Gbor Forrai (University of Miskolc)

Preliminaries

Project: to explain how logical knowledge can be a priori. Even though Ill provide material for arguing that logic is a priori, I wont argue for that.Logical knowledge consists of sentences ascribing logical properties to arguments (valid, invalid), sentences (logically true, contradiction), or sets of sentences (logically equivalent, inconsistent).We know something a priori, if its justification does not depend on anything empirical.The argument on slide 24 is invalid you need experience to understand this claim, but once you understand it, you need no further experience to justify it.

The problem of a priori knowledge

(Realism) Sentences concerning field F are objectively true/false, their truth depends on facts independent of the human mind.Denied by myself (Resnik)

(Access) In order to justify a sentence you need cognitive access (however indirect) to the facts which make it true/false.Denied by moderate empiricists: Boghossian, Peacocke, Bealer

(Empiricism) We only have cognitive access to mind-independent facts through the senses.Denied by rationalists: Bonjour

(A priori knowledge) We have a priori knowledge of field F.Denied by radical empiricists: Quine and cohorts

Knowledge of chess

Knowledge of chess consists of sentences ascribing properties to moves (legal, illegal) and arrangements (check, checmate).Knowledge of chess is a priori.Sentences in chess should not be construed realistically, because the facts making these sentences true/ false are not objective, they depend on human decisions. Alternatively: they are objectively true and the corresponding facts are independent of the mind only if the decisions about rules are already assumed.Knowledge of chess is knowledge of mind-dependent facts. We have non-empirical knowledge of them because we made them. It is a kind of makers knowledge.

The view to be defended

Two ways of construing sentences expressing logical knowledge ( is valid, is logically true): they attribute system-specific logical properties (valid-in-classical-logic, valid-in-all-systems-respecting-bivalence)they attribute absolute logical properties (valid simpliciter)(1) Facts about system-specific properties are not objective or mind-independent, since systems depend on human decisions. (We may call them objective only if we take the rules for granted.)(2) Absolute properties do not exist, there is no fact about, there is no knowledge of such facts.All knowledge of logic of kind (1). Knowledge of logic is therefore knowledge of mind-dependent facts. We have non-empirical access to them because we made them. It is a kind of makers knowledge.

Agenda

Argue that logic is an artifact, just as chess is. Deductive logic is not extracted from lay thought, it is created.Dispel intial worry about anti-realism: truth is objective, so preservation of truth is objective, and validity is the preservation of truth.Argue for logical anti-realism. The argument in brief: there are many systems of logic; the way we choose between them does not indicate that there are system-independent logical properties the various systems seek to capture.Clarifications: why the artificiality thesis is necessary, why Quines anti-conventionalist arguments do not apply, how this account differs Boghossians.

Artifact 1.

(Subconscious cognitive mechanisms do not count.)1. Deductive inference is extremely rare among laymen. Lay inference is a large leap from unarticulated premises to a distant conclusion, not a meticulous stepwise process. Inferences can be later put into a deductive form.2. Experimental studies of deductive reasoning show that people often do not identify deductive tasks as deductive ones or do not try to solve them by deductive means.Wason selection task: which card(s) do you have to turn to check the truth of if p is on the one side, then q is on the other side?

The performance crucially depends on the choice of p and q. Indicative and deontic selection tasks are different. The indicative task is sensitive to probability considerations.p~pq~q

Artifact 2.

In tasks where syllogistic or conditional inferences have to be evaluated there is an ineliminable belief bias.No police dogs are vicious. Some highly trained dogs are vicious. Some police dogs are not highly trained. valid: 10%

No addictive things are inexpensive. Some cigarettes are inexpensive. Some addictive things are not cigarettes. valid: 71%

More careful instruction merely reduces bias, but does not eliminate it.

Artifact 3.

3. Deductive inference is of little use in practical situations in which we only have partial information and ceteris paribus generalizations. Deductive inference is monotonous (remains valid if we add new premises), but reasoning in practical situations is defeasible.Evaluating candidates for the position of professor of logic.Generalization: Anyone publishing in the best logic journals should be shortlisted.Information: X publishes in the best logic journals.Conclusion: X should be shortlisted.New information: X was fired from his previous positions because of sexual harassment. Those were papers were jointly authored with his wife, a noted logician, and X has no independent publications.

