Quadro Geral do Argument Part 1 - Models in Geral
- Noção of map from the text of Borgesmaps and modelsmodels do not need to be visual representations
- to classical physics to physiology
Part 2 - Logic as a model of discourse 1. psychological and critical approach 2. formal and critical approach
- saída pelo inatismo 2. saída pelo "jogo" reason / discoursejogo and mathematical discourseconclusão
The subjects that form or content of disciplines such as logic and philosophy of science are foreign for students of higher course in human sciences. First of all, scientific activities - widely represented by natural sciences - will be very different from any daily activity, very specialized and, therefore, very difficult to understand. With logic, or quadro piora, pois or aluno it was difficult to see them as formalized arguments, in some way, to trace relevant information about the disciplines that really interest me, such as history, ethics, aesthetics, etc. Saying that the study gives logic helps to understand epistemology -e, also, the foundations of any particular discipline-, and of little help, since a statement related to two unknown fields.Saying that epistemology makes sense when studying logic poses the same problem.
A saida he, perhaps, motivate or aluno com a "model" idea. As science makes models of the world, as well as logic can be interpreted as science that makes models on correct reasoning. To avoid armadilha from just substituting "epistemology" or "logic" for "model", a more common word, but nem for isso easier to understand, we must, from simple situations and simple examples to assimilate, establish the bases of what are models and analogies. No final, basic concepts of logic and philosophy of science have been naturally discussed in a more formal and technical course with conditions to start on safer ground.
Before we enter into a more technical discussion on what models are and how scientific activities use models to create analogies and solve problems, let's look at three small texts that have been addressed.
DO RIGOR NA CIÊNCIA
… Naquele Império, Art of Cartography chegou to such Perfeição that the map of a single province occupies every city, and the map of the Empire, every province. As a tempo, these Excessive Maps will not be more satisfactory to the Cartographers' Colleges, to draw up a Map of the Empire that has the size of the Empire and that coincides with it. Less
Afeitas ao Estudo da Cartografia, as Gerações Seguintes will understand that this extended Map was
Useless and not prevented or delivered to Inclemências do Sol e dos Invernos. Our deserts from the West remain shattered Ruins of the Map, inhabited by Animais and by Beggars; In all the Country there is no other relic of Cartographic Disciplines.
INTERLUDE: OR HAMLET'S SOLILÓQUIO
SER, OU NÃO SER: isto não é a questão, plus a tautology. I am not interested in individual statements. I want to know the truth of a synthetic statement: I want to know se serei, or what does it mean, se terei coragem para vingar meu pai.
Why do I need courage? It is true that or husband of minha mãe, or king, is a powerful homem and his arriscarei minha life. Still, he can make it clear to everyone that he killed me, all ficariam by my side. It is clear to everyone…; it is clear to me.
Why is it clear? I have boas evidências. O ghost was very conclusive in his arguments. But he is just a ghost; will it exist? Eu could not ask-lhe. Maybe eu or tenha sonhado. But there is another evidence. That homem tinha um reason to kill meu pai. What an opportunity to become Denmark laughs! E a pressa com que minha mãe casou-se com ele. Meu pai semper foi um homem saudável. It is about a small piece of indirect evidence.
Meanwhile, he is so: nothing além of indirect evidence. Can I accredit naquilo that it is just provável? It is this or I do not what I lack courage. Não que eu esteja com medo do this rei; I have simmered to make something based on a mere probability. Or logical affirms me that a probability does not have meaning for an individual case. How do you handle this case? This is what happens when the logical question is asked. Naturally it gives resolution and recovers pale hair with a thoughtful hue. But what would it be like to begin to think about the action and discover that it has not been done?
Is it logical tão ruim? He told me that, I know something is provável, so I can press it and shake it as if it is something true. Fazendo isso, I will be certain in a large number of cases. But, will I be certain in this case? Sem resposta. Or logical say: aha. Na major part two cases, you will be right.
Vejo uma saída. I will return to the most conclusive evidence. É really uma boa ideia: este ato, eu irei encenar. It will be a crucial experiment; Be they or kill them, I won't be able to hide their emotions. Isso é boa psicologia. If I test for positive, I will know all the history with certainty. See or what do I want to say? There are more coisas not ceu e na Terra than or dreamed of its philosophy, more logical.
