.. .. .. .. .. .. ....

La posición estándar:

 ....

(ST) Si un agente S está justificado en creen un conjunto de axiomas A de una teoría T, y tiene una prueba (válida deductiva formal, etc.) de P en T, entonces S está justificado en creer P.

 ....

Defensa tradicional de la posición estándar.

 ....

1. Tener una prueba de P en T es lo mismo que inferir válidamente P de los axiomas A de T.
2. Si un agente S está justificado en creer un conjunto de premisas A, y de ellas infiere válidamente P, entonces S está justificado en creer P.
3. Por lo tanto, S está justificado en creer P.

 ....

Problemas con las premisas:

 ....

Contra (1): Tener una prueba de P en T no es lo mismo que inferir válidamente P de los axiomas A de T. Las inferencias son acciones mentales apriori y existen (tanto de hecho, como en principio) pruebas que ninguna persona real puede seguir mentalmente, haciendo las inferencias correspondientes a cada paso. Hay restricciones de tiempo, memoria, etc. (Kitcher 1980) que hacen al mecanismo de prueba matemático falible (y a posteriori) de una manera que la inferencia apriori no es. Por lo tanto, es posible que uno tenga una prueba, crea haberla seguido, pero no haya inferido su conclusión de las premisas de la prueba (y/o de los axiomas de la teoría a la que pertenece).

 ....

Contra (2): No siempre, si un agente S está justificado en creer un conjunto de premisas A, y de ellas infiere válidamente P, entonces S está justificado en creer P. Es posible que S tenga otras razones, de peso similar, para creer ¬P, o que dude haber realizado la inferencia bien o dude que ésta sea válida, etc. Si el agente S, pese a esto, sigue creyendo P, está siendo irresponsable epistémicamente (al no tomarse en serio sus dudas y la evidencia en contra de su creencia) y ergo, no está justificado en creer P.

My starting point is Daston’s claim that our current understanding of the distinction is based on the identification of particular subjective factors, like perspectives, linguistic conventions, psychological architecture, etc. These facts range from (i) the most personal and temporary, like our preferences, attitudes, feelings and perspectives, to (ii) those we share with other members of identifiable social-groups, like the linguistic conventions of a common language and other historical factors, and even (iii) those we share with others because of some common biological properties, like those we may share with people of our same sex or health conditions (Lloyd 1995). Whatever depends on any of these factors is broadly termed “subjective”, and what is not subjective is called “objective”. In order to differentiate between the aforementioned three different sources of subjectivity, it may be useful to talk about “private”, “social” and “psychological” subjectivity respectively (Swoyer 2008). Objectivity is thus defined in contrast to subjectivity, as that which is public (i.e. publicly accessible), universally valid and accountable.

    Once this distinction is in place, it is easy to notice that some philosophers draw broader or narrower limits around the subjective. In a very narrow sense, anything besides private subjectivity is considered objective (this, for example, is Searle’s position regarding what he calls “epistemic subjectivity” in 1995). For others, social factors are clearly as subjective as private ones, but exclude psychological factors, especially those that are species-specific. (Stitch 1990)  For them, for example, (at least some) psychological phenomena may be as objective as material ones, even if they are strongly dependant on our biological makeup. In contrast, others, most notably Frege (1884) and many other early analytic philosophers clearly took a strong view of objectivity, where psychological factors were deemed too subjective. (Jacquette 2003)

    On the other hand, “Objective” and “subjective” are adjectives that distinctly apply to entities of different categories: knowledge, judgments, propositions, objects and concepts. At the ontological level, subjective and objective are different modes of existence (Searle 1995, 8). An entity (object or concept) is subjective if its existence depends on one or another subjective factor. Toothaches, baseball teams and colors are all subjective entities, yet their subjective nature is radically different. Pains are private, baseball teams are social (or “institutional” to use Searle’s term), and colors are psychological. They would not exist, were it not for our psychological makeup, our personal subjective perspective and our sports institutions.

