• Dfpolis
    400
    You are unbelievable. I, again, repeat: What makes them (let's speak plain english) "correct thinking"? You haven't answered that, you simply said they are not accidentally so, but essentially so. No argument is given, you're just saying they are.MindForged

    Speak of unbelievable! You asked about about correct thinking, which is singular. I replied in the singular. You, in the plural, speaking of "them." As I mentioned no "them" you must be confusing me with someone else.

    Somehow, for the 3rd or 4th time, you have skipped over the core of the answer: Thinking about reality is correct when it preserves the truth of what we know of reality (is salve veritate) -- and preserves that truth, not accidentally, but in virtue of the processed followed (i.e. essentially). This is an operational, goal-oriented definition.

    It is amazing that, while noting that I said, "essentially, not accidentally," you seem unable to grasp what essential note is required. Just so you do not miss it again the essential note is truth preserving (salve veritate),

    I am not discussing any "them" such as rules, but the definition of correct thinking.

    "Foundational reflection" will necessarily presuppose other principles.MindForged

    This claim fails to see that being aware of reality as given in
    ex contradictione sequitur quodlibetDfpolis

    experience is not a deductive process based on the application of prior principles. It is simply the actualization of present intelligibility.

    There's no reason to think the rules you presuppose in entering such reflection are inherently correct.MindForged

    As no "rules" are presupposed, the question of their correctness cannot arise.

    The problem is such an examination will require reasoning.MindForged

    Awareness of present intelligibility is an immediate, not a mediated, process.

    And correct reasoning (or form of thought, correct thinking, whatever) already presupposes a set of correct logical rules you are abiding by.MindForged

    No, it does not. It presupposes a scientific examination of the kinds of reasoning that work and do not work, and then discovering why some methods of reasoning preserve truth, while others do not.

    Let me give you an example. Any sensory representation that can properly evoke the concept <apple> is identically a representation that can elicit the concept <fruit>. This identity justifies the judgement <All apples are fruit>. In the same way, any representation that can evoke the concept <fruit> is identically a representation that can evoke <a plant product>. The principle of identity then allows us to see that any representation that can evoke <apple> is identically a representation can evoke <a fruit product>.

    This line of thought can be expressed by a syllogism in Barbara:
    "All apples are fruit."
    "All fruit is a plant product."
    "Therefore, all apples are a plant product."

    We see that the reasoning in the process is not dependent on the specific concepts we are thinking about. So, we can abstract the form of reasoning from specifics of the example. Thus, the validity of Barbara is not an assumption, but a consequence of the role of identity in the corresponding thought process.

    You don't get around this by recourse to "reality" (an already contentious concept; people consider many different things part of reality).MindForged

    We can discuss this another day. i think we can eliminate much of the contentiousness.

    I gave an explosive argument in Aristotelian terms but which is not valid because contradictions do not imply anything in traditional logic.MindForged

    You are confused. Just because you could not formulate a valid example does not mean that there are none. An argument with contradictory premises cannot be sound, but it can be valid.

    The following example is from https://rationalwiki.org/wiki/Principle_of_explosion:
    Assume two contradictory premises: A.) 'All ice cream is frozen.'; B.) 'Not all ice cream is frozen.'

    Now, just to show that it's possible, say one wants to use those two premises to prove that: C.) 'Words don't exist'.

    To do so, construct a disjunction out of A and C:

    'All ice cream is frozen or words don't exist.'

    This statement appears to be perfectly acceptable here because it holds true under any of these three circumstances:

    1. All ice cream is frozen.
    2. Words don't exist.
    3. All ice cream is frozen and words don't exist.
    (Of which at least the first one is true because it was assumed as a premise.)

    Now use that disjunction for a disjunctive syllogism:

    'All ice cream is frozen or words don't exist.
    Not all ice cream is frozen.
    Therefore words don't exist.'

    This also appears to be perfectly acceptable here because if it is said that at least one of A or C are true, then when it turns out A is not true (which is B, which has been accepted as a premise), at least it can be held that C is true.

