Truth, T Truth-values, and the l like Fabien Schang National - - PowerPoint PPT Presentation

Truth, T Truth-values, and the l like

Fabien Schang National Research University Higher School of Economics Moscow (Russia) schang.fabien@voila.fr

Content

• 1. Truth
• 2. Truth-values
• 3. The like

1. Truth

A basic difference, in philosophy, between on

• ntol
• log
• gy and epis

istemol

• log
• gy

Ontology is about what is: bein ing Epistemology is about how to access to what is: kn know

• win

ing Log

• gic

ic is about everything mean anin ingfu ful A set of sets of sentences, related to each other in a formal language One common concern in ontology, logic, and epistemology: tr truth th All the three sections deal with truth, but from different perspectives Ontology and epistemology: the mat aterial al truth of atoms (p, q, …) Logic: the for formal al truth of molecules (p  q, p  q, …) At the crossroad of logic and epistemology: epis istemic ic log

• gic

A couple of different combinations between these two concepts

A basic difference, in philosophy, between on

• ntol
• log
• gy and epis

istemol

• log
• gy

Ontology is about what is: bein ing Epistemology is about how to access to what is: kn know

• win

ing Log

• gic

ic is about everything mean anin ingfu ful A set of sets of sentences, related to each other in a formal language One common concern in ontology, logic, and epistemology: tr truth th All the three sections deal with truth, but from different perspectives Ontology and epistemology: the mat aterial al truth of atoms (p, q, …) Logic: the for formal al truth of molecules (p  q, p  q, …) At the crossroad of logic and epistemology: epis istemic ic log

• gic

A couple of different combinations between these two concepts

A basic difference, in philosophy, between on

• ntol
• log
• gy and epis

istemol

• log
• gy

Ontology is about what is: bein ing Epistemology is about how to access to what is: kn know

• win

ing Log

• gic

ic is about everything mean anin ingfu ful A set of sets of sentences, related to each other in a formal language One common concern in ontology, logic, and epistemology: tr truth th All the three sections deal with truth, but from different perspectives Ontology and epistemology: the mat aterial al truth of atoms (p, q, …) Logic: the for formal al truth of molecules (p  q, p  q, …) At the crossroad of logic and epistemology: epis istemic ic log

• gic

A couple of different combinations between these two concepts

A basic difference, in philosophy, between on

• ntol
• log
• gy and epis

istemol

• log
• gy

Ontology is about what is: bein ing Epistemology is about how to access to what is: kn know

• win

ing Log

• gic

ic is about everything mean anin ingfu ful A set of sets of sentences, related to each other in a formal language One common concern in ontology, logic, and epistemology: tr truth th All the three sections deal with truth, but from different perspectives Ontology and epistemology: the mat aterial al truth of atoms (p, q, …) Logic: the for formal al truth of molecules (p  q, p  q, …) At the crossroad of logic and epistemology: epis istemic ic log

• gic

A couple of different combinations between these two concepts

A basic difference, in philosophy, between on

• ntol
• log
• gy and epis

istemol

• log
• gy

Ontology is about what is: bein ing Epistemology is about how to access to what is: kn know

• win

ing Log

• gic

ic is about everything mean anin ingfu ful A set of sets of sentences, related to each other in a formal language One common concern in ontology, logic, and epistemology: tr truth th All the three sections deal with truth, but from different perspectives Ontology and epistemology: the mat aterial al truth of atoms (p, q, …) Logic: the for formal al truth of molecules (p  q, p  q, …) At the crossroad of logic and epistemology: epis istemic ic log

• gic

A couple of different combinations between these two concepts

“Logic of epistemology”: about the foundations of scientific theories “Epistemic logic”: about the sentences with epistemic concepts “Epistemology of logic”: about the foundations of the theory of logic Two sorts of logic for epistemology: A logical analysis of epistemic concepts (Erkennntnislehre) (knowledge, belief, doubt, justification): epis iste temic ic log logic A logical analysis of the scientific methods (Wissenschaftslehre) (Bayesianism, causation, induction): for formal al epis istemolog logy Epistemic logic: What is it? A set of formal truths about sentences including modal operators Strong operators : K for knowledge, B for belief Weak operators : P for possible knowledge, C for possible belief A minimal criterion for logical relations: con