Subjective Truth
At the propositional level, a proposition is subjective if whatever makes it true (or whatever determines whether it is true or false) includes or depends on subjective factors. Once again, it may be fruitful to distinguish at this level different kinds of subjective truth: private, social and psychological. Propositions that have determinate truth values independently of any subjective (private, social or psychological) are objective. At this level, propositions like “Wheat Oats are delicious with milk”, “Austin is the capital of Texas” and “The Sky is Blue” are all subjective truths. The facts that make them true are not objective. Some are made true by private facts, others by social facts and finally some may be made true by psychological facts (Nagel 1974). Of course, some times people tend to use the term “fact” to refer only to objective facts (Kripke 1982) and not to any subjective factors that make these other kinds of truths true. So, when people talk about facts, they often mean objective facts, unless otherwise stated.

Relativism and Context-Sensitivity
Truths of this kind are also called “relative”, because their truth-value is not absolute, but sensitive to changes in perspective, context, etc. Instead of having a determinate truth-value, their truth-value is relative to a set of parameters that may vary among individuals, moments in time, social groups or even psychological features. Recent philosophy of language has exploited this feature of subjectivity to devise a test for relativity: so-called “context-shifting arguments”. The main idea behind these arguments is that if the truth-value of a sentence shifts in response to certain changes in the context of utterance or evaluation of the sentence, then the proposition may be subjective or relative (Cappelen and Lepore 2003). Of course, not any sensitivity to context is enough to talk about subjective or relative truth. Sensitivity to those features of the context associated to traditional indexical expressions like “I”, “here”, etc. are not considered as evidence of subjectivity, because such features themselves are not subjective. Otherwise, even the proposition expressed by “That tree over there is an Oak” would be considered subjective, which is nonsense. So, for a proposition to be subjective, it must be sensitive, not to any change in the context, but only to changes in its subjective features. Thus, only if the truth value of the proposition expressed by a sentence is relative to certain subjective features of the context of utterance, including personal features of the speaker (or hearer), its historical and social context or its biological makeup, then it may change truth values if it is uttered in different contexts.

    As a corollary, just as subjectivity manifests as context-sensitivity, objectivity manifests as invariability. In other words, just as every sentence that expresses a subjective proposition is context-sensitive, every objective proposition is expressible in a context-invariant proposition, i.e. one whose truth value remains stable across contexts (Lycan 1996).  But of course, as stated above, not every context-sensitive sentence expresses a subjective proposition and not every context-invariant sentence expresses an objective proposition. “Axel Barceló is in indescribable pain at 2:19 pm on the 13th of May, 2009” is an invariant sentence, yet expresses a subjective proposition.

Genuine Subjectivity
Mandik (1998), following a similar point in Searle (1995), has urged us to further refine the above definition of subjective truth (what both Mandik and Searle call “epistemological subjectivity”) to exclude those propositions that are subjective only because of the subjective mode of existence of the entities they are about, and demand that genuine subjective truth stem from the subjective nature of its predicates or the properties and relations they refer to. After all, any proposition that essentially refers to a subjective entity has truth-value only in those contexts relative to which it exists, and lacks truth-value in the rest of them. This would be enough to make it subjective, if we do not add Mandik’s further condition. In order to understand the motivation behind Mandik’s condition compare, for example, the proposition that New York is to the north from here with the proposition that New York is fun. In both cases, we are talking about the same institutional entity, New York, and therefore, in both cases we have subjective propositions (for they both would have no truth-value had things been such that New York was never founded or it had disappeared by now, for example). However, in the second case, there is a second and more fundamental source of subjectivity: the property of being fun In the first case, we say something objective (the location) of something subjective (New York), while in the second case we say something subjective (that it is fun) about the same subjective thing (New York). For Searle, this means that only the second proposition is genuinely subjective. To acknowledge Searle’s distinction, from now on we may talk of ontological subjectivity to refer to cases of subjective truth that depends solely on the subjective mode of existence of their entities, and genuine or strong subjectivity to talk about those subjective propositions that are not ontological. Thus, a proposition like “Guacamole is tasty” is strongly subjective, while a proposition like “Guacamole has avocado in it” is not, it is only ontologically subjective. Finally also, if T is a term that refers to subjective entities, then the sentence “Ts exist” expresses an ontological subjective proposition: true relative to those contexts where Ts exist and false relative to those where they do not.