Will I know about you for sure? Posso see seu ironic smile. There is no certainty. The probability of increasing your pressure will increase a higher weight. I will be able to count as a higher percentage of correct results: this is what I can achieve. I cannot escape from making assumptions. I want certainty more everything or what or logical item for me or conselho that it is supposed.
Here I am, or eternal Hamlet. What is the use of asking the logical course or what did you tell me that your assumptions were made? Seu conselho confirms minha dúvida plus that it gives me the necessary courage to agir. A logical não e feita for me. Um homem deve ter more courage than Hamlet to always be guided by logic.
Hans reichenbach
PART 1
A map of a province whose extension is a city or a map of a country that covers the entire extension of a province. Let's leave aside the question of the exequibility of these maps, it is about fiction. Even if we took these maps seriously, we would still ask: will the artifacts be useful for the inhabitants of the empire?
Maps are not correct objects that we rarely stop to examine exactly or what they are. Either a terrestrial globe on a table, a city plan, or a bus route, precisely because they accompany us every day, it seems to além from any analysis, or question, or that only seems pure loss of tempo. We lose time. Or what is a map? Ou melhor, or what do we expect from a map?
Or map, in the first place, symbolizes something. A plant in São Paulo não é São Paulo. São, therefore, two different objects that keep together a certain semelhança. More what kind of semelhança? A plant of a city as well as a map of a country must be such that the figures that appear there are a small-scale «portrait» of everything or that exists in a mapped region. This scale must be respected point by point in order that the map translates something from the city. More or what do we expect or map to translate? To form da city? O fato é que isso depends on or that we want to know when or consult. By isso we can exist -e existem- different types of maps.
Suppose the situation: we take the metro to station A and want to go to station I. We consult the fixed diagram on the wall of the car. We found it:
Diagram 1
No diagram, let's read: taking a train at station A, we should descend at station E and take another trem. We read that between C and D there are no intermediate stations. We read that between C and F there are two stations and also that, once a train trolley in E, we will have to pass through two stations where we can descend into I. Enfim, a rather artificial description of the reading process that, in practice, seems do not wrap linearity. (Na verdade, we don't read that we have to take another trem in E. It could be that a linha fosse continues and a baldeação, desnecessária. Furthermore, what would be or reason to represent such things dessa maneira? Simple representations, many things must be known in advance. For example, a certain notion of simplicity must be in mind: it is at the edge of the meter, continuous between C and G -is,If there is no need for balding, and, at the same time, on a small scale, it would be simpler to represent the non-diagram by a challenge and not by an arrangement at 90º. Here, perhaps, it is pointed out that these considerations of simplicity fit the general map concept and "metro map" is a particular type of map. Ao we will discuss the readings of a metro map, we will take into account that the individual knows what a map is and what types of rules it will direct its reading.)Ao we will discuss the readings of a metro map, we will take into account that the individual knows what a map is and what types of rules it will direct its reading.)Ao we will discuss the readings of a metro map, we will take into account that the individual knows what a map is and what types of rules it will direct its reading.)
Nesse sense, therefore, or Diagram 1 is a map of the metro lines. Therefore, the map is just as it informs the succession of stations. One wanted to know, for example, which relative distance between the stations would be totally useless, since it deliberately leaves such information. To know this new given, we would need a map like:
Diagram 2
This new map tells us as much as or first about the succession aspect, in addition to adding information. From that point on, we know that the stations are not equidistant from each other; We know that, between D and E, or route will be short and that, followed, between E and F, or route will last longer while passing through any station (supposing that or trem trip at a faster or less constant speed).
A map like that is practically satisfied with what a user wants to know about the metro. For an engenheiro, that would not be enough; Perhaps it is necessary to have a three-dimensional structure, since we know that the lines of the meter are not far from the same height of the surface. For example:
Diagram 3
Leaving aside the question of the line format, let's now analyze the question of the map scale. In the case of Diagram 1, it did not make sense to scale the scale: it was simply left behind as a representation. Scale is something that can be discussed only from Diagram 2. In this, as not diagram 3, the stations appear as points. The map does not inform about the shape, size or internal layout of each station. Why is that, in a map that does not appear all along the metro line, we will also want to represent the station format, we will have two outputs:
- Make a map of two routes on a scale on the map of stations on another map, or on a large map or enough so that both routes and stations can appear on the same scale.
