A brief history of logic: Aristotle and deduction | Math Foundations 251 | NJ Wildberger
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- เผยแพร่เมื่อ 28 พ.ค. 2024
- In this video we begin to examine the history of logic from its early beginnings in ancient Greece, with the work of Parmenides, Zeno, Plato and then Aristotle. It was Aristotle who almost single handedly set out the modern theory of logic as it was to be for two thousand years until the modern European era.
Aristotle is concerned with correct logical inference based on what are called syllogisms, and these have been categorized, and given amusing names by later writers. His aim was to strengthen dialectics, to assure correct deductions in arguments, and for logic to be an educational vehicle.
Video Content:
00:00 History of logic
01:18 What is logic?
05:21 Plato the founder of modern philosophy
07:11 Aristotle and the birth of logic
13:44 Structural statements of Aristotle
17:26 Four logical forms ( Prepositions)
20:01 Syllogism s
25:32 Potential and actual infinity
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Great videos. I would appreciate seeing more on the subject of logic. Very interesting topic!
Thank you, that's a great summary!
The lines you read from metaphysics are so intellectually packed it would take you a good year or so of studying his other works to understand what he fully says there.
Nice to know they are syllogisms. Amazing. Thankyou.
o man , this is a great work !.
Thanks for a really informative video. It is a help.
Very Helpful Lecture
Very interesting subject. I'm often not interested in history, but it's very entertaining learn about people I do care about.
Video Content
00:00 Introduction
01:17 Logic
05:20 Plato
07:10 Aristotle
17:25 Four Logical Forms(Propositions)
20:01 Syllogism
Thanks, Norman! Really enjoyed this video, especially that I wanted some introduction into logic and its history, and here's your nice installment. Though I don't share this Aristotelian view (which after watching your video I know the proper name for), that everything is purely tangible, and there's no room for ideal world, especially the conclusion that the only world that exists is this material world, I find this approach in some sense interesting and useful, I think it's a good fuel for this dialectic methodology. And applying it to the mathematics, as you like to mention, can generate in many contexts very practical results. But I think that transcendent notions give us more rich tool-set for looking at this world. To support, so to speak, Plato's point of view, I'd like to say that this world cannot be the only one real world, since it had its beginning as we all know from previous century cosmological discoveries of red shift, background radiation, expansion of the Univers - i.e. Big Bang, when time, space and matter had come into being. Therefore, the cause of Big Bang should be timeless, spaceless and immaterial. That would be my syllogism:) Just sharing with you my thoughts. Already downloaded some of your wild playlists on trig, linear algebra, history of mathematics and math foundations. As for the latter, took a deep dive into your building of an arithmetical framework for numbers, and really enjoyed that one, and at the same time had a good opportunity to recap long division, though it's simple, your explanation gave me some insights I lacked. Thanks again for what you're doing, this world definitely needs it! Looking forward to the next video.
Thanks for the comment, don't know how to render Russian symbols. I know lots of mathematicians believe in a Platonic world. I used to also. But I feel now that there is something fundamentally religious about that: the justifications you put forward are philosophical not really scientific. I believe most mathematicians who have a Platonic view point have been seduced into this by the beauty and order of mathematics, of which I am a keen proponent. But does this beauty and order need to come from outside our world? Is it not so much more interesting if it is actually built into our world? The physicist Max Tegmark has made, I think, arguments in this direction which are quite appealing.
I harbour the suspicion that the true reason why we pure mathematicians hold onto our unsupportable belief in a "universe of mathematics outside our own" is that such a world becomes a convenient parking lot for all the "infinite stuff" that we like to believe in, but which self evidently don't fit into our own world. When dogma meets reality, which is going to give way?
The Aristotelian position does not say that there is only the material world. Aristotle himself thought there was a transcendent Intelligence and that the soul was in some way immaterial. What Aristotelianism says is that mathematical properties can be realised in actual, non-ideal, things, whether material or other.
Most mathematicians don't really think that numbers exist in some mystical realm outside of this world. Indeed, if there exists something detached from all physical reality then by definition we have no way of accessing it. If we cannot access it, we cannot have any knowledge of it.
But the same mathematicians see no harm in saying that for any natural number n its successor n+1 must exist. They justify this use of 'existence' as just being something intangible and abstract that you have to just accept if you want to understand maths.
Their stance is that if we claim a concept is 'abstract' then this is justification enough to continue to reason about it. They don't want to be pressed on what it means to say a number exists or what 'abstract' really means. They want to sweep the issue under the carpet by saying it is a different type of existence, its abstract!
