father of Peter" description conveys more information than merely saying "That's Henry Fonda." — fishfry
    I have never denied this, but (in semeiotic) the information conveyed by a sign corresponds to its interpretant, not its object. If we were standing in a room with Henry Fonda--preferably back when he was alive--then we could point at him and truthfully say both "that is Henry Fonda" and "that is the father of Peter Fonda." Therefore, both signs denote the same object, despite signifying different interpretants.

    As I said, they may denote the same object, but we do not have the premises required to conclude that they do. — Metaphysician Undercover
    The only "premiss" required is the fact that Henry Fonda is the father of Peter Fonda. Someone previously unaware of this fact would learn that "Henry Fonda" and "the father of Peter Fonda" denote the same object upon being informed of it, but those two signs denoted the same object all along. Someone's ignorance does not affect the reality.

    We have a person denoted as "the father of Peter Fonda" and we have a person denoted as "Henry Fonda". We have no other information. — Metaphysician Undercover
    Again, in that scenario, I agree that we do not know that the two signs denote the same object; but that was never the scenario that I was discussing. I was simply pointing out that since I do know that Henry Fonda is the father of Peter Fonda, I also know that "Henry Fonda" and "the father of Peter Fonda" denote the same object. These are facts, not opinions.

    To say that the person denoted as father of Peter Fonda, and the person denoted as Henry Fonda, are equal, as human beings, does not justify the claim that they are the same person. — Metaphysician Undercover
    I never said anything about persons or equality. I merely made the point--which is utterly uncontroversial (in semeiotic)--that since Henry Fonda is the father of Peter Fonda, the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object, regardless of whether someone else knows it.

    The point is that "the father of Peter Fonda" gives different information from "Henry Fonda". — Metaphysician Undercover
    Again, I agree, the two signs signify different interpretants--i.e., convey different information--despite denoting the same object.
  • The paradox of Gabriel's horn.
    The way I'm hearing this, and correct me if I'm misunderstanding you, is that there's an absolute space against which everything else happens. A fixed, universal frame of reference. — fishfry
    No, that is not what I am saying. I am not really talking about physics at all, just a hypothetical/mathematical conceptualization that might have phenomenological and metaphysical applications.

    Brouwer's revenge. The intuitionists are back with a vengeance. I don't doubt the historical momentum. It's the influence of the computers. — fishfry
    Peirce came before Brouwer, and my interest in SIA/SDG has nothing to do with intuitionism or computers. If Peirce had followed through on his skepticism of excluded middle and omitted what we now (ironically) call "Peirce's Law" from his 1885 axiomatization of classical logic, then he would have effectively invented what we now (unfortunately) call "intuitionistic logic" and it might be known instead as "synechistic logic"; i.e., the logic of continuity.

    Is my end of the conversation hopeless unless I read Bell and Peirce? — fishfry
    Maybe not hopeless, but I suspect that there is a "curse of knowledge" aspect here on my part, given my immersion over the last few years in Peirce's writings and the secondary literature that they have prompted.

    Reading your paper, with much eye-glazing I'm ashamed to say. — fishfry
    Thanks for the attempt, sorry for the resulting effect.

    This sounds suspiciously like the idea of a Dedekind cut. Except that there's a point missing, as in the union of the open intervals (0,1) and (1,2). Am I understanding that right? — fishfry
    Peirce would say that there is no point missing, because there are no points at all until we deliberately mark one as the limit that two adjacent portions of the line have in common. If we make a cut there, then the one point becomes two points, since each interval has one at its newly created "loose end."
  • Platonic Realism & Scientific Method
    But if they’re real, then what kind of existence do they have? What does it mean to say abstract objects exist? — Wayfarer
    At the risk of belaboring the point, it is an all-too-common nominalist mistake to insist that if abstract objects are real, then they must also exist. These are two very different concepts--whatever is real is such as it is regardless of what anyone thinks about it, while whatever exists reacts with other like things in the environment. Again, there are varieties of mathematical realism other than Platonism.
  • Have we really proved the existence of irrational numbers?
    They clearly signify something different, and we do not have the premises required to conclude that they denote the same object. — Metaphysician Undercover
    I agree that they signify different interpretants, but this does not preclude them from denoting the same object. It is a fact that Henry Fonda is the father of Peter Fonda, so by definition, it is also a fact that the signs "Henry Fonda" and "the father of Peter Fonda" both denote the same object. Someone who does not know the first fact would not know the second fact either, but that is irrelevant to their being facts.
  • Platonic Realism & Scientific Method
    To justify calling an imaginary thing "an object" requires some form of Platonism. — Metaphysician Undercover
    No, it does not. Hamlet, the fictional character in Shakespeare's play, is the object of the sign that is the first word of this sentence. No form of Platonism is required to affirm this.
  • The paradox of Gabriel's horn.
    ... your position -- that the physical world embodies or instantiates or contains or is a "true continuum" -- is not supported by contemporary physics. — fishfry
    That is not an accurate statement of my position. I hold that space is a true continuum, but not that it is something physical; rather, it is the real medium within which everything physical exists. Ditto for time, albeit in a different respect (obviously).

