Comments

  • "ReasonLines" to determine validity in categorical logic
    Not a problem - being no doubt older, I am way ahead of you on mistakes, as even some folks here will tell you. And I should have P(rivate) M(essaged) you - my bad - but on a forum like this I think sometimes being explicit matters.

    And your "ReasonLines" imo a real accomplishment. Issues here, if any, are the need for existential qualifiers and the use of your Lines as a tool. I am unaware of any comment in Aristotle on the need for an existential qualifier. And this a strong indication that for his purposes he either did not think it worth mentioning or it didn't occur to him. Indeed, from All S is P to Some S is P is considered a valid conclusion. And the need for it in modern logic implies that Aristotelian logic and modern logic are not the same things - the whys a topic in itself.

    As a tool, your ReasonLines seems on the order of a chainsaw or bulldozer. Overkill for most projects, requiring special skills in operation and allowing the operator to proceed without needing to know what he's doing or how or why, or even needing to be concerned with the results of his work. That's my criticism - which maybe is refuted by examples of practical applications.
  • "ReasonLines" to determine validity in categorical logic
    I feel this program should make the ability to determine validity in categorical logic possible for much younger students than ever before. Moreover, I think it reveals the internal workings of such arguments more clearly than any of the other methods.

    I would appreciate any comments.
    Wallace Murphree

    Well, a comment. I think all students should learn Aristotelian logic - why not in elementary school? And they should learn it the old-fashioned way. Yours is manipulation of a machine and it is not at all clear that a machine operator would know what he's doing.

    Or in other words, yours a tool - I cannot think of any practical, real-world application; can you provide? And as a tool, useful for those who might need it.

    I have an example of the nature of my complaint. A college level course in statistics that confined itself to instruction in the operation of a certain software package, the instructor, actually a professor, refusing to answer any questions on statistics itself. Needless to say, nothing there learned.

    It's useful to reflect on what Aristotelian logic is for and what it is about - a way of testing for nonsense. Presupposed is the student's ability to recognize basic truths and simple nonsense. It seems to me your "device" eliminates the need for such presuppositions, and for such basic knowledge and recognition. Which has been happening for at least fifty years in US education, resulting in a population that cannot tell sense from nonsense and buys the nonsense. .
  • "ReasonLines" to determine validity in categorical logic
    All B’s are A
    All B’s are C
    So All A’s are C

    is invalid by breaking the additional rule
    Wallace Murphree
    Illicit major. A distributed in conclusion, not in major premise.
    All B’s are A
    (Some B’s are B)
    All B’s are C
    So Some A’s are B
    Wallace Murphree
    Not a syllogism. Maybe Some As are Cs? But then you need existential qualifiers for A nd C, yes?

    In my opinion a non-problem. Or if a potential problem then disposable in a prefatory remark not itself part of the argument.
  • "ReasonLines" to determine validity in categorical logic
    syllogisms with Aristotle's "Six Rules,"Count Timothy von Icarus
    These?
    1) Distributed middle
    2) Illicit major
    3) Illicit minor
    4) Negative premise
    5) Negative premises.
    6) Three terms.
  • Is this argument (about theories, evidence and observations) valid?
    Your language has no bones in it; thus like a sponge you can squeeze it into any queer shape you like. But stop squeezing and it will lose that shape. So as a toy maybe fun to play with but as structure, lacking any structural integrity, useless - and there are things that are more fun to play with.
  • Donald Trump (All General Trump Conversations Here)
    Have you been paying attention to his campaign (previously), his continually declining abilities and acknowledgement of such all and sundry?AmadeusD
    Your remark was categorical. As such subject to question. Biden may not be the man he used to be - none of us are. But he is still the man he needs to be with room to spare. And I notice you evade my questions, a characteristic of the toxic poster.
  • Donald Trump (All General Trump Conversations Here)
    Governing is conducting policy and organisational aspects of policy and action of a given entity (in this case, the USA). It is not my definition, but thank you for the stark illustration.AmadeusD
    Perfectly good definition.
    no real opinion on Biden beyond his ability to govern, which was lost some time ago.AmadeusD
    Great! When? Evidence - how do you know? I ask because either you're right or you're remark is toxic, to put it as nicely as I can.
  • Donald Trump (All General Trump Conversations Here)
    beyond his ability to govern, which was lost some time ago.AmadeusD
    I don't know how you define governing, but he was governing before your post and during it, and is governing after your post. You achieved either a nos4 standard of nonsense, or maybe give a definition, and hopefully a definition that is not itself nonsense.
  • Is this argument (about theories, evidence and observations) valid?
    Only if the comment of yours I replied to is a red herring - but that would be your call.
  • Is this argument (about theories, evidence and observations) valid?
    You have a whole lot of work to do on - at least - defining your terms and how they relate to each other. Until that's done there won't be much sense here. Example: in Genesis is the story of a flood. There is evidence of a flood. Therefore Christianity true??? Or more simply, in Genesis is a story of the creation of man. There is evidence that men exist. Therefore Christianity is true???
  • Books, what for, exactly?
    The question becomes not which extreme is correct but pragmatically can they be balanced?apokrisis
    And this seems to be the answer. It also makes available a possible account for choices made in the Middle Ages - or any age. Assuming people try to do the best they can, it becomes a comment on quality of life when those with the means opt for lives of meditation, the study of books, and disengagement. That is, the then correct "balance" being found more-or-less in removal - with an assurance in faith that they would live again in a better time!