We will choose alternative b, we will have a map of the metro lines quase of the size of one of its stations and we will fall de novo no case two cartographers from Borges.
From this point on it should be clear that the central question is: where to stop with the semelhanças? A map, first of all, should be useful for the orientation of a user. I do not case the Borges map, to no avail, a time to travel or map is the same as to travel or empire.
Our discussion, of course, is not exactly linked to map making. A map is a special case of a very general and abstract noção: a noção de Modelo.
A model always translated a certain aspect of the object or the process represented. Us examples above, or Diagram 1 translated or aspect succession of estações; o Diagram 2, the succession aspects and approximate distance between stations; o Diagram 3, the succession aspects, approximate distance and three-dimensional arrangement of two itineraries.
I do not sense that we saw failing, a model is useful when it «filters» or «abstracts» or «deixa de fora» aspects of the represented object considered irrelevant for the moment.
If nothing "leaks" - this model or that happens to the imperial map - becomes useless. It remains, of course, different from the object to which it refers, it remains as a symbol or symbol that it represents or object. But, being as extensive as that (or as detailed as it), examine or model is the same as examine or object, consult or map the same as percorrer or empire etc., or that becomes or symbol superfluous.
A model number is more general than a map number. Models, for example, do not need to share as represented objects any semelhança of visual character. It is convenient, at this height, to point out that the two components of an analogy do not necessarily need to be objects, or else, when we are missing models, we are not just thinking of objects representing other objects. One can think of analogies (and therefore models) between processes. Therefore, I do not know the seventeenth century, I think of an analogy between the operation of a water pump and the operation of the heart. Or what interests those investigators was less an analogy between the heart object and the water pump object and more like an analogy between the blood circulation process and the water pumping process.
A good example of a model that was adapted to the analogies available and given the metaphors used to explain or function of the brain.
“It amused me to see that Sherrington, the great British neuroscientist, thought that his brain functioned as a telegraphic system. Freud frequently compared the brain to hydraulic and electromagnetic systems. Leibniz compares him with a moinho and he told me that some among the ancient Greek achavam that the brain functioned as a catapult. Obviously not present as a metaphor for the digital computer. " (John Searle, "Minds, Brains and Science")
Another example of a model concept. When doing medical experiences aiming to find a solution for somebody who affects or home, we usually use experimentation. On one hand, of course, this procedure derives from certain ethical questions - we usually value the life of a homem more than a life of a man, not in the case of a potentially perigious experience, we prefer to sacrifice the latter. But não é só isso. Embora um cão seja, in many different aspects of a homem, as semelhanças quanto a particular point (or functioning of the digestive apparatus, for example) allow us to be a model of another. In this case, we have the same map situation. Map and metro (home and home) different more, how long or what aspect we are interested in (succession of seasons, functioning of the digestive system) both are similar.
A word "analogous" keeps interesting questões. It does not appear for free, nem convém barely exchanged with the word «semelhante». A word «similar» has a strong visual component, or which word «analogous» avoids. Also, two visually dissimilar objects (such as the metro and your map) can be analogous.
In any case, ask me what I put an object and model of another outros and ask me what I put can be fine analogies between the two.
Such analogies, like all other scientific theories attached to my propositions, do not last indefinitely.
In short, for modern science (science feita from the seventeenth century), or "free of the universe" cannot be read directly. Or the number of phenomena that appears or studious and potentially infinite and, likewise, it is not possible to progress sem fazer uma escolha de saída. In other words, it is necessary to decide what is relevant to study or what should be left aside. Ou what aspect to study and what aspects to abandon. Ou, ainda, I must finally start a model and study that model.
