A priori

1. A priori

2. Standard Distinction I. • analytic: • 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: • 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: • Logically impossible that it is false Denial of it involves a contradiction • True in all possible world II. • synthetic: • 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 • a posteriori • (“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

3. Tools Analytic: • true in virtue of meaning alone. It’s validity depends solely on the definitions of the symbols/words it contains. • Groundedinmeaningindependently of mattersoffact. • Example: I knowanalyticallythat: • No unmarried man is married • No bachelor is married • Because • The wordunmarried is definedasnot-married • The wordbacherlor is definedasnot-married

4. Tools A priori: • knowable “prior to” experienceorindependent 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” • ”Entitiesx and y are identical if everypredicatrepossessed by x is also possessed by y and vice versa” • Because • Knowingthat ”7+5=12” is truedoesnotrequiretocountonmyfingersor I donothavetomeettheseguys ”7” and ”5” inordertoknowtheirnature. • Knowingthatthe Leibniz Law is truedoesnotrequretofindtwoidenticalobjects – thatwould be, nevetherless, impossible.

5. Tools Necessary: • Logicallyimpossible that it is false / Denial of itinvolves a contradiction • Trueinallpossibleworld • PossibleWorlds: Everylogicallyconceivablenon-contradictorystate of affair • Example: I knowit is necessarythat: • A triangle has threesides • Nothing can be red and green all over • Because: • It is trueforeverypossibleworldthatif a triangle is exemplifiedinit, thenit has threesides. • There is no possibleworld/logicallyconceivablenon-contradictorystate of affairinwhich an object has an all over greem and redsurfacesimultanously

6. Problematizing • Since, theyareinterchangeable I knowanalytically/a prioriy/necessarilythat: • No bachelor is married • ”7+5=12” • A triangle has threesides • Butwhataboutthese? • Water is H2O • The standardethalon meter stick in Paris is one meter long • Everyevent has a cause / everything that has a beginning has an end • Godexists • Does a priori knowledgepose a problemforempiricism? • Or a prioryknowledge is a genuinelydifferentkind of knowledge? • Howdowejustify a priori statements?

7. Problematizing:A priori synthetic? A priori contingent? I. • analytic: • true in virtue of meaning alone. It’s validity depends solely on the definitions of the symbols it contains. • Groundedinmeaningindependently of mattersoffact • Kant: a proposition whose predicate concept is contained in its subject concept • a priori: • 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: • Logicallyimpossible that it is false Denial of itinvolves a contradiction • Trueinallpossibleworld II. • synthetic: • 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 • a posteriori • (“empirical”): can only be known “after” (on the basis of) experience • contingent: • Not necessary • Nottrueinallpossibleworld • Possible: atleastinonepossibleworldit is true

8. Outline • A priori contingent/synthetic? • Dealwiththeproblem of Empiricism and A priori • Hume, Kant, Mill, Ayer, • Metaphysical and EpistemologicalConception of Analycity • ‘Tonk dilemma’ • Justifyability of aprioricity • BonJour, Plantinga, Goldman/Peacocke • Twodimensionalsemanticsaboutnecessity • Frege, Carnap, Kripke, Chalmers

9. I. A priori contingent/synthetic? A prioriysynthetic Itshouldbe prior to/independent of sense experienceand • Its validity is determined by the facts of experience. • A proposition whose predicate concept is not contained in its subject concept • ‘Nothing can be both a cow and a horse at the sametime’ • Is it part of the meaningof “is a cow” that it excludes being a horse? • If so, this example is analytic andagain not what we’re after. • But, knowing the meaning of “cow” perfectly well does not involve having heard of horses. • If the meaningof “is a cow” included all these exclusions, no one could learn it, especially giventhat the other words would contain their own exclusions. So, the proposition that ‘nothing is both a cow and a horse’ is non-analytic Ayer: Doesitmeanthatcognitivecapacity is involvedindefinition of a priori synthetic?

10. I. A priori contingent/synthetic? A prioriycontingent Itshouldbe prior to/independent of sense experienceand • Nottrueinallpossibleworld • ‘The standardethalon meter stick in Paris is one meter long’ Itwill be discusedinIV.twodimensionalsemantics

11. II. Problem of Empiricism and A priori The empiricist must deal with the truths of logic and mathematics in one of the two followingways: • he must say either that they are not necessary truths, in which case he must account for the universal conviction that they are; or • 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! ii.No factual content! J. S. Mill David Hume

12. II. Hume and Kant • Hume’s Fork: “Tautologies” and factual claims • 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.