Consensus, Agreement and Intersubjectivity
An important phenomenon associated to subjective truth is so-called “faultless disagreement” (Kölbel 2003). This sort of subjectivity makes it is possible for two parties to disagree regarding the truth value of a given proposition, not because of any substantial fault on the part of the participants (or, to be more precise, no fault in their inquiry on the truth of such proposition), but because of the matter under disagreement itself. If the parties in disagreement do not share the subjective features that determine the truth-value of the proposition, then each one of them they may faultlessly take it to be true while the other takes it to be false (or lacking truth-value).

     Even though the term comes from the work of Kölbel, this way of cashing out epistemic objectivity originates in the pragmatism of Charles Peirce (1877), and was recently updated by Crispin Wright (1992). Like Peirce before them, Wright and Kölbel conceive of objectivity as the end result of an idealized rational inquiry, i.e. as agreement between ideal rational inquirers. Theories of objectivity of this kind are called consensus, intersubjective or agreement theories, in contrast to so-called mirroring or correspondance theories of objectivity that hold that the objectivity or subjectivity of propositions depends primarily on the objectivity or subjectivity of what those propositions are about. (Rorty 1979, Gauker 1995, )

Epistemic Subjectivity
Besides entities and propositions, there is also meaningful talk of subjective or objective judgments or beliefs. For someone’s belief to be subjective, at least one of the grounds upon which the belief is based must subjective, otherwise the belief is objective. If, for example, I base my judgement of the taste of a cigar on subjective aspects of my personal experience smoking it, then my judgement may rightfully called subjective. Notice, however, that I may make a subjective judgement on an objective proposition. I may ground my judgment of, for example, whether my parent’s place is farther from my home than my office at the university (which is clearly an objective matter of fact) on my subjective appreciation of how longer a drive to one is in comparison with a drive to the other.

    Just as we can talk about subjective and objective judgment, we can talk about subjective and objective warrant or justification, if the grounds for belief or judgment are warrant or justification conferring. It is quite controversial, however, whether it makes sense to talk about subjective knowledge or not. For a subject S to subjectively know a proposition p, S would need have subjective grounds for his belief in p that are strong enough to qualify as knowledge. For example, I may know subjectively what it is like to be me or to feel the things I do (Nagel 1974), or I may know subjectively how red things look (Jackson 1982). However, for some philosophers subjective grounds can never be strong enough to qualify as knowledge. From a physicalist perspeitve, for example, if an agent knows a proposition, all his grounds for it must be objective. (Dennett 1991)

    Just as there is a phenomenon of faultless disagreement at the level of truth, we may define an analogue faultless debate, when two parties may not be able to dissolve a dispute or disagreement, not because of any substantial fault on the part of the participants or of the matter under discussion, but because the parties may not share the subjective features that ground their judgments. Unlike faultless disagreement, in cases of faultless debate, one may be warranted, justified or even know that a proposition is true, and yet not be able to share the grounds The main idea b justification or knowledge with another party, not because of any fault on her part (epistemic or communicative), but because those grounds – even if appropriate – are relative to a subjective factor that is not shared among parties.

     Notice also that this epistemic kind of faultless debate is also closely related to subjective truth. Commonly when there is a faultless debate, one can find an epistemic proposition, i.e., a proposition about the epistemic status o the subjective judgment or belief whose truth-value is subjective in the above sense (i.e. relative). For example, one may say that whether S is warranted to hold certain belief or to assert certain proposition is a subjective matter, because the grounds S has for holding such belief or asserting such proposition are subjective.

