tag:blogger.com,1999:blog-8954608646904080796.post859818655478484016..comments2024-03-18T21:06:42.546-07:00Comments on Edward Feser: Can you doubt that 2 + 3 = 5?Edward Feserhttp://www.blogger.com/profile/13643921537838616224noreply@blogger.comBlogger127125tag:blogger.com,1999:blog-8954608646904080796.post-58263586597212106342019-08-22T08:58:03.950-07:002019-08-22T08:58:03.950-07:00Agree. If we assuming the perception is a dream th...Agree. If we assuming the perception is a dream then everything within such perception is an element of the dream and this not real, even 2+3=5 isn't real.Olehhttp://oleh.pronoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-42365471413433372532019-07-02T16:01:00.541-07:002019-07-02T16:01:00.541-07:00Ok this is what I thought of here as an extension ...Ok this is what I thought of here as an extension of your post and how it also proves epistemological realism:If you derive the abstraction/arithmetical formua "2+3=5" from an observation of two apples, three apples, and thus five apples, and then by logic can confirm that 2+3=5 (as you did in your blog), then what you have done is confirm that your perceptions (of reality) indeed are of reality, because with "truth" being the foundation of reality, the fact that 2+3=5 is true or "real", and that it was derived from your perceptions, confirms too that insofar as it was derived from your perceptions, your perceptions are also true or "real", real as in they thus correspond to real-ity, i.e that which is real, and thus your perceptions are indeed that of reality. Am I onto something [probably reinventing the wheel as this has almost 100% certainly been stated before, not claiming its a new 'profound' idea or anything] or am I wrong? Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-61545165843845674632019-05-03T13:21:14.496-07:002019-05-03T13:21:14.496-07:00"... Descartes famously tries to push doubt a..."... Descartes famously tries to push doubt as far as he can, in the hope of finding something that cannot be doubted..." Did he though? I know that's what he proposed, but even if that's what he really intended, I don't think that that's what anyone is doing when they innocently attempt to apply his 'Method of Doubt'. This has bugged me for years, and I'm curious what you might think.<br /><br />An actual Doubt, as experienced individually, is "A feeling of uncertainty or lack of conviction" which we involuntarily experience as a sensation of uneasiness that something we've heard or been exposed to "just doesn't add up". That sensation of authentic Doubt springs into our mind from beneath conscious awareness, it is not something that a person can directly will themselves to feel. Sure, you can ask some questions or discover some information that leads to the experience of a doubt, but you can't artificially will yourself to experience an authentic feeling of doubt about anything, let alone will yourself into the methodical practice of a sustained series of 'Doubts' about math, evil spirits, or anything else. <br /><br />What it appears to me that Descartes does with his Method, is use the universally familiar sensation of Doubt, as a cover for legitimizing the arbitrary, in the form of baseless suppositions & questions which, without the cover of 'Doubt', would have stood naked and exposed to the very legitimate condemnation of being an arbitrary assertion.<br /><br />Worse, a natural Doubt comes <i>in response to</i> your perception of an apparent error or deception, and it does so for initially unconscious reasons, which when followed up with responsible questioning and consideration of the matter, typically brings its cause - whether well founded or not - into conscious awareness. An artificial doubt however, which is what Descartes' method proposes and promotes, has absolutely no basis for its being. What it does instead is encourage the default mindset of a cynic, causelessly believing that all is deception and unknowable.<br /><br />Legitimate Questions, even questioning everything you encounter, would be a positive probing for greater understanding, and might even expose gaps and errors in understanding, that would be a positive result.<br /><br />An authentic doubt, followed up by responsible questioning, is also a positive process that ultimately leads to greater understanding.<br /><br />Artificial doubt, however, even if eventually followed up with sound questioning, is fundamentally corrosive, it encourages a disposition towards all of reality as it being fraudulent, and fosters an unhealthy cynicism and skepticism.<br /><br />Am I wrong in that?