It appears that everyone else understands it and you are made to feel foolish if you contest it. Also you need to accept it if you are going to get past day 1 of an Analysis course, and so most people just go along with it.
Arguably mathematics started with counting. We were doing this in the stone age circa 30,000 years ago and probably a lot earlier. So even at this very early stage (long before the ancient Greeks) we have the concept of numbers and we can attempt to clearly describe what such a number is.
The stone age person defined what was to be counted. The counting process then took place during which tally marks were added onto some material, like a cave wall or a piece of wood.
Perhaps the collection of physical tally marks is the 'number', or maybe it is merely a symbol that allows us to conceive of the number by counting the tally marks? If we count the tally marks then arguably the chemistry of our brain now contains some physical content that we perceive as being the number. In all these cases a number is something that has a physical presence.
Lets now try a non physical approach. What if the number 3 is the name given to all possible collections of 3 things? Without delving into the metaphysical aspects of this statement, we can fairly reasonably assume that this is not the definition being used by the stone age people. The group of things to which the tally marks referred was defined within the chemistry of their brains & hence it had a physical presence. And if we can describe everything the stone age people did in terms of physical reality, why should we feel the need to claim groups were somehow mysteriously defined outside of human brains and outside of all physical reality?
Outstanding!
Thank you Sir.
The ancient Greeks were geniuses
Thank you very much
Thank you so much
In answer to Adilien Lubguban 's question what is he difference between Aristotle's logic and modern logic. Aristotle's logic is called the classical logic of syllogisms.Modern logic is called mathematical logic. Mathematical logic is an extension of classical logic and is designed to deal with the logic of relations which lie beyond the scope of Aristotle's logic but which are abundant in mathematics.Mathematical logic is an extension of the formal method of mathematics to the field of logic.Given that the formal method of mathematics is axiomatization to extend it to logic is simply to extend axiomatization to logic. The result is an axiomatized mathematics and logic expressed in a symbolic language called mathematical logic.
Dear professor Wildberger thanks for this new video! I wonder if in the future are you going to talk about the Bourbaki Seminar and particularly about the work of Alexander Grothendieck
Hi David, I will probably have something to say about Bourbaki in the Foundational direction, but I will stay clear of talking about Grothendieck.
@@njwildberger Sir, can you please tell us why you would not want to talk about Grothendieck?
I would rather not talk about current mathematicians, because I do not want my criticisms of modern pure mathematicians to be taken personally. But I am happy to discuss modern mathematical ideas more abstractly.
Great lecture.
In 19:54, can't we combine 'I' and 'o' to make them same?
Hi professor i suggest to include closed captions in the video to understand thoroughly for non-english speaking person like me. Thanks
Thales did logical proof and so did the Pythagoreans. Aristotle abstracted this logic; it's his one major contribution. Logic comes out of mathematics.
- Philosophy is 'wondering what knowledge is and asking how to go about it." Something is often philosophic when we haven't got the mathematics of a given subject yet.
Van Der Waerden, in his Algebra and Geometry of Ancient Civilizations" gives some evidence for the Indians maybe stumbling upon logical proof before the Greeks. In fact, one could argue that after the Indians logical proof of the Pythagorean theorem no less, the Greeks picked it up and took it far more seriously. Logical proof has been questioned long before mathematicians from today to the middle ages.
I remember a video you made about the Fundamental theorem of Algebra. You say that none of these logical proofs are worth anything because they are not the last word. But, you also criticize infinity by saying one can come up with all kinds of finite results long before one ever conceives of infinity. All these proofs are like coming up with finite perspectives of the infinite I'm being pulled away for some emergency - i hope to come back; hopefully, I've given enough actually!
I want to know the Differentiate Aristotelian Logic from Modern Logic? I want to know thank you
You don't have a wikipedia page, man, what's wrong with this world?
That is an interesting point; on occasion someone has created such a page, but there is a Wikipedia editor who shall remain nameless who has a long-standing antagonism to my work, or perhaps to me, or perhaps I stole his girlfriend in high school. In any case he has made it a point to squash such. Unfortunately this same fellow has had a lot of influence on the Wikipedia page on Plimpton 322, so Mansfield and my work on that, despite huge international interest, rates no mention. The academic world is not as objective as outside observers might expect it to be. But it is not a big surprise, if you want to rock the boat, be prepared that people will try to make things difficult for you.
"I stole his girl friend in high school".
