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Gábor Forgács, Tihamér Margitay, Zsolt Ziegler Dept. of Philosophy and the History of Science 1111 Budapest, Egry J. st. 1. E 610. [email protected], [email protected], [email protected] www.filozofia.bme.hu A priori Standard Distinction Filozófiai és Tudománytörténet Tanszék I. analytic: knowable “prior to” experience independent of sense experience Kant: "although all our knowledge begins with experience, it does not follow that it arises from experience” necessary: 2017.05.05. true in virtue of meaning alone. It’s validity depends solely on the definitions of the symbols it contains. Grounded in meaning independently of matters of fact Kant: a proposition whose predicate concept is contained in its subject concept a priori: II. Logically impossible that it is false Denial of it involves a contradiction True in all possible world synthetic: a posteriori not analytic. It’s validity is determined by the facts of experience. Kant: a proposition whose predicate concept is not contained in its subject concept (“empirical”): can only be known “after” (on the basis of) experience contingent: Not necessary Not true in all possible world Possible: at least in one possible world it is true Epistemology Tools Filozófiai és Tudománytörténet Tanszék Analytic: true in virtue of meaning alone. It’s validity depends solely on the definitions of the symbols/words it contains. Grounded in meaning independently of matters of fact. Example: I know analytically that: No unmarried man is married No bachelor is married Because The word unmarried is defined as not-married The word bacherlor is defined as not-married 2017.05.05. Epistemology Tools Filozófiai és Tudománytörténet Tanszék A priori: knowable “prior to” experience or independent of sense experience Kant: "although all our knowledge begins with experience, it does not follow that it arises from experience” Example: I know a priori that ”7+5=12” ”Entities x and y are identical if every predicatre possessed by x is also possessed by y and vice versa” Because 2017.05.05. Knowing that ”7+5=12” is true does not require to count on my fingers or I do not have to meet these guys ”7” and ”5” in order to know their nature. Knowing that the Leibniz Law is true does not requre to find two identical objects – that would be, nevetherless, impossible. Epistemology Tools Filozófiai és Tudománytörténet Tanszék Necessary: Logically impossible that it is false / Denial of it involves a contradiction True in all possible world Possible Worlds: Every logically conceivable non-contradictory state of affair Example: I know it is necessary that: A triangle has three sides Nothing can be red and green all over Because: It is true for every possible world that if a triangle is exemplified in it, then it has three sides. There is no possible world/ logically conceivable non-contradictory state of affair in which an object has an all over greem and red surface simultanously 2017.05.05. Epistemology Problematizing 1. 2. 3. Filozófiai és Tudománytörténet Tanszék Since, they are interchangeable I know analytically/a prioriy/necessarily that: No bachelor is married ”7+5=12” A triangle has three sides But what about these? Water is H2O The standard ethalon meter stick in Paris is one meter long Every event has a cause / everything that has a beginning has an end God exists Does a priori knowledge pose a problem for empiricism? Or a priory knowledge is a genuinely different kind of knowledge? How do we justify a priori statements? 2017.05.05. Epistemology Problematizing: A priori synthetic? A priori contingent? I. analytic: knowable “prior to” experience independent of sense experience Kant: "although all our knowledge begins with experience, it does not follow that it arises from experience” necessary: 2017.05.05. II. true in virtue of meaning alone. It’s validity depends solely on the definitions of the symbols it contains. Grounded in meaning independently of matters of fact Kant: a proposition whose predicate concept is contained in its subject concept a priori: Logically impossible that it is false Denial of it involves a contradiction True in all possible world Filozófiai és Tudománytörténet Tanszék synthetic: a posteriori not analytic. It’s validity is determined by the facts of