Artifact 4.

4. Logical properties presuppose logical form, logical form presupposes logical constants. Hence, we cannot have logical properties without logical constants. But the meaning of logical constants is fairly different from that of their natural language counterparts. Misbehaving close relativesFrau Merkel likes/does not like fuzzy logic.If I have two heads, then I have three hands.I ate the pizza and ordered it.All politicians are liars, but there are exceptions.More distant relatives of &Time: after, before, when, while, since, untilCausal(?): so, because, since, for, now that, as, in order thatOpposition: although, even though, whereas, while, yet

Artifact 5.

5. Comparison with ethics. Morality is present in practice, it is not invented by moral philosophers. Even among laymen, we have: awareness of ethics ethical considerations show up in deliberations, bad conscience, educationbasic ethical thought ethics distinguished from custom and self-interest, ability to formulate rulesterminologyAmong laymenno awareness of logic: arguments and inferences are evaluated, but that evaluation is global rather than specifically logical, no attention to logical considerations, no educationno basic logical thought no distinction between inductive and deductive argument, no distinction between false moves and false premises, no ability to identify formal rulesno logical terminology, apart from terms of global evaluation

Initial worry about anti-realism 1.

We arent tempted to be realist about check because there are practically no constraints on rules. But there are strong constraints on the rules of logic. Tonk-logic (p p tonk q; p tonk q q) wont do. How could you explain that if not by assuming that there objective logical properties logic should capture?Constraints may be imposed by the description of the task. A student support scheme or a tax system must obey very strict constraints. Yet deserves EUR support is not an objective property of students and owes .EUR tax is not an objective property of citizens.The constraints on logic derive from the task it serves: managing epistemic risk involved in inference. Epistemic risk consists in drawing from true premises conclusions which are false (non-true, less true then the premises)

Initial worry about anti-realism 2.

The idea: lets develop elementary and formal rules which never lead to falsehood from true premises. We should try to reconstruct arguments as consisting only of moves sanctioned by logical theory. This may have the following results:successful reconstruction: no risk in accepting the conclusionno reconstruction possible: conclusion is risky as beforereconstruction with additional premises: shows risks not previously knownreconstruction with slightly modified premises/conclusion: shows how risks can be avoided

Anti-realism 1.

When you devise a system of rules for a certain task you seek how to best satisfy the various requirements.In choosing a logic you seek the best balance of scope, simplicity, closeness to natural language (intuitiveness), philosophical tenability (Resnik calls this cognitive equilibrium.)But we do the same in choosing between scientific theories, we just balance different considerations (empirical adequacy, simplicity, compatibility with other theories, ). This does not threaten realism about science! Why should the case of logic be different?

Anti-realism 2.

1. Why is this not a rule of logic?For all x, y, z terms and + comparative adjectives, x+y, y+z x+zPros no exception completely formal instances are not justified empiricallyCons complicates syntax (need a special class of 2-place predicates); unlike other rules: the logical form is created by a special class of predicatesWould the cons entitle us to reject this rule if we were in the business of describing mind-independent facts like in science?

Anti-realism 3.

In science we are not allowed to sacrifice scope for familiarity and simplicity unless special conditions obtain.(1) The would-be law does not yield new predictions. (2) It is reasonable to hope that a more elaborate version of the current theory will be able to explain the facts the would-be law describes(1) does not apply, since logic does not seek predictions.(2) does not apply, since there is no way to capture these inferences by the customary rules. If logic were meant to capture the objective property of validity, this rule should not be rejected.

Anti-realism 4.

2. How can we resolve conflicts in logic? Consider some (apparent?) problems with classical logic.

a. inferences involving empty namesFa x(Fx)Pegasus is a winged horse. So there is at least one winged horse.We may (C) stick to the rule and ban empty names, (M) reanalyse names as predicates or (R) develop a free logic. b. inferences with the material conditional~(A B) AIts not the case that if the greens win at the next election, theyll attack the US. The greens will win at the next election!We may (C) stick to the material conditional but be careful in translation to and from natural language or (R) develop a different system of logic which is more faithful to natural language conditional.