• nsis

istency

“Logic of epistemology”: about the foundations of scientific theories “Epistemic logic”: about the sentences with epistemic concepts “Epistemology of logic”: about the foundations of the theory of logic Two sorts of logic for epistemology: A logical analysis of epistemic concepts (Erkennntnislehre) (knowledge, belief, doubt, justification): epis iste temic ic log logic A logical analysis of the scientific methods (Wissenschaftslehre) (Bayesianism, causation, induction): for formal al epis istemolog logy Epistemic logic: What is it? A set of formal truths about sentences including modal operators Strong operators : K for knowledge, B for belief Weak operators : P for possible knowledge, C for possible belief A minimal criterion for logical relations: con

• nsis

istency

“Logic of epistemology”: about the foundations of scientific theories “Epistemic logic”: about the sentences with epistemic concepts “Epistemology of logic”: about the foundations of the theory of logic Two sorts of logic for epistemology: A logical analysis of epistemic concepts (Erkennntnislehre) (knowledge, belief, doubt, justification): epis iste temic ic log logic A logical analysis of the scientific methods (Wissenschaftslehre) (Bayesianism, causation, induction): for formal al epis istemolog logy Epistemic logic: What is it? A set of formal truths about sentences including modal operators Strong operators : K for knowledge, B for belief Weak operators : P for possible knowledge, C for possible belief A minimal criterion for logical relations: co consis istency

Epistemic logic: What is it for? A logical analysis of concepts through a set of relative axioms K-structure: p, p  q ├K q D-structure: ├D p  p T-structure: ├T p  p 4-structure: ├4 p  p 5-structure: ├5 p  p Epistemic paradoxes: unac accepted ted conclusions from ac accepted premises Examples: Fitch’s Paradox of Knowability, Moore’s Paradox How to solve a logical paradox? Resolution: reject one inference rule between axioms and theorems Dissolution: reject a premise as ill-formed

Epistemic logic: What is it for? A logical analysis of concepts through a set of relative axioms K-structure: p, p  q ├K q D-structure: ├D p  p T-structure: ├T p  p 4-structure: ├4 p  p 5-structure: ├5 p  p Epistemic paradoxes: unac accepted ted conclusions from ac accepted premises Examples: Fitch’s Paradox of Knowability, Moore’s Paradox How to solve a logical paradox? Resolution: reject one inference rule between axioms and theorems Dissolution: reject a premise as ill-formed

Epistemic logic: What is it for? A logical analysis of concepts through a set of relative axioms K-structure: p, p  q ├K q D-structure: ├D p  p T-structure: ├T p  p 4-structure: ├4 p  p 5-structure: ├5 p  p Epistemic paradoxes: unac accepted ted conclusions from ac accepted premises Examples: Fitch’s Paradox of Knowability, Moore’s Paradox How to solve a logical paradox? Resolution: reject one inference rule between axioms and theorems Dissolution: reject a premise as ill-formed

Epistemic logic: What is it for? A logical analysis of concepts through a set of relative axioms K-structure: p, p  q ├K q D-structure: ├D p  p T-structure: ├T p  p 4-structure: ├4 p  p 5-structure: ├5 p  p Epistemic paradoxes: unac accepted ted conclusions from ac accepted premises Examples: Fitch’s Paradox of Knowability, Moore’s Paradox How to solve a logical paradox? Resolution: reject one inference rule between axioms and theorems Dissolution: reject a premise as ill-formed

A trade-off between material and formal truth: in infor formal al validity (material truth of molecular sentences, i.e. logical relations) A discussion about the extr tra-valid lidity of axioms, outside logical systems How can the axioms of a logical system be justified themselves? Examples: the truth-clause Kp  p: Every sentence p that is kn known is thereby tr true If p is known, therefore p is true (in every T-model) Formal truths: logical relations true in every mod

• del

In every K-model, the truth of Kp entails the truth of p A relative sense of truth: truth-in-a-model (set of true sentences) Does it make sense to talk about extra-validity (cf. matter vs form)? Axioms and obviousness (axiom of parallels, LEM, truth-clause, etc.) Axioms are assumed to be obviously true, naturally accepted

A trade-off between material and formal truth: in infor formal al validity (material truth of molecular sentences, i.e. logical relations) A discussion about the extr tra-valid lidity of axioms, outside logical systems How can the axioms of a logical system be justified themselves? Examples: the truth-clause Kp  p: Every sentence p that is kn known is thereby tr true If p is known, therefore p is true (in every T-model) Formal truths: logical relations true in every mod