    And I asked you what a true continuum is, and how you'd know one if you saw it. And how exactly would you see it? — fishfry
    We all perceive space and time, and some of us formulate the hypothesis that each is truly continuous in a way that no collection of numbers, even an uncountably infinite one, could ever fully capture because of their intrinsic discreteness. Nevertheless, this does not preclude the real numbers (for example) from serving as an extremely useful model of continuity for the vast majority of practical purposes.

    You said math doesn't model it, as if there even is any such thing to be modeled. — fishfry
    I have said before, and I just said again, that the real numbers do very successfully model a continuum. They just do not constitute a true continuum. That requires a different mathematical conceptualization, and smooth infinitesimal analysis turns out to be a promising candidate.

    Can I get a short answer? — fishfry
    I gave it a shot, hope it helps.
  • Platonic Realism & Scientific Method
    These mathematical axioms require that a term signifies an object. Only Platonism can support this prerequisite. — Metaphysician Undercover
    This is false, since it is not necessary for something to exist--in the metaphysical sense of reacting with other like things in the environment--in order to be the object of a sign. It does not even have to be real--it could instead be fictional, as some philosophers consider mathematical objects to be. Also, as I have explained elsewhere, signs denote their objects; what they signify are their interpretants.
  • Platonic Realism & Scientific Method
    Well, what exactly does "real" in "numbers are real" mean? — TheMadFool
    That is a historical question, and my understanding is that mathematicians refer to "real" numbers only to distinguish them from so-called "imaginary" numbers; the latter term actually came first.

    The question then is, are abstractions real? — TheMadFool
    In general philosophy, "real" means being such as it is regardless of what anyone thinks about it. In philosophy of mathematics, realism ascribes this nature to mathematical objects, including both real and imaginary numbers.

    Where is a real-world instantiation of the square root of -1? Electronics? — TheMadFool
    Yes, it is routinely used in circuit analysis and design.
  • The paradox of Gabriel's horn.
    The Planck scale represents the point at which contemporary physics breaks down and is not applicable — fishfry
    I agree, this is a better concise summary of what it means.

    We're perfectly in agreement on this point except that my physics is not strong enough to catch the reference to Lorentz symmetry. — fishfry
    Heh, we are in the same boat on that, I was just quoting Wikipedia. :cool:

    I don't feel a need to justify math in the name of reality. — fishfry
    Oh, I completely agree. Again, mathematics is the science of drawing necessary conclusions about strictly hypothetical states of things. Whether those premisses match up with reality is a matter of metaphysics, not mathematics. They can be just about anything imaginable, although some of the most interesting cases come about when we remove a previously taken-for-granted axiom like the parallel postulate in geometry or excluded middle in logic, but still manage to come up with a consistent and useful system.

    You see you are trying to get me to take the other side of a question I reject entirely. — fishfry
    No, that was not my intention, and I am sorry that I came across that way. I was just trying to provide more background about my own position.

    You say that standard math doesn't apply to the "true continuum." I say to you, "Yes I certainly agree. And by the way, what do you mean by true continuum." That's the conversation I believe I'm trying to have. — fishfry
    I can only cover so much ground in this format. My long answer is the paper that I provided.

    You are arguing against multiple strawmen positions I'm not taking. — fishfry
    Again, I apologize for giving you that impression.
  • Have we really proved the existence of irrational numbers?
    In logic, there is no object, we have subjects. To denote is simply to be a sign of. — Metaphysician Undercover
    Logic generalized is semeiotic, the science of all signs--not just arguments, but also propositions and terms; and not just symbols, but also indices and icons. Subjects are the terms within propositions that denote their objects.