    Now, the central question is whether subjective truth and subjective judgment are related in such a way that (A) subjective truths can be known only subjectively (if they can be known at all) and (B) objective truths can be known only objectively (if they can be known at all).

The question may seem idle, since nothing in Gettier’s arguments in his (1963) paper precludes it from applying to mathematical knowledge and justification. Remember that Gettier’s argument are based on two simple premises:

First, in that sense of 'justified' in which S's being justified in believing P is a necessary condition of S's knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. (Gettier 1963)

And, presumably, both premises hold for both apriori and aposteriori justification.

For those who may not be familiar with Gettier’s argument, let me offer a very general and abstract reconstruction (or, at least of his disyunctive case II, the conjunctive case I is completely analogous and dual):

1. Hypothesis to be reduced: Knowledge is Justified True Belief
2. Premise 1: Justification is fallible. It is possible for a person to be justified in believing a proposition that is in fact false. Let S be such a person and p the relevant false proposition S justifiably believes.
3. Let q be some other proposition that S does not know, even thought it is true.
4. p logically entails (p v q).
5. Suppose S sees the entailment from p to (p v q), and accepts (p v q) on the grounds of (p).
6. Premise 2: Jutification transmits through at least basic logical entailments like that from p to (p v q).
7. From 1, 5 and 6, S is justified in believing (p v q).
8. q logically entails (p v q).
9. From 3 and 8, (p v q) is true.
10. From 7 and 9, S is justified in believing true proposition (p v q).
11. However, q is true in virtue of q being true (from 3, 8 and 9), and S does not know q (from 3).
12. From 11, S does not know that (p v q).
13. Therefore, S is justified in believing a true proposition – (p v q) – that S does not know, which contradicts our hypothesis 1.

The argument is perfectly sound, so the only way to resist its conclusion would be to attack one of its substantial premises. Premise 2 seems reasonable beyond doubt, but what reasons should we have to accept the fallibility of justification? Gettier does not say, but this clearly seems like a presupposition of the very definition of knowledge under discussion. For knowledge to be justified true belief, every element of the definition must do some work. If justification was not fallible, it would entail truth, and so truth would be disposable from the definition. Furthermore, since justification presupposes belief, being justified would be both a necessary and sufficient condition for knowledge. In other words, justification would just be a fancy word for knowledge. Since this is clearly not what supporters of the definition intended by it, justification cannot entail truth, i.e., it must be fallible.

It must be clear by know that the argument applies mutatis mutandi to mathematical beliefs and justification (if there is such a thing). If mathematical justification is fallible (as it presumably is), then it is possible for a person to be justified in believing a mathematical proposition that is in fact false. Furthermore, for any mathematical proposition P, if S is justified in believing mathematical proposition P, by proof, intuition or whatever, and P logically entails mathematical proposition Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. In particular, since P logically entails PvQ for any mathematical propositions P and Q, if S is justified in believing mathematical proposition P, and S deduces PvQ from P and accepts PvQ as a result of this deduction, then S is justified in believing PvQ. This is all it takes to use Gettier’s argument to show that it is possible for someone to come to believe a true mathematical proposition PvQ because she is justified in believing its false disyuncts, say P. That is all it takes for there to be a mathematical Gettier case.

Imagine a mathematician who is reliable enough to thoroughly check and produce formal proofs. As good as she may be in math, it is still possible that she might get it wrong at least some time. Let p then be one such false statement she mistakenly, but justifiably believes to be true (say, because she has a proof, she mistakenly believes to be correct). Let q be another mathematical proposition, one that is both true and unknown to our imaginary mathematician. Suppose now that she sees the entailment from p to (p v q), and accepts (p v q) on the grounds of p, for which he has proof. In this case, she is clearly justified in believing that (p v q) is true. But it is equally clear that she does not know that (p v q) is true; for (p v q) is true in virtue of q being true, not in virtue of p being true, which is the basis for our mathematician’s belief in (p v q). Since she does not know that q, she does not know that (p v q) either, even though her belief in (p v q) is both justified and true.