experience. Kant: a proposition whose predicate concept is not contained in its subject concept (“empirical”): can only be known “after” (on the basis of) experience contingent: Not necessary Not true in all possible world Possible: at least in one possible world it is true Epistemology Outline I. A priori contingent/synthetic? II. Deal with the problem of Empiricism and A priori III. Hume, Kant, Mill, Ayer, Metaphysical and Epistemological Conception of Analycity ‘Tonk dilemma’ Justifyability of aprioricity IV. BonJour, Plantinga, Goldman/Peacocke Two dimensional semantics about necessity 2017.05.05. Filozófiai és Tudománytörténet Tanszék Frege, Carnap, Kripke, Chalmers Epistemology I. A priori contingent/synthetic? Filozófiai és Tudománytörténet Tanszék A prioriy synthetic It should be prior to/independent of sense experience and i. Its validity is determined by the facts of experience. ii. A proposition whose predicate concept is not contained in its subject concept ‘Nothing can be both a cow and a horse at the same time’ Is it part of the meaning of “is a cow” that it excludes being a horse? – If so, this example is analytic and again not what we’re after. But, knowing the meaning of “cow” perfectly well does not involve having heard of horses. If the meaning of “is a cow” included all these exclusions, no one could learn it, especially given that the other words would contain their own exclusions. So, the proposition that ‘nothing is both a cow and a horse’ is non-analytic Ayer: Does it mean that cognitive capacity is involved in definition of a priori synthetic? 2017.05.05. Epistemology I. A priori contingent/synthetic? Filozófiai és Tudománytörténet Tanszék A prioriy contingent It should be prior to/independent of sense experience and i. Not true in all possible world ‘The standard ethalon meter stick in Paris is one meter long’ It will be discused in IV. two dimensional semantics 2017.05.05. Epistemology II. Problem of Empiricism and A priori Filozófiai és Tudománytörténet Tanszék The empiricist must deal with the truths of logic and mathematics in one of the two following ways: i. he must say either that they are not necessary truths, in which case he must account for the universal conviction that they are; or ii. he must say that they have no factual content, and then he must explain how a proposition which is empty of all factual content can be true and useful and surprising i.Not necessary truths! J. S. Mill 2017.05.05. ii.No factual content! David Hume Epistemology II. Hume and Kant Hume’s Fork: “Tautologies” and factual claims Filozófiai és Tudománytörténet Tanszék The a priori: mathematics and logic Factual claims: science and everything else Kant: ‘In all judgments in which the relation of a subject to the predicate is thought … this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A… In the first case, I call the judgment analytic, in the second synthetic…I merely draw out the predicate in accordance with the principle of contradiction, and can thereby at the same time become conscious of the necessity of the judgment’ Analytic sentences are true in virtue of language alone They’re a priori (knowable independent of experience) because they’re empty of factual content. They’re necessary because we don’t allow them to be false, e.g. – if the angles of a figure don’t add up to 180 degrees we don’t count it as a Euclidean triangle. 2017.05.05. Epistemology II. Objection and Answer Filozófiai és Tudománytörténet Tanszék Objection: If all the assertions which mathematics puts forward can be derived from one another by formal logic, mathematicians cannot amount to anything more than an immense tautology…Can we really allow that these theorems which fill so many books serve no other purpose than to say in a roundabout fashion A = A? There is a sense in which analytic propositions do give us new knowledge. They call attention to linguistic usages, of which we might otherwise not be conscious and they reveal unsuspected implications in our assertions and beliefs. The business of philosophy is analysis: to elicit those features linguistic usage and reveal entailment relations 2017.05.05. Epistemology II. A priori: only about lingustic usage? Filozófiai és Tudománytörténet Tanszék Hypothesis: v(B) > v(S) 1. entailment: v(B) > v(B+S) > v(S) 2. entailment: v(B+S) > v(B) > v(S) Concluion: v(B+S) = v(B) = v(S) Hypotheis is false Know without any reference to experience Task: How is that possible? (Agree or Disagree) 2017.05.05. Epistemology II. Mill Filozófiai és Tudománytörténet Tanszék J. S. Mill's radical empiricist alternative: Maths and logic are inductive generalisations Argument against Mill If mathematical propositions are inductive generalisations, it's possible to have refuting instances Take a putative refuting instance: count 5 pairs and get 9. If the angles of a figure don’t add up to 180 degrees we don’t count it as a Euclidean triangle. 