    Then you're not addressing the issue we've been discussing. — Metaphysician Undercover
    I never claimed otherwise, I was simply correcting a misuse of the technical term "denote." Again, "Henry Fonda" and "the father of Peter Fonda" denote the same object, even though what they signify about that object is different. If we were looking at a photo of the Fonda family, and someone asked me to point to Henry and you to point to the father of Peter, then we would both correctly point to the same person.

    It is claimed that if two signifiers signify things of equal value, they are exchangeable, therefore they signify the very same object. — Metaphysician Undercover
    This reflects more terminological confusion. What a sign signifies is not its object, but its interpretant.
  • Platonic Realism & Scientific Method
    I think that since the success of the nominalist attitude, which was one of the main forerunners of empiricism generally, that scholastic realism has been forgotten to such an extent that there is barely any awareness of what it meant. — Wayfarer
    :up:
  • Platonic Realism & Scientific Method
    Wasn't the whole issue of scholastic realism versus nominalism is that the former accepted the reality of universals (in Aristotelian form, as mediated by Aquinas), while the nominalists did not? — Wayfarer
    That was indeed the medieval debate, but its modern manifestation is affirming the reality of generals in addition to the existence of individuals. Peirce described himself as an extreme scholastic realist in this sense, maintaining that reality includes some possibilities and some conditional necessities, rather than consisting only of actualities.
  • Have we really proved the existence of irrational numbers?
    Denotation is a form of signification. — Metaphysician Undercover
    Completely wrong, denotation and signification are two different aspects of a sign, corresponding respectively to its object and its interpretant. This is Semeiotic 101.

    Therefore the argument that "the father of Peter Fonda" denotes the same thing as "Henry Fonda" is a fallacious argument, by means of begging the question. — Metaphysician Undercover
    I offered no argument at all, I simply stated a definition--if one sign can be substituted for another in any and every proposition without changing the truth value, then both signs denote the same object. This is also Semeiotic 101.
  • Have we really proved the existence of irrational numbers?
    ↪Metaphysician Undercover

    Again, this confuses denotation with signification. In any and every proposition about "Henry Fonda," we could substitute "the father of Peter Fonda" without changing the truth value. That is what it means for two signs to have the same denotation.
  • Have we really proved the existence of irrational numbers?
    Do you apprehend the flaw in your example, and the difference between what "the father of Peter Fonda" denotes, and what "Henry Fonda" denotes? — Metaphysician Undercover
    The terminology here is incorrect--these two signs denote the same object, even though what they signify about that object is different.
  • Platonic Realism & Scientific Method
    No, they're abstracts, by definition. — Wayfarer
    You are right, my bad--but that is precisely why I maintain that mathematical objects cannot exist in the strict sense of reacting with other like things in the environment. In accordance with that metaphysical definition, anything that exists is concrete.

    It is the nature of the reality of number that is the point at issue. — Wayfarer
    I agree, and I maintain that reality is being such as it is regardless of what anyone thinks about it. In accordance with that metaphysical definition, the mistake that Platonism has in common with nominalism is treating reality as synonymous with existence. On the contrary, although whatever exists is real, there are realities that do not exist--including numbers and other mathematical objects.
  • The paradox of Gabriel's horn.
    Your intuition is seriously at odds with modern physics. Do you think physics is wrong? — fishfry
    No, I think that anyone who interprets the Planck length as a discrete constituent part of space is wrong. I interpret it instead as a limitation on the precision of measurement, or as Wikipedia puts it, "the minimum distance that can be explored. ... The Planck length is sometimes misconceived as the minimum length of space-time, but this is not accepted by conventional physics, as this would require violation or modification of Lorentz symmetry."

    Secondly I wanted to repeat in case you missed the ps to my last post, that SIA denies excluded middle. — fishfry
    I did not see your PS until now, but I am well aware that the logic of SIA is what has come to be known as constructive or intuitionistic. Peirce was skeptical of excluded middle, but for very different philosophical reasons than Brouwer and Heyting--he believed that reality itself does not conform to it, because it is fundamentally continuous and general, rather than discrete and individual. He stated this in slightly different ways in alternate drafts of the same text.
    To speak of the actual state of things implies a great assumption, namely that there is a perfectly definite body of propositions which, if we could only find them out, are the truth, and that everything is really either true or in positive conflict with the truth. This assumption, called the principle of excluded middle, I consider utterly unwarranted, and do not believe it. — Peirce (NEM 3:758, 1893)
    No doubt there is an assumption involved in speaking of the actual state of things ... namely, the assumption that reality is so determinate as to verify or falsify every possible proposition. This is called the principle of excluded middle. ... I do not believe it is strictly true. — Peirce (NEM 3:759-760, 1893)
  • The paradox of Gabriel's horn.
    But why should space be a continuum at all? That's an open question. — fishfry
    I agree, it is a hypothesis--one that I happen to find much more plausible than space consisting of discrete parts. I would say the same about time, which Peirce considered to be "the continuum par excellence, through the spectacles of which we envisage every other continuum."