    Please do not tell me there are no disjunctions in Aristotelian logic, because the Principle of Excluded Middle involves one.

    I didn't say Frege created the principle of explosion, I said it was not what you might call logical orthodoxy until Frege made it part of Classical Logic.MindForged

    OK. I admit that the history of the principle is complex. Pseudo-Scotus stated it in the late medieval period, but the Scholastics were more concerned with consistency and truth, than inconsistency. So, the point of arguments such as that above, was to show that forms cannot be applied blindly, Thus ex contradictione was not a major principle.

    The works of medieval logicians cannot in any way be said to have been the standard logic, ever. By Kant's time they had been lost to history and not even remembered.MindForged

    Only in Protestant countries -- due to prejudice against the Scholastic tradition. For example, John Poissot's Cursus philosophicus Thomisticus, which includes his famous Ars Logica, was reprinted in 1883 -- the year before Frege published his Die Grundlagen der Arithmetik.

    "Two case" as in two cases of observation, not two cases of different objects. Schrodinger goes to pains to make clear that the object is not self-identical despite the reasonable assumption of there being a causal connection between what one observes.MindForged

    As you have just pointed out, in addition to identity, your example requires additional assumptions that you consider reasonable, but those of us who've studied the matter don't. Once you grasp this, you see that your example is not a valid argument. ~(~(p && q) => ~p)

    In addition to assuming a causal connection between the observations, you need to assume that the causality involved ensures object persistence. It does not.

    Just so you know, one of many possible ways (Feynman diagrams) to get two successive electron observations is for a second electron to leave the Dirac sea of negative energy electrons and the first electron to fill the resulting hole. (This process can be described in other ways, involving virtual positron creation and annihilation.) Thus, when you understand quantum field theory, your assumption ceases to be "reasonable."

    Still, you do not need to know QFT to see your error. All you really need to know is that 2 != 1.

    Identity entails that objects are individuated. If some object (or set of objects) lacks individuation conditions, then they are not self-identical.MindForged

    Yes, if a putative "object" is not individual, then it is not individual. That has nothing to do with the ontological principle of identity which only requires that whatever is the case, be the case.

    Consider an ocean wave field. It is the superposition of many waves of a range of wavelengths, so that there are no "individual" waves, except as abstractions. Still, if the wave field, or a portion thereof, existents, it exists.

    I did not say the rule was different, I said the rules were different. I went on to say that, according to Aristotle (as per your quote), Excluded Middle does not apply to future contingents.MindForged

    You seem not to understand scientific principles. They are not bare propositions, they also have conditions of application (the "such that" phrase of universal quantification). The condition for applying traditional logic is that we are dealing with an existential situation. The fact that future contingents are not such that they are existential situations does not change the principle. It simply makes it inapplicable.

    In the case of future contingents, we can still reason about them. Aristotle does not say Non-contradiction no longer applies, nor does he say that Identity fails to apply. But that Excluded Middle no longer does.MindForged

    First, the existential condition can be granted conditionally. That is to say that we can reason on the assumption of actual existence, even when there is no actual existence, but in doing so, we must remember that our conclusions are not categorical, but conditional.

    Second, in the context of assuming that the see battle will occur, we can apply all of the principles of being, including excluded middle. (Contrary to your claim, "Future contingents require dropping Excluded Middle to reason about them") For example, it is rational to say "Either the enemy commander will be killed, or the enemy commander will not be killed." Similarly, we can apply all the principles on the condition that the battle will not occur.

    What we cannot do is combine conclusions conditioned by the occurrence of the battle with conclusions conditioned by the nonoccurence of the battle. This is what the paradox attempts to do.

    One way to see this, that chosen by Aristotle, is to say that propositions conditioned by the assumption of an existential state can be neither true nor false (for they are not adequate to reality, but to assumed conditions). Thus, the logical principle of excluded middle, dependent as it is on the impossibility of a a state both existing and not existing, does not apply. This is not changing the rule, just abiding by its conditions of application.