Crítica, Revista Hispanoamericana de Filosofía, Vol. 40, No. 120, diciembre 2008, pp. 3-35

Patrones inferenciales

Axel Arturo Barceló Aspeitia
Instituto de Investigaciones Filosóficas
Universidad Nacional Autónoma de México
abarcelo@filosoficas.unam.mx

Resumen: El objetivo de este artículo es proponer un método de traducción de tablas de verdad a reglas de inferencia, para la lógica proposicional, que sea tan directo como el tradicional método inverso(de reglas a tablas). Este método,además, permitirá resolver de manera elegante el viejo problema, formulado originalmente por Prior en1 960, dedeterminar qué reglas de inferencia definen un conectivo.
Palabras clave: inferencialismo, Gentzen, Peregrin, Prior, lógica

PDF en español (243 KB)

http://critica.filosoficas.unam.mx/120/res120_barcelo.html
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The main difficulty in trying to understand the role of ordinary language in Wittgenstein’s later Philosophy is to understand what it means for language to be ordinary? All through the Philosophical Investigations, Wittgenstein uses terms like common, ordinary, everyday, etc. while talking about the relation between Language and Philosophy. One may assume that all those expressions are synonyms, and that their multiplicity is owed more to stylistic criteria than to philosophical ones . However, one could also try to understand the distinctions and relations between them.
    The first and easiest distinction to draw is between common [allgemeinen] and everyday[alltäglich] language. In both German terms there is a reference to a certain generality or commonality. Allgemeinen literally means ‘belonging to every person’, while alltäglich means ‘belonging to the every day’. Wittgenstein uses the first term to contrast our common language with putative private languages (§261), and the second to contrast our everyday language with the metaphysical language (§116) of philosophy. The later term shows up again in §134, as part of an example of a philosophical analysis of the application of sentences. A small variation of alltäglich, that is, täglich, is used in §197, as part of the expression “everyday practice”, which connects intentional actions with their intention.
    Ordinary Language, on the other hand, is that which we use in our ordinary [gewöhnlichen] life [§108]. Here, the German word for ordinary, means ‘the way in which we live’ but the verb Wittgenstein uses for ‘living’ here [whonen] also means dwelling. So, ordinary language is also the language where we dwell. Wittgenstein uses the expression ‘ordinary life’ again in §156, to differentiate between the use of a term, and its role in our life. The same word for ‘ordinary’ appears in §132, and later in §402 where he talks, not about ordinary life, but ordinary language and ordinary linguistic forms. In these texts, Wittgenstein talks about the ordinary character of Language in terms of Language working properly (§108) that is, functioning, fulfilling its role (§402) for the satisfaction of certain needs (§132), In both cases, Wittgenstein is talking about looking at language as it works in our ordinary life, in contrast of looking at it laying idle (§132) outside of time and space (§108).
    Another important word in the same semantic circle is Heimat, i.e. fatherland. In §116, Wittgenstein calls “the everyday use or words” that which is practiced in their fatherland. There is a very engaging spatial metaphor in this same paragraph about taking words back into their everyday, that is, back to their fatherland. Here, we are no longer talking about looking at language in its ordinary use, but about taking it back to its everyday use. While the first one is passive, the second one is active. What Wittgenstein means here is that, when facing the metaphysical excesses of Philsoophy, we cannot take a mere passive attitude towards language. We must actively take language back to its original everyday use. Once there, we should ‘drop the ladder’ and take a more passive stance.