    And balance as pragmatic astute. Taking Aristotle's mean as close kin to balance, we may discern in the Ethics a taxonomy of practical sensibility - although exactly to what end in Aristotle I am not sure, whether for virtue, happiness, goodness, or something else, and these all needing clarification in Aristotle's thinking (anyone?). For example, he would have known perfectly well all of the Homeric virtues, and that they in part differed from his own....

    "Balance" itself comes into closer view. Is it means or end, both, neither? And it would seem to matter who or what is manning the scales. If imperatives of history, the balance may seem indeed more like the rack, stretching some parts to this end, others to the other, without regard for the center's being able to hold. Or if a man or woman can set their own balance, that seeming luxury. But balance with respect to what in service of what? Virtue? Avarice? Concupiscence? I don't think philosophy gives ready answers to these, instead going in circles or into dead-ends. But the world seems to, and simply.
    ..
  • Books, what for, exactly?
    Is it a mistake to seek knowledge and understanding to the exclusion of all elseLeontiskos
    Usually a mistake, I say. Sex and marriage come to mind, concerns for Heloise and Abelard; one can study and read about them and ask others about them all the day long, but not really know about them until they're experienced - and then one is launched on whole new and unexpected paths of discovery and knowledge to be learned. And even geometry: if a person does not him- or herself go through a few proofs on their own, they cannot really be said to know geometry. And I think this is just common sense, which makes me wonder just what the sense, common or otherwise, that informed the judgment of some people in the Middle Ages.

    And while knowing the answer to that may not change what we do, it seems it might be instructive to know with some exactness just what their error was, why or how the the exclusive study of (in their case) books was thought better than life itself.

    Yet the point is not to avoid finite realities, but instead to see in and through them something beyond them. The problem is not the focus on the finite reality, but the fixation and coagulation on the finite reality.Leontiskos
    Well, at least to look for something beyond - and maybe wisdom to recognize that what is present is also the beyond. But I like what you said and how you said it.

    This is a fairly complicated subject. To begin to breach it, I would ask: Supposing that the meaning is fixed and this is bad, is there then something whose meaning is not fixed?Leontiskos
    Indeed it is! I'll add here some clarity that I chose to leave out of the last post. By "fixed" I mean that a text establishes a field of meanings, or a set of meanings within a horizon of possible meanings, or however works best to express it. That is, those that can be got from the text, and not those that are not got from the text but are speculatively inferred from it.

    E.g., there is the main story of Moby DIck, but there are also derivative stories that might be told from the standpoints of different characters, the stories not themselves in the book, but based on the book, from Queequeg to Starbuck to even the whale and the Pequot, the boat itself. On the other hand, there are books about St. Paul that argue, with some plausibility, that Paul's internal strife and angst come about because he was homosexual, and that was unacceptable. And while that might be an astute psychological conjecture, so far as I know there is no direct basis for it in any text.

    Or, is there something whose meaning is not fixed? I say no. Meanings can be wide and broad, but there must be some connection between meaning and text, else the meaning is properly identified as being independent of the text.