Isso wanted to say that, at any moment, the scientist knows that he is not studying the universe directly and impartially. He knows that he is studying an aspect of the universe, or an aspect that proves that he is capable of understanding how he can make predictions. Ou seja, one time that it is impossible to run through the universe, study a scheme give it in order to discover new properties etc… Or model or guide does not study of a given subject, orients to research, apon direções to trilhar, print an order onde, otherwise, there would hardly be a chaos of sensations and phenomena.
Models are either chosen or discarded depending on their usefulness for a given study or moment. It makes little sense to ask, then, about the given model, whether it is true or false. Face felt as soon as you ask, is it useful or not for the study of the aspect that you are currently interested in studying.
Also, the models have a narrow limit: they are very close ("proximity" wanting to say both "coextensiveness" when "equal level of complexity") two objects to be studied, deixam-us as cartographers of the empire. It was very different, then go ahead. A model is something that should not, therefore, be very close, very distant from the studied object and, also, a concept that, like so many others, is easier to apply than to define. In spite of this, when we talk about models, we are just idealizing a very familiar procedure.
Either homem built models from empirical science and, as we have seen, or homem always tends to be a model when undertaking some action, whichever it is. This insightful notion can be used as a way for me to understand myself or to understand that modern logic and how it is articulated as studies in science philosophy.
PART 2
You give different ways of interpreting logic, you deserve more attention not to cover history: a psychological interpretation and a formalistic interpretation. Let us first examine the main points of psychologism.
We all think, and it is also true that we always think bem. Sometimes we think badly due to or lack of awareness of a certain situation of fato. For example: we make an erroneous forecast regarding the production of one more plantation, if that is the case, we could not have foreseen an extension of the period of chuvas or we could not know (we were not informed of) that the seeds purchased were of higher quality etc. In the meantime, we may think badly due to a de facto lack of formal reasoning. In this case, all the premises are understood, but we fail to reach a certain conclusion due to our inability to think. For example,
- Nenhum cão vive na Lua.Nada que vive na Lua é cat.Nenhum cão é um gato.
It seems a plausible "argument" one time that three sentences are true. In the meantime, let's look at an analogous argument:
- Nenhum with 3 orelhas Nothing with 3 orelhas and animal Nenhum with animal.
ou pior ainda:
- Nenhum cão vive na Lua Nothing that lives na Lua é cão Nenhum cão é um cão.
These examples show that, even with all relevant information, we can err on the basis of our use of reasoning. Na verdade, nothing absolutely follows the joint consideration of (1) Nenhum cão vive na Lua e (2) Nada que vive na Lua é um cat. We use bad reasoning when we try to derive a conclusion from two negative premises. Not the first example, this fact was less apparent, one time that at the supposed conclusion «nenhum cão é um cat» is, sem dúvida, verdadeira. There are two examples below that show that in conclusion nothing deviated from the premises, or perhaps there was really no argument. It is another important thing to note at this point that, as we show examples, there is a fairly obvious difference between true and valid. No first example, add the sentences (1), (2) and (3) sejam true,or I argue that they seem to be valid. Another important point to highlight is that it is possible to draw analogies between arguments and between individual sentences. Na logical terminology, two arguments or two analogous sentences are "bearers of the same logical form."
A question that is now possible: is it that the use of reasoning and governed by the law gives logic?
It responds for sim, follow hair less duas consequences:
- A logic descreve the atos corretos de raciocínio. A logic dita rules of reasoning that must be oiled by all.
On the other hand, however, many of the correct reasons for reasoning, this is, many actions with a happy and expected result, they cannot be described as being less sanctioned by the law.
Or Reichenbach's text is an exemplary disso: Hamlet gives enormous weight to the emotions of his relatives during the encenação. However, there is no logical way to discern or weigh two statements. Submitting a proposal based on experience, psychology, no direct knowledge, etc., will be able to give greater weight to this or that sentence.
On the other hand, there are logical norms not only oils but most of the people. For example, pelas regras do propositional calculus, a sentence: «Se a Lua é feita de queijo, so Socrates is a philosopher» and is true for all implicative sentences with false and true antecedent. Another more obvious example: strictly following this is logical, or following argument is valid:
- It is meu filho for homem, eu ficarei happyLogo, se meu filho for homem e have problems mentais, eu ficarei happy. (note 2).