    How would anyone know what a "true continuum" even is? — fishfry
    I guess it comes down to definitions. Modern mathematicians stipulate that the real numbers constitute the (analytical) continuum, but (at least arguably) that approach is not entirely consistent with the common-sense notion of what it means to be continuous.
  • The paradox of Gabriel's horn.
    Unless you reject the intermediate value theorem, my point stands. ... Some version of the IVT is always valid regardless of one's model of the real line. — fishfry
    Well, the IVT is not valid in smooth infinitesimal analysis. As Bell states in his book that I suggested a while back, "the classical intermediate value theorem, often taken as expressing an 'intuitively obvious' property of continuous functions, is false in smooth worlds." The Wikipedia article on SIA explains:
    Intuitively, smooth infinitesimal analysis can be interpreted as describing a world in which lines are made out of infinitesimally small segments, not out of points. These segments can be thought of as being long enough to have a definite direction, but not long enough to be curved. The construction of discontinuous functions fails because a function is identified with a curve, and the curve cannot be constructed pointwise. We can imagine the intermediate value theorem's failure as resulting from the ability of an infinitesimal segment to straddle a line.
    It is presumably less surprising that the Banach-Tarski paradox also does not arise in SIA.

    In other words space is not described by the mathematical real line. As I've written in this thread at least ten times now. — fishfry
    So we agree, then? The mathematical real line is an extremely useful model of a continuous line, but like all representations, it does not capture every aspect of its object--in this case, a true continuum.
  • The paradox of Gabriel's horn.
    She passes through each point or she passes through each location that is the address of a point. Not sure what you are getting at. — fishfry
    Put another way, there are no real points or locations that she passes through, only the ones that we invent to describe her motion. Again, space does not consist of such discrete points or locations, we introduce them for our own purposes. Not sure I can convey what I mean any more clearly than that.
  • The paradox of Gabriel's horn.
    A true continuum is indivisible. — Metaphysician Undercover
    In itself, yes; but we can still "divide" it at will to suit our purposes. That is what I mean when I say that the whole is real and the parts are entia rationis, creations of thought. For example, we can conceive space itself as continuous and indivisible, but we can nevertheless mark it off using arbitrary and discrete units for the sake of locating and measuring things that exist within space.
  • The paradox of Gabriel's horn.
    ↪Gregory

    A one-dimensional line does not "contain" anything. We can mark it with as many zero-dimensional points as we can imagine, but those points are not parts of the line itself.
  • The paradox of Gabriel's horn.
    The continuum could easily be a dog instead of a segment. — Gregory
    Responses like this are why I rarely bother jumping into these discussions.
  • The paradox of Gabriel's horn.
    Nothing potentially has parts. It HAS the parts whether they are separated or not — Gregory
    I obviously disagree. Again, a true continuum has no definite parts except those that we deliberately mark off within it for a particular purpose. It is infinitely divisible, but not actually divided.

    One foot does not potentially have two united six inches. The 12 inches are there — Gregory
    Neither the foot nor the inches are "there" unless and until we mark them. They are arbitrary units of length for measuring things, not intrinsic to space itself.
  • The paradox of Gabriel's horn.
    I've been arguing that to be infinitely divisible means that it has infinite parts. — Gregory
    The parts are always there! — Gregory
    No, this is a confusion of "infinitely divisible" with "infinitely divided." The former means potentially having infinitely many parts, while the latter means actually having infinitely many parts. A true continuum is infinitely divisible, but this does not entail that it is infinitely divided. It is a whole such that in itself it has no actual parts, only potential parts. These are indefinite unless and until someone marks off distinct parts for a particular purpose, such as measurement, even if this is done using countably infinite rational numbers or uncountably infinite real numbers. A continuous line does not consist of such discrete points at all, but we could (theoretically) mark it with points exceeding all multitude.