Sometime Norman, while learning an incredible amount from you, I feel like I just simply just want to wait for your one liners... Hilarious.
We are not allowed to idealise concept in math? The diagrams in geometry have no value? Use stones to count numbers is not valid? Approximations are not allowed? What is the difference between idealised and abstracted? I'm confused...
Existential quantification (e.g. metaphysical postulation of slash, empty set etc.) is idealization and abstraction to begin with. To lend your language, numbers are pulled from your ass, supposedly real(?) but we can't gather any evidence that numbers exist anywhere else except in some fantastic hallucinations of some human beings.
OK Let us go back in time when numbers did not exist. People in those days, saw two trees over here, two pigs over there, two people talking, and came up with the concept of number 2 (which is roughly how it happened). The question is - does number 2 exist in nature (as pair of objects close together), or just in the peoples heads. I tend to think that people saw groups of objects, saw that they had something in common and came up with new category of words called numbers to answer the simple question - How many objects there are in these group. After that it got complicated. But that was the beginning. Idealization or abstraction? I do not think it was either. It was simple practicality. Idealization and/or abstraction came much later when the new question arose - OK we got numbers now. What can we do with them, how can we use them?
@@aleksandarignjatovic3130 That is all true and yet it's also false: maths has taken many forms in many cultures, as has the notion of numbers. The notion of 1 or 2, say, could be arithmetic numbers as we are used to them, or they could be viewed as relational concepts, or geometric concepts, or something to do with symmetry groups, and that's just frameworks taken from modern maths. This reverse engineering of maths to try to see what people might have thought about maths in the early days is a fiction: we really don't know how people thought back then, and we're talking about a massive diversity of cultures, eons, and even biologies. Animals, plants and ecosystems - and of course Mother Nature's far superior technology - and even chemistry and physics - can all do maths. It's nothing special to us; it's part of most things. Do most things have concepts of mathematical objects such as numbers? Plants and non-human animals do, at least in the sense that they can do simple arithmetic and logic as individuals (which is the same for most humans) and do very complicated maths when working together (which is also true for humans). Reductive maths - breaking problems down into tiny parts, doing stuff with those parts, and then trying to build up the solutions again - is only one very narrow form of maths, but there are heaps of other forms. Swinging a rock around on a piece of string and watching how the rock flies around in a circle gives a far simpler and more accurate solution than modelling and solving equations, let alone our present super-reductive use of digital computers. Interestingly, quantum computers take a big step back (in a good way) to these simpler forms of maths, though with their own limitations: there are always trade-offs.
Norman's lectures are great but they are stuck in old and narrow paradigms that are more history of maths and history of philosophy than actual maths and actual philosophy. We're vastly ignorant - but vastly less ignorant than back when Chinese, Indians and Greeks were trying to figure out the basics. The last century of physics, maths and psychology has made these old paradigms quaintly redundent, to the point that Norman's lectures are really not even about the history of maths - but on the history of 19-20th century Western theories and ideologies of how the history of maths might and should have been. The actual history of maths is far broader and more interesting.
Worth pointing out that J. Franklin disagrees with Aristotle about distinguishing between potential and actual infinity. (You don't actually say he agrees with that, so fair enough, but the juxtaposition of these on the same slide might suggest to some readers that he agrees with Aristotle there).
Is this video 251 the first video of logic series?
Yes that’s right
It seems as though Aristotle was putting the form into boxes, instead of the objects.
Always dig the drum stick because math is time is math.
And I really appreciate the video you posted naming the most high God: Jah/Jehovah.
Another great video as usual in this series.
I can't get excited about 'potential infinity'; it is as meaningless as 'actual infinity'. For me, anything containing the word 'infinity' should be avoided. In computing where everything is finite it is still possible to encounter 'endlessness' but there is no potential for anything to be 'not finite'.
If someone says "keep peeling potatoes" then we have a set of instructions where no end point is specified. The instructions are just three words and so are finite. If someone tries to follow these instructions we have an occurrence of a process that tries to follow the instructions. In computing terminology this is misleadingly called an 'infinite loop'. To date, all instances of such loops have only ever iterated a finite number of times. Any occurrence of any process can only ever iterate a finite number of times.
So a finite set of instructions can describe a process where no end point is encountered. The described process is endless in that it has no defined end point. Even though the process is endless, it can only ever consist of a finite amount of steps.
There is no potential for 'reaching' a non finite quantity. Never has been, never will be.
Karma Peny: Thanks for a great comment. I agree with you completely!