2017.05.05. Epistemology II. Ayer - Devoid of factual content Filozófiai és Tudománytörténet Tanszék Empirical justification is inductive No Empirical justification can support necessary truths Ayer (& moderate empiricists): analytic truths give no information about the world, but reveal linguistic usage of it ‘Either some ants are parasitic or none are’ If one knows what is the function of the words ‘either’, ‘or’, and ‘not’, then one can see that any proposition of the form ‘Either p is true or p is not true’ is valid, independently of experience. What does ‘see’ mean here? →The explanation of knowledge of logical truths is not further explained 2017.05.05. 1. On what depends the truth of a priori statements? 2. How do we grasp it? (Ch. III.) Epistemology II.Metaphysical and epistemological conception of analyticity Filozófiai és Tudománytörténet Tanszék Mathematics and logic statements are analytic Their truth depends on the meaning of words ('metaphysical' conception of analyticity) We can know whether they are true or false just by knowing the meaning of words ('epistemological' conception of analyticity) Critique of the metaphysical conception “Isn't it in general true that for any statement S, S is true iff for some p, S means that p and p? How could the mere fact that S means that p make it the case that S is true? Doesn't it also have to be the case that p?” (Paul Boghossian “Analyticity reconsidered”) 2017.05.05. Metaphyical conception but epistemological Ayer? → by knowing the meaning of ‘either’, ‘or’, ‘not’, (logic connectives) the validity of ‘either p is true or p is not true’ can be known. Epistemology II. The ‘tonk’ dilemma Filozófiai és Tudománytörténet Tanszék By knowing the meaning of ‘either’, ‘or’, ‘not’, (logic connectives) the validity of ‘either p is true or p is not true’ can be known. Standard Locic Connectives: ‘&’, ‘V’, ‘→’, ‘↔’ e.g: ‘&’ p&q → q; p&q → p; p, q → p&q - we mean by '&' whatever makes these schemas valid Problem: “tonk”. Define Tonk [۞ - “tonkjunct”] as the following connective, From any ψ to be derived from any φ: p → p۞q; p۞q → q By knowing the meaning of “tonkjunct” the valifity of ‘If Zsolt is a philosopher, then you are a BIV’ can be known. Absurd! Why is it absurd? ‘I see it as absurd’ – and here we are again: ‘see’… 2017.05.05. Epistemology III. Justifyability of aprioricity Filozófiai és Tudománytörténet Tanszék How can we explain a priori justification – how can we ‘see’? Task: How cognitive studies want to give an account for understanding mathematical and logical statements? How economists account for the phenomena that mathematics can work in calculating the movements of the market? – Both A and B groups work independently 2017.05.05. Epistemology III. Justifyability of aprioricity Filozófiai és Tudománytörténet Tanszék How can we explain a priori justification – how can we ‘see’? I. II. a person might have an intuition that the proposition is true based on understanding the concepts involved she might have an intuition that based on her inability to think of counterexamples to those claims / intuition on → inconceivability of PW → Necessary falsity of the claim BonJour: non-inferential grasp, apprehension, or “seeing” that some proposition is necessarily true. these appearances are not propositional, they are unlike beliefs and more like perceptual sensations. (J) S's belief that p is likely to be true, if S has a rational intuition that necessarily p, (i) after, considering p with a reasonable degree of care (careful understanding: p) (ii) having at least an approximate understanding of the concept of necessity” and (iii) S is neither dogmatic nor biased regarding p. BUT the PROBLEM: If the justificatory force of rational insights requires that a premise like (J) be justified, then it begs the question. 