    .
  • Books, what for, exactly?
    I have spent long periods of my now long life....Fooloso4
    Has any of it taught you how to tell the young both what to do and not do in such terms as they get it? I suppose knowing these might be accounted wisdom, but how to tell it! (Or do we in age forget that youth, and each age, is governed by its own imperatives - another topic.)
  • Books, what for, exactly?
    So again: does your critique of books also apply to the posts you write on TPF? It seems that your critique will apply to every (completed) linguistic work of art.Leontiskos
    I think I must agree with you, here.

    and because the author is dynamic so too is the book.Leontiskos
    then one book's meaning need not be as static or fixed as another's.Leontiskos
    If there's disagreement between us, it may be here. I hold that as the text is fixed, so too the meaning. That leaves on the one hand understanding the text, on the other interpretation. Understanding a discipline, interpretation an exhibition.

    A quick example comes to mind: the commandment until recently translated as "You shall not kill." But the original is "You shall not murder." (Actually, modern bibles are stuffed full of eisegetic mistranslations/interpretations - another topic.) A bad thing? Not in itself, but bad as misrepresentation.

    My overall point, now getting obscured, is that an original standard of behaviour, to study books to the exclusion of all else, is now pretty much dismissed. And that granted, it's worth (imho) a dive into the reasons for that dismissal. The most general expression of which seems to be that such a life is for most just not a life at all, and a life misspent. The roots for this seeming to be at least the enlightenment, the sense of freedom and liberty and duty under these, and a sense of the possibility of a science of the world. This latter being a movement from the acceptance of the mysteries of things to the possibility of understanding them, the desirability of that understanding, and the invitation to do so based on a Cristian model that perfection is here in the world (because God made the world and thus it is perfect) and here to be understood - the methods of understanding to question and to test.

    Edit: yes, walls can make good tennis players. Perhaps not great ones, I evidence of that.
  • Does physics describe logic?
    Copied from an old thread:
    From a pretty good book, The Overstory (Richard Powers, 2018), ISBN-10: 039363552X.
    Page 132. "Life will not answer to reason. And meaning is too young a thing to have much power over it."
    Page 432. "[R]eason is just another weapon of control. ...the invention of the reasonable, the acceptable, the sane, even the human, is greener and more recent than humans suspect."

    If the subject of physics taken broadly is life, and logic taken broadly is the structure on which physics is built, then at a stretch they can be taken to describe each other, perhaps in the same way a game and the rules of the game "describe" each other, although to be sure they do not instantiate each other. The rules of chess encompass all the possible games of chess without themselves being one, and a game can provide examples of the rules in action, without being them.
  • Books, what for, exactly?
    Mainly agreed, with some qualifications.
    I think books are the highest form of discourse,Leontiskos
    I had to look up discourse, and I find that discourse can refer to a back-and-forth, a discussion, which a book cannot do, or itself a fixed text.
    Like books, we can say new things as we grow and change our minds.Leontiskos
    You mean unlike books, yes?
    they generate new insights and new interpretations with each passing decade.Leontiskos
    I do not think books do this: people - readers - do this. And it can be an open question as go whether theirs is exegesis or eisegesis.
    The thoughts most worth thinking will generally be written in books.Leontiskos
    Agreed. And just this arguably why the admonition to study them. I reckon my break is to question the ultimate worth of the study-in-itself. Perhaps a thousand years ago it might have been felt to be the way to heaven, and no doubt some people think so today. But most of us - and I think you're an example - are so accustomed to the sense of entitlement and freedom to question and test a text that we begin to think of reading as a kind of interaction, forgetting, if we ever knew, that such freedom is relatively new.

    If discussion is like a game of tennis, reading a book is like hitting the ball against a wall.
  • Books, what for, exactly?
    The reader is not looking backward but inward. While the book does not change the reader can, and in that way the book changes for that reader. The book that was cast aside in my youth remains ready for when I am ready for it.Fooloso4
    Hmm. Not a criticism, just a hmm. Is yours to say that the book is a path of sorts that individual readers can travel to varying distances? Or an open field to be continually explored, investigated, expanded? I do not think it is quite to the point to invoke beginner readers v. advanced - that distinction not really a matter of the book itself.

    And I can suppose that "looking inward" can be a way of challenging the book - but not in itself a way of moving forward with the book. An example comes to mind: to build the foundation for a house, you might well look at a book that tells how to do that. And then you either set the book aside, or use it as a reference, an archive, and move forward and build, or, challenging the book, you might set it aside and build your own foundation. And either way you move beyond the book - or you don't get the foundation built.