    Note the explicit reference to reality in the following:
    When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. — Aristotle, De Interpretatione, 9

    Later in the chapter, Aristotle makes it clear that the reason we cannot apply Excluded Middle is not because the principle is false, but because truth and falsity are not well-defined:
    in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial — Aristotle, De Interpretatione, 9

    To make clear that the Principle of Excluded Middle is not false, but merely inapplicable when truth is ill-defined, Aristotle gives us its correct usage near the end of the chapter:
    A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. — Aristotle, De Interpretatione, 9

    And to make clear that his logic is ontologically based he concludes:
    This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated. — Aristotle, De Interpretatione, 9

    It's a view that liar-type sentences are not well-formed, not that truth-values are not well-formed.MindForged

    Yes, I know how the analytically inclined try to bend language to their preconceptions. Still, as shown by Jourdain's and Kripke's Paradoxes, this is at best a patch. My solution works for all three paradoxes.

    Note that "Everything Jones says about Watergate is true." is not a statement about the reality of Watergate, but one about Jones' statements. Similarly, "Most of Nixon's assertions about Watergate are false," is not a statement about Watergate, but about Nixon's locutions. Thus, it cannot be counted among "Nixon's assertions about Watergate."

    Statements that people make are real. Statements made about other statements are common,
    MindForged

    Quite true, but that does not make statements about sentences statements about Watergate.

    I've no idea how you came to that conclusion. If Jones only says Nixon is mostly lying about Watergate, and Nixon says everything Jones says about Watergate is true, then the issue is these cannot be jointly true and yet they *entail* each other.MindForged

    I came to the conclusion by reading the text (as you suggested). The text refers to certain statements, not to events at the Watergate apartments.

    To be true, a statement must be adequate to reality. If a statement, or a system of statements, cannot be cashed out in terms of one or more claims about reality, then it is neither true nor false, but simply non-referential. Here the system of statements makes no empirical claim.

    Your suggested revision does nothing to make the system referential.

    You went beyond that, you said your understanding was sufficient to claim (as you did) that the principles are true essentially, rather than accidentally.MindForged

    You continue to ignore and distort what I actually said. For the 6th or 7th time, I define correct thinking as thinking that is salve veritate, not accidentally, but essentially. So, I gave "essential, not accidental" as an attribute of correct thinking abstractly considered, not as an attribute of principles or rules. Once you have the goal of understanding correct thinking, the scientific approach is to study thinking that is actually truth preserving or fallacious, and see what rules can be extracted and how they may be justified by our understanding of being. So, the rules are not the starting point, but the result of a scientific process.

    My point is your experience doesn't generate anywhere near the justification for that. Experience is fine for generation provisional assumptions that go into your logic, but that's not what you've argued for.MindForged

    The reason you think "experience doesn't generate anywhere near the justification for" infallible principles of being is that you are stuck with the Hume-Mill model of induction. In it, I experience a certain, hopefully large, number of cases, and frame the hypothesis, that all cases are like those I've experienced. Treating this as a true universal requires adding the assumption that all other cases are like those I have observed. As the extending assumption has no intrinsic justification, the resulting universal judgement is inadequately justified.

    There is another type of induction that avoids problem inherent in the Hume-Mill model. Suppose I count apples for my job, and notice that after I've counted 2 apples, if I count two more apples I always have four apples. On the Hume-Mill model, I can only hypothesize that 2+2=4, and assume that other cases will give the same result.

    However, that is not what actually happens. After children count apples, pennies and pebbles, they notice that the counting process does not depend on what is counted. (I call this the "arithmetic insight.") Once you have the arithmetic insight, you understand that the relation, 2+2=4, does not depend on what is counted, and so is universally true.

    How does this differ from the Hume-Mill case? In the H-M case, we have to add an assumption to arrive at a universal judgement. In the second case, we abstract, which is to say that we subtract information actually present to arrive at the universal judgement. (Specifically, we abstract away from the kind of thing being counted.) As this is a subtractive process, no assumptions are added.