<br />Van Harveyhttps://www.blogger.com/profile/08470413719262297062noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-21933357134513186952019-04-21T15:12:52.163-07:002019-04-21T15:12:52.163-07:00But if we were absolutely forced to start thinking...But if we were absolutely forced to start thinking in such ridiculously unrealistic terms (that our senses and logic are wrong yet in such a way that they seem to work and be true among all people would require a mighty big deception so far removed from experience it is worth ignoring even if it were somehow true) this type of thinking would cast doubt even on the cogito ergo sum, as Feser points out in the latter paragraph (s). Anonhttps://www.blogger.com/profile/11122746359465351676noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-10784646994897346192019-04-12T13:20:40.190-07:002019-04-12T13:20:40.190-07:00@PhilipRand you are talking about hysteresis. You ...@PhilipRand you are talking about hysteresis. You are a Time Lord, so concepts like hysteresis come naturally to you.<br /><br />The answer is not that transitivity fails. The answer is that whether B = C depends on the history of the system. Even though you can't discern any difference between B= 1.0000000 cm and C= 1.0000001 cm, B is only equal to C when you're not moving from 1.0000000 cm to 1.0000001 cm in time.<br /><br />Let me give you a Time Lord metaphor to help you understand. An air conditioner is set to turn on at 22 degrees centigrade. The ambient temperature is 22.00001 degrees centigrade. There are two cases.<br /><br />The first case is that the air conditioner is turned out for the first time. It sees that it is 22.00001 degrees centigrade and cools. Here 22.00001 != 22.00000.<br /><br />The second case is that the air conditioner already cooled down the room but the temperature rose to 22.00001 anyway. Here the air conditioner knows the history of the room, and says that 22.00000 = 22.00001 <b>until</b> the temperature rises to 25 degrees.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-52947238555591706902019-04-12T11:57:45.641-07:002019-04-12T11:57:45.641-07:00I think Feser is not claiming that skepticism abou...I think Feser is not claiming that skepticism about basic mathematics is impossible, but merely that it turns out to be incoherent. Skepticism about the external world, regardless of whether it is similarly incoherent, is awarded a privilege over skepticism about basic mathematics (it can “get off the ground”) because it is more “<em>prima facie</em> plausible”, due to the “simplicity of cognition” involved in basic arithmetic. Failing to enjoy this privilege is said to mean skepticism about basic maths cannot “get off the ground”, but I do not take that to mean it is impossible. You can simply lie down on the floor and be a skeptic from there, until you get up and notice that you were lying down on a bed of incoherence.Thiago V. S. Coelhohttps://www.blogger.com/profile/12820290613203484073noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-49466058698959832282019-04-12T10:56:55.258-07:002019-04-12T10:56:55.258-07:00Like Professor Pruss, I continue to doubt Professo...Like Professor Pruss, I continue to doubt Professor Feser's argument on this. <br /><br />Let me use as an example the tribe of primitives (in the Amazon jungle?) who do not have words or names for most numbers. They have one, two, and many. And that's it. Now, it is not fair to urge that THEY can doubt "2+3=5", because the doubt Feser is talking about is the doubt that holds when a person <i>understands the proposition</i> but can be indeterminate about whether it is a true or a false proposition. Tribesman Bill who doesn't understand the proposition doesn't have the first element of the required sense of doubt. <br /><br />No, my counterproposal is more involved. Let's take Bill and start TEACHING him higher numbers, with the aim of eventually being able to do math. First we must start teaching him numbers above 2, and we will have to take it slowly. Perhaps it takes some time before he gets "3" down, and then more time to get "4", and still more time to get "5" and "6". Let us suppose that he has been exposed to "7", but has not yet absorbed the concept, but that he has "6". Now we start to explain addition to him formally, not just the implicit addition in the counting upwards from 2. We do 1+2, 1+3, and 1+4. He has to work at it to get the <i>idea</i> of "plus", but work at it he does, and he gets it at least as a basic principle, although this is all so new he remains very much in dismay at all these new thoughts. So you have taught him his "1 plus" table up to 1+5, and now introduce the following questions: <br />A: What is 2+2?<br />B: What is 2+3?