Assim, we find that logic nem descreve nem normalises or rationale da medias das pessoas. It is important to note that it is not necessary to conclude that logic fears nothing to see as human reasoning. Obviously she was raised with her own hair for her purpose and some relationship as reason. The only thing that can be done with two examples is higher than a logical / human reasoning or logic / psychology relationship and less direct than it might seem at first glance. Uma saída, perhaps, for that question, it is said that logic decries and the same standardizes or rationality of some human beings: two own logicians, two mathematicians and some natural scientists.
A purely formalistic approach to two logical procedures would seem to be so exaggerated as an exclusively psychological approach. Saying that logic is completely alheia to rational behavior would create difficulties when someone tries to explain or why so many logical laws will be perfectly plausible for most people. It changes logical laws that are really plausible -even considered definitive- for part two human beings, isso becomes a fate of these leis refletirem something two processes of reasoning do homem. Attributing such analogies to an accident or even saying that they are not important for the development of the logic would be to bring obvious facts.
A basic support of the formalistic approach sees a large part of the distinction between two moments of scientific activity: either the context of disclosure or the context of justification. This is the attention given to psychology or to a formal description of ordinary or ordinary discourse, hardly in the context of discovery. Já no context of justification -quando or main objective of the researcher and explain (justify) or that was obtained at the time (no context) of the uncovered-, or scientist would not support the history of the event studied and, assim, would leave aside considerations how many years of phenomena occurred at no time is uncovered. I see, such a clear distinction between these two contexts was quite difficult to sustain (see TS Kuhn for a critique of the distinction between natural sciences and P. Davis and R.Hersh, for the same criticism, does not dominate the formal sciences), since a large part of it is two arguments that scientists use to justify (explain) or that supposedly discover the basis of history, or that, we have steps that will lead and continue to be uncovered. A separation between the two moments, argued by these authors, would be not just artificial -pois nenhum group of scientists discovers "first" and justifies "depois" -, but also responsible for covering a relevant part of what is considered scientific activity.It would not be just artificial -pois nenhum group of scientists discovers “first” and justifies “depois” -, but also responsible for covering a relevant part of what is considered scientific activity.It would not be just artificial -pois nenhum group of scientists discovers “first” and justifies “depois” -, but also responsible for covering a relevant part of what is considered scientific activity.
In order to escape two extremes of pure psychologism or formalism, we could try a saída, affirming or a priori character of logical laws, as quais seriam em nos ideias inatas. Assim, ao "observe" his modes of reasoning, or homem select some like bons and deploraria others like maus, deceitful. Fazer essa escolha would imply that he had some knowledge about how to escolher between bons and maus arguments. It would imply that we had an idea of what was logical. Isso, no entanto, would bring many complications pois: (a) it is logical and inattentive, how to explain that as people make logical mistakes? Uma saida, perhaps, it would be said that, all saibam logic, nem all develop equally; She would be a kind of latent talent whose development would depend on individual history. Mais ainda,It is possible to live -and it- in constant collision as the logic is given, therefore the logic would occupy no more than a peripheral place in the decision-making. As usual, all the questions related to nature are complex, but they all come up with the same objection: "I know something and innate, why doesn't it appear or the same in all of you?" Let us remember that Platão, to escape such objections, creates a complex theory reminiscent of the transmigration of souls and that Descartes has to launch the complex concept of "natural light gives reason" in order to avoid the nature of logic laws.Why don't you show up or the same to all of you? » Let us remember that Platão, to escape such objections, creates a complex theory reminiscent of the transmigration of souls and that Descartes has to launch the complex concept of "natural light gives reason" in order to avoid the nature of logic laws.Why don't you show up or the same to all of you? » Let us remember that Platão, to escape such objections, creates a complex theory reminiscent of the transmigration of souls and that Descartes has to launch the complex concept of "natural light gives reason" in order to avoid the nature of logic laws.
A more modern and perhaps less controversial way to approach or issue and consider the relationship between logic and human reasoning a kind of game on a calibrate or another and both, like passing the tempo, modifying-it was tied to find a point of common equilibrium.