    To add to that example, I have bought books with the half-baked idea that the book will solve whatever problem I bought to the book to solve, which of course by itself it cannot. And this all-a-piece with the notion that meditation/study of books, at the expense of all else, is a destructive practice. E.g., watching, or reading, pornography probably won't get you laid and it may make it less likely - not a good outcome if such is held to be a valuable part of life.
  • Books, what for, exactly?
    Some are static, some are archival, and many are not.Leontiskos
    By static and archival, I meant fixed; i.e. their text is set. When you say many are not, what do you mean?
  • Anxiety - the art of Thinking
    Being, as are others of us here, older (read: old), I can and do reflect on times of anxiety in my life. And it seems to me that anxiety qua is not itself a problem to be solved- because it is not really a problem that can be solved. Thus many responses to anxiety, especially from persons not themselves anxious, simply miss the mark. Not to disqualify insights about anxiety or the distinction between fears and anxiety, but instead to try to get to what, exactly, anxiety is. When young, I think anxiety comes about because a brain/mind (I mean here two different things working at the same time) lacks maturity and maybe chemical balance needed to not be anxious - and one grows out of this. For older folks, I suspect it arises from situations of the threat of loss of control, again likely a brain/mind condition.

    I find it can be useful when anxious to ask myself explicitly, "What purpose are these feelings that I am having right now doing for me?" I find a double benefit - one in being able to ask, the other in trying to answer.
  • Donald Trump (All General Trump Conversations Here)
    Your contention is that Trump did nothing wrong?
    — tim wood
    That’s right.
    — NOS4A2
    tim wood

    Just a reminder to folks that nos4 is a complete something. What, exactly, I'm not sure, but its not good, and on TPF it - he - is a waste of time.
  • What can we say about logical formulas/propositions?
    No, I am saying he is a dimwit, which he is.Lionino
    No doubt, just not about English. From your failure to answer a couple of questions I infer you did not understand them or their significance. And your resort to invective and insult merely the droppings of a troll, as we who have been around for awhile have learned to recognize, sometimes the hard way.

    Do you really not see a difference between, "If you do x I'll do y," and, "If you do x then I'll do y. Or the distinction between how chess pieces move and how they are to be moved?

    And I observed above that I understood the purpose of logic to be to demonstrate, of language to communicate, the two being different - did you overlook that?
  • What can we say about logical formulas/propositions?
    Is grammar not the rules which give us what can be said right or wrong in language?Lionino
    In a word, no.
    In everyday discourse, people write "If ___, then" commonly.
    — TonesInDeepFreeze
    My point is that they write it wrongly.
    Lionino
    And bumblebees cannot fly. Can you see a difference between, "If you do x, I'll do y," and, "If you do x, then I'll do y"?

    And can you recognize the difference between the rules of how the pieces move on a chessboard, and how the pieces are to be moved on a chessboard? Grammar is guidance and suggestion, nothing more. But not to be thereby dismissed. Bad grammar, as with bad behaviour at the chessboard, can get you thrown out.

    So, unlikely as it seems, you apparently don't know what "rules" means, or "language" for that matter. Part of both, perhaps, but part isn't the whole. Stick to logic; you seem to know that well. Language, not so much.
  • What can we say about logical formulas/propositions?
    So I think it is very much worthwhile to look into how we can bring language into logic.Lionino
    Ah, well, hmm. No doubt in some circumstances it has to be done; writing laws comes to mind. But the caveat being that natural language is about communication while logic is about demonstration. Two very different animals - two different languages - though sometimes they're on the same path and drink from the same stream.
  • What can we say about logical formulas/propositions?
    Two approaches. First, with any negation, to use as needed the locution, "It is not the case that...". Thus for ~(p -> q) I'd say, "It is not the case that p implies q." Or second, relying on the equivalence of (p -> q) <=> (~p v q), I'd say, "Either it is not the case that p, or (it is the case that) q."

    In any case, going back and forth between "logical formulas" and natural language" is always going to be problematic. Presumably with natural language the purpose is successful communication, and for that there is no "logical formula." Instead, one simply has to do whatever it takes, which is often not-so-easy.
  • Donald Trump (All General Trump Conversations Here)
    Repeating the lies isn’t going to make them any more real.NOS4A2
    What lies, please? You seem akin to a climate change denier - maybe you are one. "Don't bother me with facts! Don't bother me with science!"