You just said all these endless presses end...doesn't that make the word endless just as meaningless as the word infinite. Spooky. Seems to me both words have the same meaning, ie infinite = endless.
Bazzmond Why: Every process must end, and so strictly it cannot be endless in terms of execution.
However, it must be stopped by something other than the set of instructions (algorithm) it is following.
The instructions being followed can be said to be endless in that they do not contain an END instruction.
Consider the following algorithm:
Step 1: X=0
Step 2: x+x+1
Step 3: If x=5 then END
Step 4: Go to Step 2
If we remove step 3 then this algorithm will be endless (as it will have no END instruction) even though it is entirely finite.
I see your point. but..
Following Aristolian logical forms,
All infinite things have no end point defined.
All endless process have no end point defined.
All endless process are infinite.
Bazzmond Why: Okay, what about this one...
Paper beats rock,
Rock beats scissors,
Paper beats scissors
We test logic by finding tangible examples to test if the proposed logic works or not. This is what I think should be the validity test for logic - if it stands up to real world examples or not.
We cannot validate your first statement with any tangible example because we have no real world object that is 'infinite'.
I would clarify your second line as 'All endless processes are only endless in so much as they are following a set of instructions that have no end point defined"
I think we should strive for as much clarity as possible to avoid problems caused my misinterpretation of terminology.
When you say you don't think like philosophers, isn't a mathematician simply a philosopher utilizing symbolic logic? You're simply a specialized philosopher in a more narrow field (mathematics).
I suppose he's erring on modesty for his analytic thinking is very much indicative of a philosophical mind, but for what it's worth Plato argued that mathematics is the penultimate step to philosophy, and not philosophy itself. Regardless, he could most definitely do philosophy, particularly logic but also philosophy of science and similar.
I learned a lot about Aristotelian logic from this video. I'll have to commit the 8 names of the syllogisms to memory. Can't wait to hear the arguments against infinite sets. I'll look up James Franklin in the meantime.
I give up trying to find latin names.
Daisi, Pellio, Tiphani, Orlando
Excellent video. In reading the comments, some people disapprove of the notion of abstract. I would warn that abstract is indeed often used in OOP. For instance, an abstract class (object) has an "is-a" type relationship with a sub-class. So for instance, you could have an abstract class "Shape", which has properties that all shapes have, like a draw function. We then have a class called SquareShape. Then in true Aristotle fashion, we have, every squareshape is a shape, but not all shapes are squareshapes. So I hope that people can understand the concept of abstraction does have its place in the world of mathematics, but perhaps most often found in software development. One of the 4 pillars of OOP is Abstraction; A process of exposing essential features of an entity while hiding the internal details. Now I realize what occurs in software development does not always translate very well back into pure mathematics, but just thought I'd mention it.
Physics historically belongs to philosophy.
Some thing u need to know.
Aristotle, "mathematicians 'do not believe in Infinity'"
I am disappointed that your first slide (Sep 28, 2014)
was not an Aristotelian proof that Jim Franklin is not
a mathematician.
One of my goals is to convince Jim that a true Aristotelian position requires letting go of the Platonic "infinities". :)
I was disappointed as well, but it's because you wrote 151 instead of 251
That's not likely. The chapter on infinity in An Aristotelian Realist Philosophy of Mathematics argues that mathematics can mostly do without infinities but on the other hand there's nothing wrong with them.
It is not coincidence that many quantum physicists become some sort of Platonists, as the quantum coherent superposition can be considered analogous to Platonia of Pure Forms, and these decoherred or collapsed classical states as analogous to cave mechanics. ;)
I'm not at all happy with speculative hypothesis or even worse, presupposition, that mathematics is epiphenomenon of classical physics.
As an educator who is interested in providing "good instruction" and "good guidance" to students, I feel morally obligated to give them finite instruction.
Can you see what the issue would be if the mathematics I was teaching them was riddled with "infinite processes"?
As an educator I do not want, or deserve, an "infinite" amount of time with my students. I simply want them to engage in processes that are productive to them as they learn to be more efficient with an intellectual workflow(whatever that means to them, in other words: they get to use the mathematics, finite mathematics as if there were any other, to define their own workflow).
Philosophically, it is quite an interesting subject to ponder and consider(just checkout any of the TH-cam comment boards of Prof. Wildberger's videos). And it can be quite productive. But these questions occur to those who can already ponder and realize the power of mathematics. This view is for the privileged for the most part.
If we are going to teach the world then let those we consider student be the first to critically judge us for wasting their time or spending it wisely.