2017.05.05. Epistemology III. Justifyability of aprioricity Filozófiai és Tudománytörténet Tanszék How can we explain a priori justification – how can we ‘see’? I. II. a person might have an intuition that the proposition is true based on understanding the concepts involved she might have an intuition that based on her inability to think of counterexamples to those claims / intuition on → inconceivability of PW → Necessary falsity of the claim • Plantinga: analyzes that “seeing” in terms of immediately believing, and being convinced, that a proposition is necessary – ‘an indescribable mental state’ • Goldman/Peacocke:concept possession guarantees reliably (ikelihood) that these sorts of intuition are based on concept possession. To possess a concept, you must be reliable in your judgments involving application of that concept to hypothetical cases. • 2017.05.05. Reliability, however, does not guarantee justification (as we have learnt from Gabor) Epistemology My questions - Tasks Filozófiai és Tudománytörténet Tanszék Suppose, we are hard-wired for the logic that we have - hypothesis But, with a different brain structure we would have a different logic – There is nothing prescriptive in our logic – E.T would find the tonk connective naturally true If our brains perform logic (inductively → contingently), how logic is possible to be deductive and necessary? 2017.05.05. Epistemology VI. Bypass: Philosophy of Language Filozófiai és Tudománytörténet Tanszék Frege: the extension of an expression does not determine its cognitive significance Clark Kent = Superman Clark Kent = Clark Kent ‘Hesperus’ = ‘Phosporus’ ‘Hespherus’ = ‘Hespherus’ Cognitively Significant Cognitively not Significant We need an aspect of meaning that is tied constitutively to cognitive significance: sense. Fregean Thesis: ‘A’ and ‘B’ have the same sense iff ‘A=B is cognitively significant. 2017.05.05. Epistemology VI. Carnap on Intension Filozófiai és Tudománytörténet Tanszék Carnap: Expressions have intensions, capturing their extensions across possible tates of affairs. Intension = function from possibilities to extensions Intension can play the role of sense. Carnapian Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is necessary. From the Carnapian Thesis: 2017.05.05. Apriroicity defines identity: it is necessary that if ‘A’ and ‘B’ have the same intension, then they are identical. Epistemology VI. Carnap & Kant → Frege Filozófiai és Tudománytörténet Tanszék Carnapian Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is necessary. From the Carnapian Thesis: It is necessary that if ‘A’ and ‘B’ have the same intension, then they are identical. & Kantian Thesis: P is necessary iff P is a priori Neo-Fregean Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is a priori. From the Neo-Freagen Thesis: It is a priori that if ‘A’ and ‘B’ have the same intension, then they are identical: from the pure notion of A(cows) B(not-horse) should be known - Ayer 2017.05.05. Epistemology IV. Kripke Filozófiai és Tudománytörténet Tanszék Kripkean Thesis: P is necessary P is a priori. Nec (water=H2O) ~A priori (water=H2O) ~Nec (Hesperus=evening star) A priori (Hesperus=evening star) Nec (I am Zsolt Ziegler) ~A priori (I am Zsolt Ziegler) Denies Kantian thesis: – P is necessary iff P is a priori Denies Neo-Fregean Thesis: – ‘A’, ‘B’ have the same intension iff ‘A=B’ is a priori Carnapian thesis is retained – ‘A’, ‘B’ have the same intension iff ‘A=B’ is necessary. Names, natural kind terms, indexicals are rigid designators 2017.05.05. Pick out actual extension at all possibilities Epistemology IV. Two-Dimensional Semantics Filozófiai és Tudománytörténet Tanszék Core idea of 2-D semantics: There are two sorts of dependence of extension on possible states of the world, and so two sorts of intension. First dimension: Extension in possibilities considered as actual (‘context of utterance’) – Second dimension: Extension in possibilities considered as counterfactual (‘circumstance of evaluation’) – 2017.05.05. The very thing itself! The reference-fixer: according to which the object can be picked out in possible worlds Epistemology Examples E.g. ‘I’ 2-intension picks out ZsZ in all worlds 