    You seem to live in BS universe. And being a BS person you think that BS is the common coin. It isn't and your offerings of BS are offensive and insulting. You don't even rise to the level of nonsense - you don't possess any of the redemptive qualities of nonsense.
    Your contention is that Trump did nothing wrong?tim wood
    That’s right.NOS4A2
    Disgusting.
  • 10k Philosophy challenge
    I could boil the problem down to "how do we resolve conflicts between the freedom of different persons over things choices that belong to them?"Dan
    Well, this is simple and obvious: you get a PM like your Jacinda Ardern and do what she says.

    Less perfectly but more durably (so far - we'll see if it lasts!), a democratic form of government is established that acknowledges three unalienable rights, to life, liberty, and the pursuit of happiness, which to secure makes all others alienable, and which adopts a general set of rules for governance that holds itself as subject to its own laws. And this more-or-less the model for the free countries in the world.

    And manifestly imperfect - and just here may be a clue. Freedom is about the future, and the future is always at least in part unknown. Therefore the exercise of freedom can never guarantee future results.

    And so you wisely confine your question to present considerations, "How do we resolve...?" But this question must itself evolve to, "How best to resolve.., is there a best way to resolve,... and of best ways is it a one or they a many?"

    After many qualifications it becomes clear that certainty is itself housed only in the most general of observations, and those at a considerable distance from any particular application. Among these the golden rule, the two fundamental commandments, and Kant's good will and his categorical imperatives.

    That leaves the practical considerations of a particular matter and the need for some action, a significant waypoint in the navigation of such problems being Aristotle's Rhetoric, that is, persuasion, the need of it, the need for it to be done well, how to do it, and how to judge it. One word seems to cover all of this, "heuristics," with the proviso that what is sought is not "the good enough," but instead the best possible. And the repository of such wisdom is the society/culture itself, subject to the critical analysis of the moment.
  • 10k Philosophy challenge
    I looked at your "here" and my computer didn't blow up - yet, and you've been a member for years. So you seem legit. But it would be helpful if you could boil the problem down to a sentence or two or three. After an admittedly very quick read, it appears to me to be the sequence, should I act, and how do I know. And what should I do and how do I know; in particular how do I weigh competing or seemingly incommensurable demands and values?

    And why is not Kant's deontology a complete and comprehensive answer?
  • Devil Species Rejoinder to Aristotelian Ethics
    The noun τέλος, τό (telos) is one of a group of similar words with similar meanings. It can be instructive to give some of them a look.

    Verb, τελέω (teleo): complete, accomplish, perform, execute. To make perfect, bring to an end, finish.
    Adverb, τελέωσ (teleos): completely, perfectly.
    Noun, τέλοσ: an end accomplished, the completion or fulfilment of anything. And like many ancient Greek words it has other meanings, e.g., a body of soldiers, a tax to the city, the rating of a citizen (in Athens) in terms of property, initiation into religious mysteries, generally any religious ceremony, especially marriage. ("Little Liddell" Lexicon, 1977, p. 697).

    And obviously Aristotle has his own usage for the word. But it is good to remember that Aristotle's purpose was the combined making sense of the world by giving an account of it. He was not in the magic business. Thus for modern purposes and understanding, DNA would seem to be what drives a living thing to fulfill its telos to be what it is - and this is both simple at first, and then also not-so-simple. But DNA the director. In terms of other things, telos seems to be used to refer to what the goal or purpose is.

    Nor is it clear to me whether things have a telos apart from what their specific use is. An example given is that the telos of a blacksmith is to forge a sword, that of a soldier to wield it. But neither of these is the telos of the sword itself.