Anti-realism 5.

c. sorites(antecedent) My daughter is not an adult at time t.(conditional) If my daughter is not an adult at time t, she wont be an adult one second after t.Instantiating (antecedent) now and iterating modus ponens, we may conclude that my daughter wont be an adult even when she is 90.We may (C) simply take care when dealing with vague predicates, (M) adopt a metaphysical view which makes (conditional) false at one point (epistemicism), (M) adopt a semantic view that makes the (antecedent) not true for a range of instantiations (supervaluation), or (R) adopt fuzzy logic which does not support modus ponens. d. ex contradictione quodlibetWe obviously do not want to infer to all propositions from a contradiction. So we may (C) abstain from using logic when we find a contradiction or (R) develop a paraconsistent logic.

Anti-realism 6.

We may choose between four types of solutions:(Conservative) Stick to classical logic but apply with care.(Moderate) Put the blame on metaphysical views, semantic views, etc. and not on classical logic.(Radical) Abandon classical logic in favour of another one.(Opportunistic) Keep classical logic and use non-classical logic in the problem cases.Claim: the way we decide shows that logical properties are not objective.If you are an opportunist, you have abandoned realism. Classical logic and non-classical logics are compatible only if they are taken to make claims about system-specific properties, but are not compatible if they are taken to capture absolute logical properties.

Anti-realism 7.

The arguments between the various options are inconclusive, which shows that they do not concern matters of fact.Irresolvable conflicts do not imply that debate is not about objective facts. It might happen that we are just ignorant of the facts knowledge of which would be sufficient for the decision (e.g. debates about past events). In these conflicts, however, it is hard to see how the case could be decided if we knew further facts.The disagreements concern which considerations (scope, simplicity, intuitiveness, philosophical considerations)should be given priority. Such disagreements are not factual in nature.Objection: isnt there a common core between various systems of logic which yields an objective property of validity?Reply: the various logics have so few rules in common that this common core logic would be practically useless.

Clarification: Is the artifact thesis necessary?

Cannot we argue for a makers knowledge view simply on the basis of anti-realism?Suppose logic is not an artifact, but we are all natural born classical logicians, even though logical properties are not objective.Then it needs to be explained why this is the case, and the most probable answer is an evolutionary story: classical logic leads from truths to truths in cases important for our survival. (How else could it be explained on evolutionary grounds?)But then logic is not a priori in a deep sense: it comes about through empirical learning on the level of the species.It is also a matter of fact that certain inferences lead from truths to truths. So validity is after all an objective property and anti-realism cannot be sustained.

Clarification: has not Quine refuted this kind of conventionalism?

Quines target is the view that logical truth is true by convention. The present account holds that logical truth is logically true by convention.If Frankfurt is in Germany, then Frankfurt is in Germanyis true partly in virtue of the meaning of the words, partly in virtue of the facts, as all other true sentences. It is logically true in classical logic. It is true but not logically true in Kleenes strong 3-valued logic. (When p is indeterminate, p p is indeterminate and not true.)Similarly for logical validity. If Gbor is in Frankfurt, then Gbor is in GermanyGbor is in FrankfurtSo, Gbor is in Germanyhas true premises and a true conclusion. It is a valid argument in classical logic, but not in fuzzy logic. (If the premises are not fully true, the conclusion is may be less true than the premises.)

Clarification: Boghossian (2003)

Logical constants are defined implicitly in terms of the validity of certain patterns of inference. So inferences according to these patterns are justified by the meanings of logical constants.Any rules that are written into the possession conditions fora non-defective concept are a fortiori entitling. 1. In contrast to Boghossian, I dont want to account for lay inferences, because I dont think they are deductive. Standards rules of logical employ logical constants and not their natural language counterpart. (Modus ponens may fail with natural language conditional, McGee.)2. Boghossian is criticized for not advancing a positive reason for the non-defective character of our logical concepts. I advance a positive reason: good balance between scope, simplicity and other considerations. In constrast with him, I dont believe that logical validity is something factual.

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