    Mathematically there is no question that she passes through every point indexed by a real number. — fishfry
    This is one particular mathematical model of the interval--the dominant modern one, to be sure, but not the only one. Again, it is not mathematically necessary to treat a spatial interval as somehow consisting of unextended points. We can understand them instead as denoting locations in space, not constituents of space. As such, she does not really "pass through" them, we just just use them to track her progress.
  • Platonic Realism & Scientific Method
    Hence the necessity of Platonic realism to the natural sciences. — Wayfarer
    There are varieties of mathematical realism other than Platonism. The fact that certain relations among phenomena hold regardless of what anyone thinks about them does not entail that the corresponding mathematical objects metaphysically exist in a realm of concrete forms. As Charles Peirce maintained, echoing his father Benjamin, mathematics is the science of drawing necessary conclusions about hypothetical states of things. Abductive/retroductive explanations (theories/models) are fallible idealizations that require deductive explication (predictions) and inductive evaluation (experiments/observations) to ascertain whether and how well they match up with reality.
  • Changing screen name
    ↪StreetlightX

    The issue is that if I click on the @ button while composing a post and type only a portion of his name, he does not show up in the list of options. Even just "Ry" brings up seven choices, but not Ryan O'Connor.
  • The paradox of Gabriel's horn.
    ↪jgill

    The consensus among Peirce scholars seems to be that SIA/SDG comes the closest among modern mathematical developments to capturing his notion of a true continuum. Bell also has an excellent primer specifically on SIA, and Sergio Fabi wrote something similar for SDG.

    https://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf
    https://pages.physics.ua.edu/staff/fabi/InvitationSDG.pdf
  • The paradox of Gabriel's horn.
    In line with Aristotle's solution to Zeno's Paradox, my view has continua (not points) being fundamental. — Ryan O'Connor
    Sounds like a Peirceian viewpoint, about which I don't know much. — fishfry
    I have not had the time, energy, or patience to jump into the substance of this discussion so far, but I can offer a couple of reading suggestions based on these two comments.

    The first is John Bell's book, The Continuous and the Infinitesimal in Mathematics and Philosophy. It provides an excellent historical overview followed by chapters specifically on topology, category/topos theory, nonstandard analysis, constructive/intuitionistic mathematics, and smooth infinitesimal analysis/synthetic differential geometry.

    https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.307.7578&rep=rep1&type=pdf

    The second is my own recent paper, "Peirce's Topical Continuum: A 'Thicker' Theory." Its thesis is that a collection--even an uncountably infinite one, like the real numbers--is bottom-up, such that the parts are real and the whole is an ens rationis; while a true continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for the latter: rationality, divisibility, homogeneity, contiguity, and inexhaustibility.

    https://www.jstor.org/stable/10.2979/trancharpeirsoc.56.1.04
  • Question for the math folk
    And they're physical, not mathematical assumptions. — fishfry
    I disagree, everything that is physical occupies space, but space itself is not physical.

    When speaking of something that exists, the phrase "potential parts" is an oxymoron. — Gregory
    I agree, but again, space is not an object that exists--something that reacts with other like things in the environment. Instead, it is a reality--something that is as it is regardless of what anyone thinks about it.
  • Question for the math folk
    Objects don't potentially have parts. The parts are actual, and also spatial. — Gregory
    Sure, but space itself is not an object in that sense. It has no actual parts, only potential parts, and it is obviously not spatial in the same sense as a physical body. It is the continuous medium in which discrete objects exist.

    If you have a proof that space is continuous that would be a discovery on a par with the revolutions of Newton and Einstein. — fishfry
    Likewise if you have a proof that space is discrete. They are two different mathematical assumptions.

    I just pointed out that Max Planck introduced the Planck length as something aliens would discover. It's intrinsic to space itself as I understand it. — fishfry
    Yes, but I understand it to be a limitation on measurement, not a discrete unit of space itself.
  • Question for the math folk
    if space is infinitely divisible than it has infinite parts — Gregory
    Since space is continuous, it has infinitely many potential parts, but its only actual parts are those that we create by marking them off.