13. II. Objection and Answer • 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

14. II. A priori: only about lingustic usage? 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)

15. II. Mill 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.

16. II. Ayer - Devoid of factualcontent • Empiricaljustification is inductive • No Empiricaljustificationcansupportnecessarytruths • Ayer (& moderate empiricists): analytic truths give no information about the world, but reveal linguistic usage of it ‘Either some ants are parasiticor none are’ • Ifoneknowswhat is thefunction of thewords ‘either’, ‘or’, and ‘not’, thenonecanseethatanyproposition of theform‘Either p is trueor p is nottrue’ isvalid, independently of experience. Whatdoes ‘see’ mean here? →The explanation of knowledge of logicaltruths is notfurtherexplained • 1. Onwhatdependsthetruth of a priori statements? • 2. Howdowegraspit? (Ch. III.)

17. II.Metaphysical and epistemological conception of analyticity 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 thatfor anystatement 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”) • Metaphyicalconceptionbutepistemological • Ayer? → by knowing the meaning of ‘either’, ‘or’, ‘not’, (logicconnectives) thevalidity of ‘either p is trueor p is nottrue’ can be known.

18. II. The ‘tonk’ dilemma • 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’…

19. III. Justifyability of aprioricity How can we explain a priori justification – howcanwe ‘see’? • Task: • Howcognitivestudieswanttogive an account forunderstandingmathematical and logicalstatements? • Howeconomists account forthephenomenathatmathematicscanworkincalculatingthemovements of the market? • Both A and B groupsworkindependently

20. III. Justifyability of aprioricity How can we explain a priori justification – how can we ‘see’? • a person might have an intuition that theproposition is true based on understanding the concepts involved • she might have an intuition thatbased on her inability to think of counterexamples to those claims / intuitionon→ inconceivability of PW → Necessaryfalsity of theclaim • BonJour: non-inferential grasp, apprehension, or “seeing” that some proposition isnecessarily 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 intuitionthat 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. BUTthePROBLEM: If the justificatory force of rational insights requires that a premise like (J) be justified, thenitbegsthequestion.

21. III. Justifyability of aprioricity How can we explain a priori justification – how can we ‘see’? • a person might have an intuition that theproposition is true based on understanding the concepts involved • she might have an intuition thatbased on her inability to think of counterexamples to those claims / intuitionon→ inconceivability of PW → Necessaryfalsity of theclaim • 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. • Reliability, however, doesnotguaranteejustification (aswehavelearntfromGabor)

22. My questions - Tasks • 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?

23. VI. Bypass: Philosophy of Language • Frege: the extension of an expression does not determine itscognitive significance Clark Kent = Superman Clark Kent = Clark Kent ‘Hesperus’ = ‘Phosporus’ ‘Hespherus’ = ‘Hespherus’ CognitivelySignificantCognitivelynotSignificant • 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.

24. VI. Carnap on Intension • 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. Fromthe Carnapian Thesis: • Apriroicitydefinesidentity: it is necessarythatif ‘A’ and ‘B’ havethesameintension, thentheyareidentical.

25. VI. Carnap & Kant → Frege • Carnapian Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is necessary. Fromthe Carnapian Thesis: It is necessarythatif ‘A’ and ‘B’ havethesameintension, thentheyareidentical. & • 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. FromtheNeo-FreagenThesis: It is a priori thatif ‘A’ and ‘B’ havethesameintension, thentheyareidentical: fromthepurenotion of A(cows) B(not-horse) should be known - Ayer

26. IV. Kripke • Kripkean Thesis: P is necessary  P is a priori. • Nec(water=H2O) ~Apriori(water=H2O) • ~Nec(Hesperus=evening star)Apriori(Hesperus=evening star) • Nec (I am Zsolt Ziegler) ~Apriori (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 • Pick out actual extension at all possibilities

27. IV. Two-Dimensional Semantics 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’) • The verythingitself! • Second dimension: Extension in possibilities considered as counterfactual (‘circumstance of evaluation’) • The reference-fixer: accordingtowhichtheobjectcan be picked out inpossibleworlds

28. 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 secoondarilynecessarythat ‘I am ZsZ’ • It is primarilypossiblethat ‘a speakersays 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 secoondarilynecessarythat ‘H is Ph’ • It is primarilypossiblethat ‘theeveningstaristhe Moon’ • E.g. ‘water’ • 2-intension (theverything) 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 secoondarilynecessarythat ‘wateris H2O’ • It is primarilypossiblethat ‘wateris XYZ’

29. Necessary A posteriori and Contingent A priori ‘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 standardmeter 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 ‘

30. End(?) • …

31. If you are smart enough “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) • PrimaryIntensioncan be know a priori • S is a priori iff S has a necessary 1-intension

32. paper: prove it is false or not 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 1-conveivable that in the actual world I have those (reference fixing) superman properties.