<br />C: What is 3+2? <br /><br />He has never tried any of the "2 plus" table identities, so these are brand new questions. At the moment he views the QUESTION, he know <i>what the question means</i>, but he does not know the answer. He must think about it, and he might get it wrong. In fact, he knows HOW to get the answer to <br />D: "What is 1+5" <br />from what he was taught in doing 1+2, 1+3, and 1+4, (rooted in counting) so he can go about (finding?, constructing?) the right answer for 1+5. But we have not yet given him any method for converting the problem "what is 2+..." into an equivalent problem of "what is 1+...", and that's the only sort of math he knows yet. So not only does he not KNOW the answer to "what is 2+3", he doesn't have the tools for coming up with the answer reliably. Yet. If you then asked "is 2+3=5", he would quite reasonably say "I don't know". <br /><br />All this is just making clear and concrete what Dr. Pruss said above. Basic math or not, the statement is NOT "self-evident" and thus it is open to the possibility of doubt. <br /><br />My own preferred "we cannot doubt" proposition, after we have gone beyond "I am", is this: "The whole is not less than the part". This proposition still requires a pre-existing set of understood concepts, including the right "less than" concept. But once they are understood, no person can be in doubt as to the truth of the proposition. (And it is much simpler than the statement of non-contradiction.) So, it's not like I dispute that there ARE such things that you cannot doubt - and that such can be used in Dr. Feser's point about "the demon making you think..." I just don't think "2+3=5" is a good candidate. I think Dr. Feser needs a proposition which is technically self-evident. (Note that moderns tend to dispute that there is such a thing as a self-evident truth other than a tautology, but Aristotle and St. Thomas clearly say there is such a thing.) Tonyhttps://www.blogger.com/profile/07159134209092031897noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-22135234926405285732019-04-12T03:15:16.706-07:002019-04-12T03:15:16.706-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-26556538615825480732019-04-11T11:31:27.166-07:002019-04-11T11:31:27.166-07:00Then by using the law of transitivity you come to ...<b><br />Then by using the law of transitivity you come to the conclusion that bar A and bar C are the same length.</b><br /><br /><a href="https://en.wikipedia.org/wiki/Sorites_paradox" rel="nofollow">Sorites Paradox</a>. And the answer depends on hysteresis. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-39735718362099001902019-04-11T10:46:39.058-07:002019-04-11T10:46:39.058-07:00> Really... but if God created a world where re...> Really... but if God created a world where reading is impossible we would not have the Word.<br /><br />The Word of God is properly the Second Person of the Trinity, but I'm guessing you mean the written Bible. Luckily, transmission of the Bible does not require writing nor reading, though they are helpful tools. In many cultures, oral tradition is the ways stories are passed along from one person to another.Tomnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-365375398741709302019-04-11T10:35:53.694-07:002019-04-11T10:35:53.694-07:00Ed:
The simplicity here comes in degrees. There a...Ed:<br /><br />The simplicity here comes in degrees. There are lots of logical steps involved in proving 2+3=5. It would be odd if scepticism about things that involve, say, five steps were possible but scepticism about things that involve only one four steps were impossible.<br /><br />The only reasonable place I could see placing a cut-off is where there is only one logical step. 5=5 may be like that (immediate application of the rule of identity introduction, and if you don't know how to use that rule, you don't know what "=" means). But 2+3=5 is definitely not a one-step inference (unless we're just relying on a memorized result).Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-58988622508274924902019-04-11T07:47:27.515-07:002019-04-11T07:47:27.515-07:00I don't understand principle 2. What do "...I don't understand principle 2. What do "commensurate" and "measurable" mean in this context?Lagrange Squaredhttps://www.blogger.com/profile/14220923491528658731noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-90055187605511033562019-04-11T06:36:06.287-07:002019-04-11T06:36:06.287-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-35745755726707526242019-04-11T06:31:37.871-07:002019-04-11T06:31:37.871-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-38829752525120294902019-04-11T05:41:53.242-07:002019-04-11T05:41:53.242-07:00Philip, the stick example involves an error of per...Philip, the stick example involves an error of perception, which is an error of the senses, not in the property of transitivity. How would Thomism be defeated by this? <br /><br />Descartes seems to be dealing with a different kind of error. Lagrange Squaredhttps://www.blogger.com/profile/14220923491528658731noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-31612861538210541282019-04-11T03:12:48.573-07:002019-04-11T03:12:48.573-07:00To