La confianza es antagónica a la duda. Si confías en alguien, no dudas de él. Ahora, dado que la duda precede la investigación (inquiry) y sólo de ésta brota el conocimiento (excepto en creencias básicas, para las cuales tampoco tiene sentido hablar de confianza); tal parece que la confianza excluye también al conocimiento. En otras palabras, no puedo confiar que harás algo si sé que lo vas a hacer. (Nótese que esta tesis es más fuerte que la tradicional tesis de que alguien no puede confiar en que x hará y si cree que sabe que x hará y.)
    Es ya tradicional distinguir dos tipos de confianza, que en inglés corresponden a dos palabras distintas que en español se traducen con el mismo vocablo “confianza”: “confidence” y “trust”. La confianza en el primer sentido – llamémosla “c-confianza” – es muy cercana a la mera creencia: admite grados de certeza, se justifica a través de evidencia y en combinación con ciertos deseos y otras creencias nos mueve a actuar de terminadas maneras. En general, c-confiamos que alguien hará algo porque creemos que esa persona hará ese algo. La confianza en el segundo sentido – llamémosle “t-confianza” –, en contraste, aunque se comporta como una creencia, obedece a reglas muy distintas de justificación. En especial, si sé que p, mi creencia en p está muy justificada . Por el contrario, si sé que p, mi t-confianza en p es absurda. En general, como he mencionado en el párrafo anterior, si realizo una investigación para fortalecer mi creencia en p, dicha búsqueda disminuye mi confianza. También, si trato exitosamente de forzar o amenazo a un agente a para que realice una acción A, he ganado mayor “c-confianza” en que a haga A, pero también he mostrado mi falta de “t-confianza” en a. (Smolkin 2008)

Es un lugar común decir que la filosofía del lenguaje ha de ser una disciplina empírica. Sin embargo, no es trivial determinar exactamente en qué sentido ha de serlo. ¿Qué datos empíricos son relevantes, y cómo se relacionan con las teorías filosóficas? En el caso de las teorías del significado y/o de la interpretación, hay dos tendencias generales de entender la relación entre teoría y datos:

Hipótesis I : Externalismo
Los experimentos nos dan datos sobre el uso del lenguaje, sobre del cual producimos nuestras teorías del significado, la interpretación, etc. En estas teorías, por lo tanto, “significado”, “interpretación”, “contenido” etc. son términos teóricos, no experimentales. Es decir, so se pueden detectar directamente a través de ningún tipo de observación o experimento. Son lo que solía llamarse “inobservables”. En consecuencia, preguntar a los hablantes “¿qué es lo que el hablante quiere decir?” no tiene mucho sentido y diseñar experimentos dónde se le hace este tipo de preguntas a los sujetos tiene poca utilidad teórica.

Hipótesis II : Internalismo
Además del uso lingüístico, nuestras teorías del lenguaje (del significado, la interpretación, etc.) deben también rescatar y/o dar cuenta, dentro de lo posible, de nuestras propias intuiciones sobre lo que significan nuestras expresiones lingüísticas. En estas teorías, por lo tanto, el significado, la interpretación, etc. no son términos teóricos puros (tal vez sean experimentales, o mixtos). En consecuencia, determinar experimentalmente de los hablantes “¿qué es lo que el hablante quiere decir?” sí tiene utilidad teórica. Una teoría del significado que tenga como consecuencia que los hablantes están sistemática y masivamente equivocados en su introspección sobre lo que significan las cosas o lo que se dice en situaciones lingüísticas concretas debe ser rechazada como insatisfactoria.

Para nuestro lanzamiento número 22 dentro de la serie de descarga gratuita No Copy Protection, tenemos "Izkierda", el segundo disco de DRXL. Samples, beats y ruidos entretejidos en piezas eclécticas, funky y experimentales. Entre el hip hop instrumental y la experimentación sónica, bricolajes sonoros al ritmo de la calle, el laboratorio y la biblioteca.



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