    The same thing happens with the principles of being. We understand that an apple is an apple, a penny is a penny, etc. Then we have an ontological insight, and see that the identity in these cases does not depend on what is being considered, so, for all reality, whatever is, is -- and similarly, whatever is not, is not. That is how we come to know (and justify) the Principle of Identity.

    If you're interested in pursuing this further, you might want to look at Aquinas's Commentary of the De Trinitate of Boethius.

    You think there is one correct way of thinking and that traditional logic corresponds to that thinking (correct me if I'm mistaken).MindForged

    You persist! Yes, you are wrong again -- and on this very point. For the 8th or 9th time, to think correctly is to think in a way that preserves truth, not by accident, but because the way we are thinking will always preserve truth. This makes no a priori assumptions about what ways of thinking preserve truth, and what ways don't. To discover that, we have to examine actual ways of thinking, find those that seem to work invariantly, and then find justifications for the claim of invariant correctness.

    With the lack of conditionals in traditional logic I'm not even sure this is consistent with the logic being proposed.MindForged

    The lack of a formal theory of conditionals is not a lack of conditionals. For example, in the discussion of the sea battle (above) Aristotle is quite clear about the conditions under which the Principle of Excluded Middle applies.

    An imagined world is by definition non-existent so how are you reasoning correctly about it? After all, the principles which apply to existing things is not supposed to apply to that which has no being.MindForged

    As I said, we grant "existence" by a willing suspension of disbelief. This means that we treat the imagined world as if it existed and instantiated the principles of being.

    What I was saying was that if we take your view that truth-values are an "incoherent concept" (as you said), then modern maths/logic are not usable because they make crucial use of this and other concepts (conditionals), and dispenses with aspects of traditional logic (existential import is not assumed in quantifiers).MindForged

    Once you realize that truth is a binary relation (the adequacy of thought to reality) and truth-value is a unary property of propositions, it is clear that they are very different concepts. The fact that truth-value is problematic is shown by the paradoxes we have been discussing.

    So you can define whatever you like (including truth-values) and work out rules to try to make your set of posits self-consistent (creating meta-linguistic structures, Russellian type theories, etc, etc.). If you take that course (and traditional logic is open to it), then in view of Goedel's work, you may never know that the system you have defined is actually inconsistent and you have wasted your life's work.

    Alternately, you can abstract systems from reality, or from systems traceable to
    And I don't see how traditional logic has done anything to further knowledge in these areasMindForged

    reality -- and you will be guarantied that you are dealing with a self-consistent structure (because reality is self-consistent) and know that you will not have wasted your life's work on a possibly self-contradictory system.

    Strange, I just showed you how a single insight can dispose of a whole series of paradoxes you admit vex modern logicians.

    In the traditional case, it only meets this criterion if we only talk about what we know to be true about reality, so it's application to hypothetical and mathematical cases becomes less usefulMindForged

    As with the sea battle, we can apply logic to any premises we assume true for methodological purposes.

    Science woks quite well applying the hypothetico-deductive method with the deductions using traditional logic. Just because we are treating a hypothesis as conditionally true does not mean that we cannot work out its consequences with a view to confirming or falsifying them.

    I already pointed out examples of what I was talking about (e.g. uniform continuity vs continuity of a function).MindForged

    And I showed you how to restate quantified sentences in traditional proposition form.

    Traditional logic had no theory for the quantifiers it used, the quantifiers weren't detachable, and that's in part why its application to mathematics was so limited and thus Frege had to develop a new logic. Prior, until the medieval logicians there was no real understanding of them, and even the medieval logicians treated quantifiers sort of like names. Frege made them clearer by making them a new kind of linguistic object.MindForged

    Without going into the innards of modern logic, either it deals with correct forms of thought, or it deals with other subject matter, such as linguistic forms or rules of symbolic manipulation that can be isomorphic to features of systems we are interested in.