Sometimes the answer to your argument is already embedded in the question, its waiting to be found fore someone how dares to ask better questions and finding out the Truth.
Hence "Socratic Method"
One can imagine two mathematicians arguing heatedly whether PI exists as a potential or actual infinity. One says potential, the other actual. An engineer standing by, looks at them pitifully as they waste their time, plugs in his calculations PI to the 14th decimal and sends the vehicle to Mars.
Aleksandar Ignjatovic said "... looks at them pitifully ..."
The engineer is using standard calculus to accomplish sending the vehicle to Mars, so why would he look at mathematicians pitifully.
Would a mathematician, standing by, look pitifully at two physicists arguing heatedly whether a cat is alive or dead in a closed box? I don't think so.
But there is no argument whether pi exists as a potential or actual infinity (it depends upon your viewpoint and what assumptions you are willing to entertain). Aristotle wanted to rule out actual infinity and accept only potential infinity because he didn't see a good way to resolve paradoxes like Zeno propounded. Modern logicians think they have set up a framework where the paradoxes can be resolved. Some mathematicians want to take a finitist (or ultra finitist) approach and reject actual infinity (or potential infinity for the ultra finitist).
Also, pi is not a potential or actual infinity, but rather a finite (real) number.
:"Would a mathematician, standing by, look pitifully at two physicists arguing heatedly whether a cat is alive or dead in a closed box? I don't think so."
Erwin''s wife. "Erwin, what have you done to our cat? It looks half dead!"
You really bar no holds with that "tell me which syllogistic forms are valid" problem lol
27:37 youre rather disparaging of Platonism. Could it not be the case that something like Platonism could be correct for (say) integers and then everything else is a kind of constructed fiction (or something)
Plato, Aristoles and the many other "classical" philosphers in Greece, India, China and elsewhere were trying to sort of some basic notions of cosmology, mysticism, religion, philosophy, language, ethics, maths, "science" (in quotation marks because modern science was not yet invented as a concept), and much more, all mixed together in ways that are hard for us to think about. Among Aristoles' valuable insights was the fact that you can achieve insights by observing the world around you. That might seems like a strangely obvious insight to us, but even today, most people don't actually do that but instead mostly believe what they are told to believe (especially in anti-thinking cultures such as the dominant ones here in Australia). Plato sharpened (and actually made less insightful) the important insights from Buddhism and Hinduism before that, that what we perceive through our sense is just an illusion, or at least a pale and far-removed reflection of some other world. That's also strangely obvious to say nowadys, given what we know from science: we can't see or hear or imagine just about anything of the world around us. Plato was clever and insightful but also dogmatically stupid (check out his crazy thoughts on what a perfect city-state must be, for instance), seeing things too clunkily in blacks and whites, not subtle grays, let alone colours. That's a pity because he thereby dumbed down the Buddhist philosophers' more subtle and deep thoughts which had, directly or indirectly, inspired him: very simply put, these included the observation that our perceptions of the world around us are constructs ("illusions") created by each of us - which of course we know now is true - and the world does not even necessarily exist - which we now now is truer, and in far weirder and un-understandable ways, than we even today can imagine. Truth is not always fixed either, and contradiction is often possible. In other words, they introduced context and subjectivity, and many other important and useful philosophical notions and tools. It's an age-old mistake to fixate on any other these philosophers, let alone join a team and argue who was right or wrong: they all contributed simple and naive but valuable insights and tools that we can refine and use for each their appropriate application. Come to think of it, it's sort of funny, though sad to think of the two millenia of wasted thinking, that the disciples of Aristoles - a guy who told us to look at what is and think for yourself - was and is slavishly followed by ardent and dogmatic disciples. A bit like Christ (allegorical or real) and presumably countless other philosophers who encouraged independent thinking but mostly managed to make people even more dogmatic.
Why does Mathematics need to be limited to describing our world? Why not use it to imagine worlds that do not exist?
Good point! Most maths is just about maths. When a tiny part of that maths can be used to - very roughly and inaccurately - described a miniscule aspect of our world, we rightly rejoice, partly because it's a rare achievement. What is maths? What is our world? These are fascinating questions but are ultimately naive and outdated, stuck in paradigms are trying to define "what is". That's not compatible with modern physics, let alone maths: noone can tell us what an electron "is". In fact, physics tell us that our concept of "is", while nice and comforting, makes limited and decreasing sense. The world is far weirder and more subtle than our normal brains and languages were designed to deal with. Modern physics makes this point brutally clear all the time, so it takes some wilfull blindness - faith and dogma - for anyone intelligent and reflective to not understand this. So it's not so impressive that we understand that the world - and even ourselves (enter modern psychological research) - don't exist in classical sense. It is however impressive, to me at least, that many cultures prior to the Greeks (who both contributed excellent ideas and insight but also, through their influence, blocked other good ideas), understood the unreality of the world, and the multifacetedness of truth.