    In geometry, all space is divisible and its impossible to find the basic unit. — Gregory
    That is because there is no basic unit intrinsic to space itself, only arbitrary constructs that we impose in order to measure length/area/volume.
  • What is the main difference between Inductive and Abductive Reasoning?
    ↪Michael
    :up:

    ↪Samuel Lacrampe

    Note that in @Michael's examples, it is probable (96% chance based on available data about a random sample of Flemish college students) that Louise speaks both Dutch and French, while it is merely plausible (no known counterexamples yet) that all elephants are grey.
  • What is the main difference between Inductive and Abductive Reasoning?
    ↪Samuel Lacrampe

    No, but I have explained it as well as I can at this point, and a dictionary will tell you the difference between "probable" and "plausible." Cheers!
  • What is the main difference between Inductive and Abductive Reasoning?
    ↪Samuel Lacrampe

    Conceiving a hypothesis to explain past experience is not the same as testing that hypothesis against subsequent experience. Inferring that a white bean of unknown origin (plausibly) came from a bag known to contain only white beans is not the same as inferring that all the beans in a given bag are (probably) white because one bean known to have come from that bag is white. More to the point, induction calls for taking additional random samples of beans from the bag to see whether those always consist entirely of white beans. Pursued indefinitely, if in fact there are some non-white beans in the bag (or even just one), then this method would eventually reveal it.
  • What is the main difference between Inductive and Abductive Reasoning?
    But now, how is induction different from abduction? — Samuel Lacrampe
    Abduction is formulating a hypothesis, while induction is testing a hypothesis. Abduction offers a plausible explanation of a previously observed phenomenon, while induction evaluates whether that explanation is actually borne out by additional experience.

    Premises are built from abduction, and conclusions are built from deduction. — Samuel Lacrampe
    No, all three types of reasoning can be illustrated with syllogisms having two premisses and a conclusion. The key difference is how the conclusion follows from the premisses in accordance with what Charles Sanders Peirce called the "logical leading principle." He helpfully characterized the three propositions as rule, case, and result.

    Deduction: The result (conclusion) is a necessary inference from the rule and the case (premisses).
    • Rule: All the beans in this bag are white.
    • Case: This bean is from this bag.
    • Result: This bean is white.

    Induction: The rule (conclusion) is a probable inference from the case and the result (premisses).
    • Case: This bean is from this bag.
    • Result: This bean is white.
    • Rule: All the beans in this bag are white.

    Abduction: The case (conclusion) is a plausible inference from the rule and the result (premisses).
    • Rule: All the beans in this bag are white.
    • Result: This bean is white.
    • Case: This bean is from this bag.
  • What is the main difference between Inductive and Abductive Reasoning?
    So we falsify the hypothesis with deduction as you've defined it. — Samuel Lacrampe
    No, we falsify the hypothesis by observing a black swan. "If some swans are black, then not all swans are white" is deductively valid regardless of whether there actually are any black swans. Induction is the method that tells us to keep checking whether we ever see a non-white swan. Its validity lies in the fact that if there are any, we would eventually find one if we were to keep looking indefinitely.

    Otherwise, in general, all deductions must contain some experience since it checks for possible contradictions between premises that are built from experience. — Samuel Lacrampe
    Indeed, experience only contributes to the premisses, not the conclusion. Deduction derives necessary conclusions based strictly on formal considerations. It takes no experience at all, just competence in the English language, to deduce that there are no married bachelors. Induction is not required, since looking for a counterexample would be pointless.
  • What is the main difference between Inductive and Abductive Reasoning?
    As the original hypothesis is in contradiction with the new data, then it is necessarily false. So this is deduction. — Samuel Lacrampe
    No, it is not necessarily false, it is contingently false--it is contradicted by experience, not logic. That is what makes it inductive, rather than deductive.

    As the original hypothesis is not in contradiction with the new data, then it is not necessarily false. This is also deduction. — Samuel Lacrampe
    Again, if the conclusion is not logically necessary, then it is not a deductive inference.
  • What is the main difference between Inductive and Abductive Reasoning?
    ↪Samuel Lacrampe

    Again, abduction is formulating hypotheses, deduction is making predictions accordingly, and induction is testing those predictions against actual experience.

    Abduction: We observe the surprising fact that every swan we have ever seen in the past was white, so we hypothesize (plausibly) that all swans are white.

    Deduction: If all swans are white, then (necessarily) every swan that we will ever see in the future will be white.

    Induction: We go looking for more swans and see a black one, so our hypothesis is falsified. If we were never to see a black swan, then the hypothesis would not be falsified, but that does not warrant certainty that it is true since we only ever observe a finite sample of swans.
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