All, apparently, have the ability to reason. Such reasoning is used for an infinite number of practical tasks. Uma between them is or study of own reasoning; I attached this point there is no difference between logician and psychologist. The student notes that some arguments are infallible, they are not dependent on the material conditions on which they are enunciated, and then go on to study them further. This study leads to two preliminary alternatives: (a) some rationales that are shown to be infallible to Falham and must be abandoned -example of standardizing logic or rational behavior- and (b) some rationales that follow from infallible rationales to their own infallible, emboldened sejam pouco plausíveis e, assim,Têm to be oily, we will oily the arguments from where the derived foram -example not that new behavior changes due to logic. Nessas duas alternatives, or rational behavior yields its place to the demands of logic. A third alternative: (c) a seemingly infallible argument shows a lack of a more central element, so important, for human activities, that there is no other way to decree that logic must give in prolific psychology or the demands of a scientific theory is established. Or problem and how to decide in which cases logic should prevail over psychology and natural sciences and in which cases should happen or vice versa. A decision involves a new investigation that will be carried out by logicians and psychologists. O jogo no te fim e the possibilities are always open. I don't know XX,Many non-classical logics will appear in order to dislocate traditional logic in favor of some requirement of a psychological character (a paraconsistent logic, for example) or a scientific character (a quantum mechanical logic, for example). It should be noted that this game is not played by all the people. Note that, at the time of deciding what melhores intuições, what must be saved by logic, or melhor juiz will be or own logical. Still, do not run after the inquiry, or logically you will change your intuitions in function of your study and, likewise, or your intuition x logic will always recommend. Naturally, this is not a historical narrative of how it is logical as we know it, it is only a suggestion about how the current state of things was done.
Or important now to see how this discussion fits into the model's concept.
Before, however, I would like to make some considerations about the words of reason, reasoning and discourse.
By reason, this power present (by definition) in all, or quase all, you homens, seems to manifest itself in two ways;
- as a capacity to "see" truths and abstract things such as essays or qualities, capacity is designated by intuition, as a capacity to "pass from premises to conclusions", isto e, to reason. To this, we call discursive reason
Dessas duas maneira de a reason is expressed, subject to second serious object of logic.
Ainda assim, or rationalize não é barely or apply abstract logical laws. Or homem, like Hamlet, reason in concrete situations; Besides going through logic, it goes through its de facto knowledge of the situation. Hamlet runs to logic, sem dúvida; but it also goes through psychology, upon finding two games of power involved in a situation in the questão etc… Logo, reasoning and exercising a series of argumentative cadeias, all sanctioned by logic, exercise this subject to injuries of a local, personal, temporal and assim por diante.
Or that is of particular interest to a logical or non-qualifying case or reasoning produced by a discourse. Nesse case, or object of the logical study will be precisely that discourse. Pouco imports or reasoned that or produces. Reasoning acts on individual and local phenomena that a psychologist or historian should study. However, it is true that a logical year is hardly interesting or speech produced by reasoning, not any speech that is interesting to study, or even that it is possible to study. By reason he produced poetry, theater, fiction, and fiction. Logically, it is only possible to study the discourses with pretensions to the truth, or discourses you refer to.
These referential discourses appear more clearly in scientific accounts, but there are still many other examples of this type of discourse, and not argumentative discourse of scientific activities that are more carefully expurgated manifestations of a non-referential character that normally appear in everyday referential discourse. In the meantime, study logically or scientific discourse in addition to a complex task further (at the end, or what would be a «logical» study of «Origem das Espécies»?).
It is due to such considerations - other of a character more intimately linked to genuinely mathematical problems, such as the question of the consistency of non-Euclidean geometries - that the logicians of the XIX century (Frege em especial) will place two logical studies on speech. mathematical, as we will see adiante (note 3).
Of all the human activities, mathematics is dúvida, the one that most explicitly and continuously uses argumentation. It is clear that quasi all the human activities or fazem more, in mathematics, the argument always appears dismissal of any subjective emotional or local character or of any material or temporal trait. Assim, any theory of correct argumentation will, of course, validate everything or quase everything that the mathematical culture registers, or that it is different from saying that it must validate what the mathematical culture really faces. As a matter of fact, it was also that it proceeds to modern logic since, by modern logic, it is understood to be logic after the publication of Conceitografia by G. Frege in 1879.