    But the important point, imho, is not to imbue the word with magical or mystical meanings or power or properties, but to think of it instead as an idea-as-tool extant in Aristotle's language and adopted by him to develop and articulate hi ideas.
  • Are "cause" and "sake" in Plato's Lysis parallel to Aristotle's efficient and final causes?
    Hi and welcome - if you haven't already been welcomed. A word about MU: you're probably OK asking MU about Aristotle; on that he has well-developed and strong opinions. But he also seems unable to distinguish between his beliefs and what is the case, thinking that what he believes actually is the case. And if pressed he will retreat in a familiar pattern, usually repeating his claims without substantive argument, ending with his saying that he does not understand what you wrote and that he is not interested in continuing the discussion. This isn't to say you will have this experience, but if you do and you feel the worse for it, know that many of us have been there, and that the remedy is just simply to disengage. I myself am not so good at taking my own advice: I have questions pending to MU which he disdains to answer.
  • Donald Trump (All General Trump Conversations Here)
    Nos4, you endlessly miss the point. Trump is a very bad man. That's not relative to or compared to anyone else. And as it happens he happens to draw to himself other bad and very bad people. I think you're English, not American, but even so if he is elected - God help us - as I observed in 2020, Americans will get what they wish for and regret it, and even people like you will rue it.
  • Donald Trump (All General Trump Conversations Here)
    the other did nothing wrongNOS4A2
    Your contention is that Trump did nothing wrong?
  • Are actions universals?
    but then a processual universal must....Count Timothy von Icarus
    I want to credit yours a great answer, but need a little expansion. Not sure what a processual universal might be. I can imagine the idea of a universal tree or horse - not without some problems. That is, in some sense these universals ought to be things of some kind - presumably other than just ideas, which is what I think they all are. But of running or jumping? Or, how does a process become a thing? Or if not a thing and not just an idea, then what?
  • Are actions universals?
    Maybe genera and also species. The trick not to be confused by language's sometimes referring to different things either ambiguously or with the same word.
    Edit: An arrow flies, a bird flies, a squirrel flies, a jet plane flies. We all understand what is meant in each case, but it would be not-so-easy to make clear just exactly what the understanding of "flies" is with any reasonable rigor.
  • Donald Trump (All General Trump Conversations Here)
    Both sides have claimed....RogueAI
    This seeming even-handedness contains a fatal flaw: that one side may be right and the other lying. Consider just plain folks over here and a monster over there. "Oh no!" cry the folks, "There's a monster over there!"

    The monster roars back, "You folks over there are the monsters, not me!" And apologists and spinners - and foolish people - talk about "both sides." The trouble - the fatal flaw - is that one side is speaking truth and the other lies.

    But it's an old, old and ancient story, the good and true v. bad and evil. The corollary lessons being that the lessons are there, but some people never learn.
  • Donald Trump (All General Trump Conversations Here)
    I'll opine about he shooter, based on very little evidence. A recent high-school graduate from small-town Pennsylvania a few miles from Pittsburgh, a registered Republican in the heart of republican country. But a smart kid. To be brief, he probably drank a lot of the Republican Kool-aid but couldn't handle the lies. That is, the cognitive dissonance of Republican rhetoric destroyed him. Being no doubt idealistic, he may have thought he could fix it and should try, which he did. Bottom line, only one person turned him loose in his state, and that is the individual he tried to shoot. @180Proof got this in one word,
    Karma.180 Proof
    And I think that is exactly right. Bad, bad shooter. Bad, very bad Trump
  • Donald Trump (All General Trump Conversations Here)
    The Secret Service needs something - maybe a lot of people to be fired. Never mind that some fool with a rifle (apparently), conspicuous enough so that (apparently, again) some people saw him minutes before the shooting and tried to alert police, got close enough - never mind that. What the videos show is that once shot, it took them too many seconds to get to him, and when they got to him and finally got him up, his head is presented for long seconds as a perfect target. Some held up their hands to block any view, but unless those hands are made of solid steel.... In sum it is clear that once shot, the Secret Service did not really know what it was doing or how to do it. Maybe they need to practice, like any football team needs to practice.

    The reports on this event are going to be interesting.
  • Donald Trump (All General Trump Conversations Here)
    Trump has been hurting people for five+ decades. But of course a troll like you wouldn't miss an opportunity to be a troll.
  • Donald Trump (All General Trump Conversations Here)
    And no one else wounded?
    Assuming he was shot - and that not yet reported - I wonder how many people there are with a possible motive. A million or more?
  • Infinity
    Explicitly stated....Metaphysician Undercover
    I'm jumping in here not because anyone needs my help, but instead because I have questions pending before you that you have not even attempted to answer, and because of your claims and lack of substantive response I hold you obliged to answer them. You will find them above on page 20 where you left them.