I don't think it makes sense to say predicates are more like types than sets.
In type theory, any object only belongs to one type, while in set theory, an object belongs to multiple sets. Greeks belong to both men and mortals, which is never the case in any type theory.
Also types vs sets doesn't have much connection to the debate of finite vs infinite. There are infinite type theories, and finite set theories.
Aristotle
Musician to a man means being musician is accident to the man
In how many sense a thing is,
Shown in forms of predicate (thinking of it)
For to be has many senses as there are forms
Somewhere predicates tell
1.what The thing is
2. Others its quality
3.Others its quantity
4.others it's relation
(to sth else)
5.others it's activity or passivity
6. Its place
7. Its time
For each of these predicates there is
To be & is may mean some statement is true
& is not
This is so, in both affirmation & negation
I. E. Socrates is musical true
Socrates is not pale true
The diagonal of square is not commensurate with the side
(sign of a diagonal)
It is false to say it is
11:44 diagonal of square
13:27 a corresponding sense of being & is means potential being &
Important & relevant to set theoretic discussion
In the 20th century
Thank you for uploading such wonderful and knowledge related content. I am very greatful to you sir. 🙏🫡
I am currently studying for lsat if anyone has any advice or can help me with logic games and reasoning I can use the help. I am an english major at one of the cuny colleges in nyc.. please if anyone can help me I want to ace it so i
can get a scholarship to cuny law. I dont want to go to some fancy school. I will go to cuny even if I get a perfect score of 180..👩⚖I will also add that I am seeking a law degree to protect the constitutional rights of citizens and even perhaps work.with Legal Aid...
Aristotl was not right! Уже разработана (аналогичная менделеевской) таблица для ЛОГИЧЕСКИХ ЭЛЕМЕНТОВ? (см. 07-04. ПЕРИОДИЧЕСКАЯ СИСТЕМА ЛОГИЧЕСКИХ ЭЛЕМЕНТОВ (ПСЛЭ): th-cam.com/video/S1YHvYEleto/w-d-xo.html ) и составлен список из 32-х типов суждений, включающих два понятия (две логических переменных)? (07-05. ПОЛНАЯ СИСТЕМА СУЖДЕНИЙ СИЛЛОГИСТИКИ ПСЛО-2: th-cam.com/video/QOmjAtANOvQ/w-d-xo.html )
А тут - о совместимости понятий: 06-09. АЛГЕБРАИЧЕСКИЙ РАСЧЁТ СИЛЛОГИЗМОВ - ЭТО ПРОСТО! (суждения, кванторы, модусы): th-cam.com/video/a8A3DI9qUYY/w-d-xo.html
If A implies B and B implies C, then A implies C. Why is this true? Because Aristoteles is believed to have said this? A famous contra-example: Chicken A dominates chicken B, chicken B dominates and chicken C dominates chicken A, does happen, all the time, but is logical not allowed. What more is impossible but does happen nonetheless?
How does this transfer to mathematics? Can we have different lines of reasoning, all being valid, yet not equivalent? Can a line be both an equation, and the meet of two planes at once? Is this Aristoteles' kind of logic really what explains our world?
Sure it helps. But does it answer all our questions?
+C Fortgens Well, we have now many kinds of logic, 'mathematical logic' for mathematics, for example, which is not built for chicken propositions. A logic is a kind of language, with certain allowed propositions and rules.
C Fortgens He is only showing you valid forms of syllogistic argumentation. Of all possible combinations, most are invalid. Example: 1. All humans are mammals (A); 2. All mammals are animals (A); 3. No human is an animal (E). The combination AAE does not work because you can't infer a negative for the middle term of two affirmative premises. So there are two ways to refute a syllogism: 1) demonstrate that it is formally invalid or 2) demonstrate that one of the premises is false. I don't see why this isn't transferable to any discipline.
@Mister Li: But then why are not chicken propositions allowed?
@C Fortgens: But there is surely a separation, or at least a distinction, between implication and dominance.
+njwildberger If a chicken is interpreted as a mathematical object, then sure. But why should it?
"the man of Science is a poor philosopher" ~Einstein
Where did u get that quote from?