Or the logical procedure followed to build your discipline from the observation of mathematical discourse would be approximately or following:
- Question: What face are these arguments infallible? Answer: são infalive because there are cases of tais or tais logical laws. Question: What other consequences do you have these leis recorded by me?
As you respond to (c) we can oblige or logic to change its original intuitions, isto é, logical laws can appear as quais, but impecáveis, be in conflict with those.
d. depois do survey, follow a systematization of the material. It is worth noting that, in practice, there are no different stages of survey and systematization (we are here just outlining a model).
c. Once the logic underlying the mathematical discourse has been systematized, we turn to it and pass on to the examination of that discourse. It will be able to happen of many mathematical procedures not satisfying the canons of logic. Or what fazer? Give preference to a mathematical procedure or try to correct it in light of new logic?
Nesse ponto, recomeça or jogo.
The final result of such a game will be a model of mathematical discourse and, generally, of a large part of discourse considered rationally correct. An example will show how logic is a model of discourse:
Mathematical speech: x - 3 = 5 Logo: x = 8
Logical translation:
- Premissa: x - 3 = 5 Premissa: If we are the same, the results are the same. If x - 3 = 5 then, it is valid to premise (2.), then x - 3 + 3 = 5 + 3 Intermediate conclusion: x - 3 + 3 = 5 + 3 Conclusion: x = 8, doing the operations second to the canons of arithmetic.
I want to tell you, what mathematician really thinks that way? It is certain that no: or mathematical goes directly to the result. Na verdade ele não passa -e maybe nem think- sentences sentences (2), (3) and (4). Also, it is not true that mathematics has developed in the same way; Many advances in mathematics are given in the absence of logical justification.
A relation of Mathematical Discourse / Logic Translation is the same Map of the Metrô / Metrô that we saw in the first part. A Lógica does not faithfully translate the mathematical reasoning, the mathematical discourse or the mathematical discourse (and much less or general reasoning) and nem intends to do so. A activity that we chama of reasoning and a set of fatores for or that, perhaps, does not make a model. I also respect mathematical reasoning, perhaps the only way of mapping - two cartographers from Borges will point it out: o map must be equal to o country. (But then, what use would the map be?) Those questions about the cartography of reasoning should, in the meantime, be left to psychologists. A logic is a map does not make the sense of the word. Leaving aside the question of mathematical reasoning,or mathematical discourse not equal to its logical translation as well as a «map» object and not equal to the «mapped region» object. This, however, systematizes that discourse, explains all the premises involved and, also, allows the discourse to be read with reference to talent or to a special knowledge about the content. A map, analogously, is such that it serves as a guide and requires that any coisa of the mapped region be found. Um bom map can, enfim, be «lido» with reference to what is being mapped. Assim, to logic é or map daquele that provides the foundations two procedures used both non-dedutive discourse of mathematics and non-explanatory discourse of natural science.It allows the speech to be read with reference to talent or a special knowledge about the content. A map, analogously, is such that it serves as a guide and requires that any coisa of the mapped region be found. Um bom map can, enfim, be «lido» with reference to what is being mapped. Assim, to logic é or map daquele that provides the foundations two procedures used both non-dedutive discourse of mathematics and non-explanatory discourse of natural science.It allows the speech to be read with reference to talent or a special knowledge about the content. A map, analogously, is such that it serves as a guide and requires that any coisa of the mapped region be found. Um bom map can, enfim, be «lido» with reference to what is being mapped. Assim, to logic é or map daquele that provides the foundations two procedures used both non-dedutive discourse of mathematics and non-explanatory discourse of natural science.to logic é or map daquele that provides the foundations two procedures used both non-dedutive discourse of mathematics and non-explanatory discourse of natural sciences.to logic é or map daquele that provides the foundations two procedures used both non-dedutive discourse of mathematics and non-explanatory discourse of natural sciences.