    If it deals with correct forms of thought, it is part of what I've been talking about, and if it presents new, correct ways of thinking, these are to be greeted with jubilation. If it deals with other subject matter, as scientists we need to think about that subject matter in truth-preserving ways -- and so employ traditional logic (as founded by Aristotle and advanced subsequently).

    It is my view that modern logic is not concerned with correct thinking (as its object), but has for its object of study the manipulation of symbolic forms that may be isomorphic to various systems of scientific interest.

    So, I see comparing them as involving a category error.
  • Dfpolis
    400
    You will be happy to know that Rudy Giuliani has come out in support of your denial of the Principle of Identity, asserting "Truth isn't truth!"
  • SophistiCat
    475
    Somehow, for the 3rd or 4th time, you have skipped over the core of the answer: Thinking about reality is correct when it preserves the truth of what we know of reality (is salve veritate) -- and preserves that truth, not accidentally, but in virtue of the processed followed (i.e. essentially). This is an operational, goal-oriented definition.

    It is amazing that, while noting that I said, "essentially, not accidentally," you seem unable to grasp what essential note is required. Just so you do not miss it again the essential note is truth preserving (salve veritate),

    I am not discussing any "them" such as rules, but the definition of correct thinking.
    Dfpolis

    I am sorry, I haven't been closely following this entire exchange, but this just sounds like a wordy way of saying that the correct way of thinking is the way of thinking that is correct ("preserves the truth of what we know of reality," etc.) Not terribly illuminating.
  • Dfpolis
    400
    just sounds like a wordy way of saying that the correct way of thinking is the way of thinking that is correct ("preserves the truth of what we know of reality," etc.) Not terribly illuminating.SophistiCat

    Yes, that is why it is annoying to have to repeat it multiple times. Once, in my first post, should have been enough.

    Once you get the point, the next obvious thing is to examine cases of truth preserving and fallacious thinking to discover rules that preserve truth, and then seek to justify them by showing how they reflect the nature of existence.

    The next step cannot rationally be to posit axioms without examining how they relate to thought about reality.
  • Cabbage Farmer
    165
    1. It claims that to question logic is, itself, to be logical and therefore all criticisms of logic already subsume the principles of logic - we are looking for reasons to justify our doubts about logical authority.

    2. Others claim that to justify logic is to, again, assume logic's authority. This, they allege, is a circularity and therefore logic has no justification.

    So, it appears that we can neither justify nor critique logic. Both are circular.
    TheMadFool
    It's not clear in this story what sort of question is being asked, and what sort of justification is being provided.

    What does it mean to "question logic"? Is the question whether logic is useful for some purpose, or perhaps for every purpose?

    Is logical consistency essential for good cinema, for amusing rhymes, for effective persuasion of millions of voters? Clearly not. Must we say that trees or stones are in themselves "logical", or that they somehow "employ logic"? No. Are these logically valid claims? So it seems. Does this amount to "questioning [the role of, or the limits of] logic? I guess so.

    As a sort of skeptic I have wondered whether all my experience, including my memory and current use of a set of practices I associate with the terms "logic" and "language", are just so many incoherent figments of a confused dream. This sort of thought lands arguably at the boundaries of coherence, but I suppose it involves a logically consistent "questioning" of, say, the ultimate validity of logic. I suppose so... but if in fact the answer to the question were affirmative, and this logic were just an illusion, then my supposition may be false, and the question may not have been logical to begin with....

    Need every "questioning" be a questioning in explicit language? Imagine I protest my friend's or my employer's overestimation of the power, utility, or purview of logic by farting, or by making some other extralinguistic gesture. I suppose I could translate the protest into any of a range of utterances with the grammatical form of a question. Some of these questions might involve vague poetic allusions or logical contradictions or grammatical nonsense. I'll allow that such illogical questions may be employed to satisfy a logically coherent intention by "questioning [the power, utility, purview of] logic".


    What does it mean to "justify logic"? Justify it in what regard, for what purpose, against what charge...
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