anyone coming later, please read further commen...To anyone coming later, please read further comments below, where Feser seems to ground the privilege on “simplicity of cognition”, thereby restricting it to the most basic arithmetics. The privilege is thus fully grounded and explained, though it does not exist for the large sum at hand, and our poor proverbial preschool child (or “much stupider” man, as I had it) may still doubt our titular sum, which I believe is merely a minor exception that can not be further generalized to ground the skepticism of the able-minded.Thiago V. S. Coelhohttps://www.blogger.com/profile/12820290613203484073noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-6384743024926390602019-04-11T03:06:43.128-07:002019-04-11T03:06:43.128-07:00To anyone coming later, please read further commen...To anyone coming later, please read further comments below, where Feser seems to ground the privilege on “simplicity of cognition”, thereby restricting it to the most basic arithmetics. The privilege is thus fully grounded and explained, though it does not exist in my exchange with the stickmaker, and our poor proverbial “someone much stupider” (later phrased as a “preschool child”) is still doubting our titular sum. Hopefully a tutor can help him.Thiago V. S. Coelhohttps://www.blogger.com/profile/12820290613203484073noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-27048852866134166732019-04-11T02:25:58.479-07:002019-04-11T02:25:58.479-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-84548765030173162892019-04-11T02:21:01.308-07:002019-04-11T02:21:01.308-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-62840930291426523922019-04-11T02:19:12.851-07:002019-04-11T02:19:12.851-07:00I think you are mistaken about the Trinity. Now, G...I think you are mistaken about the Trinity. Now, God could also create a universe where reading is impossible, but that would not allow you to doubt you have just read this. So, your question is irrelevant to the point at hand.Thiago V. S. Coelhohttps://www.blogger.com/profile/12820290613203484073noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-29973538990868110952019-04-11T02:12:47.451-07:002019-04-11T02:12:47.451-07:00Well, Feser’s last comment appears to me to grant ...Well, Feser’s last comment appears to me to grant the “someone much stupider” argument, a.k.a. the “preschool child” argument, since it consists in pointing out cases where there is no such “simplicity of cognition”. So, if I am stupid enough, I can certainly doubt that 2+3=5, though not otherwise.<br /><br />Now, for the proverbial moron, there might be something even simpler which even he cannot doubt, such as that 5=5. If someone were stupid enough to doubt all of mathematical logic in this way, then we would probably not be speaking anymore of a mind intelligent enough to even doubt anything. So I suppose the “stupid preschool child” argument (as we might call it?) only presents a very limited set of exceptions, and not something that can be generalized.Thiago V. S. Coelhohttps://www.blogger.com/profile/12820290613203484073noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-37581336773538987552019-04-11T02:10:45.415-07:002019-04-11T02:10:45.415-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-8397788170442313262019-04-11T01:52:00.815-07:002019-04-11T01:52:00.815-07:00In the Holy Trinity 3 = 1 metaphysically. Could G...In the Holy Trinity 3 = 1 metaphysically. Could God not create a reality where things are so different that (approaching things from an Aristotelian perspective) what we witness in that reality would in fact require a different mathematics?Jamesnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-41169036068060923392019-04-11T01:35:00.316-07:002019-04-11T01:35:00.316-07:00@Phillip Rand
@Thiago V. S. Coelho
Phillip, if by...@Phillip Rand<br />@Thiago V. S. Coelho<br /><br />Phillip, if by "1.0000000001" you actually meant to write "1.000000000...1", with the '...' standing for an infinite series of zeros, well then Thiago response is sort of right. However, I use the qualification "sort of", because in fact, there is no such number in the Real numbers (R). In R, there can be no limit number following the "..." representation. <br /><br />With that said, you could identify the following well-ordered set:<br /><br />2,3,4...1 to correspond to the infinite ordinal number w+1.<br /><br />Likewise,<br />3,4,5...1,2 = w+2<br /><br />But of course, infinite ordinal numbers are not members of the set of real numbers (R). <br />Tritiumhttps://www.blogger.com/profile/09898318643029403042noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-20836008589911051902019-04-11T01:04:27.009-07:002019-04-11T01:04:27.009-07:00This comment has been removed by the author.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.com