It also becomes logic, transforming itself from the same formal science, to a semi-mathematical theory, it becomes a model of itself and passes to it as an object and as an instrument of study. Fala-se in metalogical studies when or logical instrumental is used to study logic itself. These studies are only in line with logical inquiries, I don't know XX. Reichenbach's text makes clear that this aspect gives logic as a model to note that Hamlet can only partially trust logic. This is something ideal that, if it serves as an orientation, we cannot give an account of a particular case because it was not thought of as this. The rational behavior of Hamlet depends on several factors, two quais a logic and only part, and, no truth, small part. Hamlet acknowledges the limitations of logic in his most damaging case, not concluded by its uselessness. Ruim eat her,pior sem ela. Or the same thing happens when we stop or map the metro lines. Embora does not remain the same as linha nem possa guide us at the level of detail, its validity as a guide remains.
It is precisely to the side or aspect of the model of logic (and the same mathematics!) That Bierce extracted or ridiculous from his definition and conclusion. Of course, its purpose was to make it easy to detect any deep problem, not two logical studies. Also, serve as an example of what may happen if it is not taken into account or character of a logical model, in particular, in general science. The model does not need to be in accordance with all the particular cases to be oil-assimilated as a map does not need to be absolutely perfect to be a bomb guide. Contrary or common sense (sixty homens digging a few seconds) does not constitute a reason for abandoning a model; at the end nem semper or common sense is certain and, just as it is shown certain in some cases more correct,I do not want to say that your criteria can be extended to the most affluent regions of your daily life.
Not correcting the history of logic, there is now room for thinking within the purely psychologist approach, facing as a faithful expression two phenomena that occur "behind" two correct reasons. Também houve - and continues to have - place to think - it in a purely formalistic manner, as a simple set of symbols and regras, sem relação com o mundo. A recently proposed way of considering logical systems e tê-los as "merely devices to represent our practice and not representations dela" (Resnik, p. 224.). Isto é, a Lógica does not represent the practice of reasoning and nemé completely detached. It is only through which we can find some way to study this same practice, except that this practice must be expressed through a sensible referential discourse. Or the same applies to a plant in a city:It does not represent faithfully but serves to collect information that, in another way, ficariam for always hidden. Or the same is true for natural sciences: no fossem suas theories and conjectures, or no passaria world of a continuous flow of sensations sem repetição e sem order.
Notes
- Na true, at most two components of the scientific community possibly credited to be studying directly or universe. In other words, the scientist or scientist knew that, indeed, he is always manipulating a model, which accredits the ontological claims of this model: the scientist studies a more true model (and not only useful) of the model.:
a → b
(a → c) →
or that the deduction theorem results in a tautology
(a → b) →
Naturally, a counter-example arises from the qualities of "being homem" and "ter mental problems" present in the conclusion expressed in ordinary language, not independent, from where they are used as a translation of two different symbols with original intentions. Express argument in symbolic linguistics.
- Such a movement of "restraint" can also be observed without knowledge of the theory of knowledge.
In no case of logic, it abandoned the pretense of studying the bases of generally valid reasoning in favor of studying the bases on which the valid inferences in arithmetic and geometry would be established.
With respect to the theory of knowledge, the idea was to restrict the study of scientific discourse. The parallels with the mathematical / logical relationship are obvious. There are many forms of vehicle conhecimento. Delas, interest in philosophy mainly those that or veiculam through a discourse. Still, or general discourse (same aquele com pretensão ao conhecimento, or called referential discourse) is always permeated with non-referential discourse. Assim, check out what or my best speech for the study of the theory of knowledge of those natural sciences. As it is possible to construct a theory of this discourse, it would be useful to think about extending this theory to other forms of discourse. Give the same shape,It is logical to think of extending his theories to more complex discourses by submitting or establishing a solid theory about mathematical referential discourse.
BIBLIOGRAPHY
- DAVIS & R. HERSH. The Mathematical Experience. Penguin Books, London, 1984D. RESNIK. «Logic: Normative or Descriptive? The Ethics of Belief or a Branch of Psychology? ». Philosophy of Science, 52, 221-238, 1985. R. LACEY. A Dictionary of Philosophy. Routledge & Kegan Paul, London, 1976.S. KUHN. A Estrutura das Revoluções Científicas, translated by BV Boeira and N. Boeira, Editora Perspectiva, São Paulo, 1976.