1-intension picks out speaker/center in all worlds ‘I’ and ‘ZsZ’ have same 2-intension, different 1-intension – It is secoondarily necessary that ‘I am ZsZ’ – It is primarily possible that ‘a speaker says I’ E.g. ‘Hesperus’ 2-intension picks out Venus in all worlds 1-intension picks out evening star in all/many worlds ‘Hesperus’ & ‘Phosphorus’ have same 2-intension, different 1-intension – It is secoondarily necessary that ‘H is Ph’ – It is primarily possible that ‘the evening star is the Moon’ E.g. ‘water’ 2017.05.05. Filozófiai és Tudománytörténet Tanszék 2-intension (the very thing) picks out H2O in all worlds (Earth, Twin Earth) 1-intension (transparent, odorless) picks out H2O in Earth, XYZ in Twin Earth ‘water’ & ‘H2O’ have same 2-intension, different 1-intension – It is secoondarily necessary that ‘water is H2O’ – It is primarily possible that ‘water is XYZ’ Epistemology Necessary A posteriori and Contingent A priori Filozófiai és Tudománytörténet Tanszék ‘Water is H2O’ – Necessary A posteriori It is 2-necessary: in every possible world where ‘this/our’ water is exemplified it is necessarily H2O It is 1-contingent: it is not necessary that in every possible world (water) odorless-drinkable-tranparent-liquid is exemplified You can justify it only empirically/a posteriori - The notion of Water does not imply H2O ‘The standard meter stick in Paris is one meter long’ – Contingent A priori It is 2-contingent: it is not necessary that ‘this/our’ standard meter stick is exemplified in all possible worlds. It is 1-necessary: in every possible world where there is a stick ‘called standard meter stick’ is one meter long Because of the definition of ‘meter’ so can be known a priori ‘ 2017.05.05. Epistemology End(?) Filozófiai és Tudománytörténet Tanszék … 2017.05.05. Epistemology If you are smart enough Filozófiai és Tudománytörténet Tanszék “A priori reasoning from PQTI, puts one in a position to know all about the physical composition, the phenomenal appearance, the spatial structure and dynamic behavior of macro physical system, along facts about their relation to oneself and their distribution to know all ordinary macro physical truth S about such systems, as long as one possesses the concepts involved in S.” (Chalmers 2002: p. 179) i. Primary Intension can be know a priori ii. S is a priori iff S has a necessary 1-intension 2017.05.05. Epistemology paper: prove it is false or not Filozófiai és Tudománytörténet Tanszék Superman does not exist in the actual world. But let us primarily conceive a comic possible world where Superman exists, call it marvel universe. Moreover, “Superman” and “Clark Kent” are proper names, and according to Kripke, they are rigid designators and primary intension of them is necessary. Hereby, the assertion “Superman is Clark Kent” is a metaphysical necessity. The marvel universe is a metaphysically possible centered world satisfying the primary intensions of “Superman” and “Clark Kent”. More precisely, the secondary intension of Superman (in the marvel universe) picks out Clark Kent and Superman in every possible world (where he is exemplified). Now, suppose that Lex Luthor (the greatest genius enemy of Superman) has a limitless cognitive power (like an ideal reasoner). Furthermore, he also knows PQTI of the marvel universe – since PQTI is speaker relative. According to Chalmers, by limitless reasoning and PQTI in his armchair Lex Luthor would know a priory that “Clark Kent is Superman” (and it is metaphysically necessary). Chalmers' strategy is that a complete qualitative description of a world, which is epistemically complete, can built up any epistemic possible scenario. This PQTI, which is absolutely epistemic, allows identity statements formed by proper names such as “Superman is Clark Kent” or “(twin-) water is XYZ”. Naturally, in the actual world there is no such thing as Superman. However, the assertion “Superman is Clark Kent” is metaphysically necessary in that epistemic word that is 1-conceived. Viz. the secondary intension of Superman picks out that very (Clark Kent) object in every possible world. Of course, it is possible that Zsolt Ziegler (me) is superman, but it is an epistemic possibility. It is 1conveivable that in the actual world I have those (reference fixing) superman properties. 2017.05.05. Epistemology