• del

In every K-model, the truth of Kp entails the truth of p A relative sense of truth: truth-in-a-model (set of true sentences) Does it make sense to talk about extra-validity (cf. matter vs form)? Axioms and obviousness (axiom of parallels, LEM, truth-clause, etc.) Axioms are assumed to be obviously true, naturally accepted

A trade-off between material and formal truth: in infor formal al validity (material truth of molecular sentences, i.e. logical relations) A discussion about the extr tra-valid lidity of axioms, outside logical systems How can the axioms of a logical system be justified themselves? Examples: the truth-clause Kp  p: Every sentence p that is kn known is thereby tr true If p is known, therefore p is true (in every T-model) Formal truths: logical relations true in every mod

• del

In every K-model, the truth of Kp entails the truth of p A relative sense of truth: truth-in-a-model (set of true sentences) Does it make sense to talk about extra-validity (cf. matter vs form)? Axioms and obviousness (axiom of parallels, LEM, truth-clause, etc.) Axioms are assumed to be obviously true, naturally accepted

A trade-off between material and formal truth: in infor formal al validity (material truth of molecular sentences, i.e. logical relations) A discussion about the extr tra-valid lidity of axioms, outside logical systems How can the axioms of a logical system be justified themselves? Examples: the truth-clause Kp  p: Every sentence p that is kn known is thereby tr true If p is known, therefore p is true (in every T-model) Formal truths: logical relations true in every mod

• del

In every K-model, the truth of Kp entails the truth of p A relative sense of truth: truth-in-a-model (set of true sentences) Does it make sense to talk about extr tra-validity (cf. matter vs form)? Axioms and obviousness (axiom of parallels, LEM, truth-clause, etc.) Axioms are assumed to be obviously true, naturally accepted

What if given axioms happen to be false? The whole argument is made irrelevant … … but neither mat ateriall lly, not for formall lly false Extra-validity has to do not with truth, but relevance Can an axiom be said to be “relevant” and “false” at once? Relevant for what? For whom? False of what? For whom? Is “relevance” another name for prag agmatic tic tr truth th? Back to the truth-clause Kp  p p: “I have a hand” The skeptic accepts this axiom, but denies the premise Kp Is such an axiom relevant for a skeptic, especially a Pyrrhonian?

What if given axioms happen to be false? The whole argument is made irrelevant … … but neither mat ateriall lly, not for formall lly false Extra-validity has to do not with truth, but relevance Can an axiom be said to be “relevant” and “false” at once? Relevant for what? For whom? False of what? For whom? Is “relevance” another name for prag agmatic tic tr truth th? Back to the truth-clause Kp  p p: “I have a hand” The skeptic accepts this axiom, but denies the premise Kp Is such an axiom relevant for a skeptic, especially a Pyrrhonian?

What if given axioms happen to be false? The whole argument is made irrelevant … … but neither mat ateriall lly, not for formall lly false Extra-validity has to do not with truth, but relevance Can an axiom be said to be “relevant” and “false” at once? Relevant for what? For whom? False of what? For whom? Is “relevance” another name for prag agmatic tic tr truth th? Back to the truth-clause Kp  p p: “I have a hand” The skeptic accepts this axiom, but denies the premise Kp Is such an axiom relevant for a skeptic, especially a Pyrrhonian?

Pragmatism, as understood here, means a way

• f doing philosophy that takes seriously the

practical human life as a starting point for all philosophic contemplation. (Martela 2010: 2)

Entailment thesis K,    ├ K ( and  are metavariables) : “I have a hand”, : “I am not a brain in a vat” A case of deaf dialogue: logical agreement, material disagreement

• G. E. Moore, Pyrrho: both accept the entailment thesis
• G. E. Moore: accepts K, accepts   , accepts K

Pyrrho: denies K, accepts   , denies K accepts K, accepts   , accepts K

• G. E. Moore: reasons by Modus Ponens

Pyrrho: reasons by Modus Tollens Dialogue needs a minimal ag agreement about the premises to be relevant (cf. Socratic dialogues: from for formal to mater terial al agreement, through consistency of the whole)

Entailment thesis K,    ├ K ( and  are metavariables) : “I have a hand”, : “I am not a brain in a vat” A case of deaf dialogue: logical agreement, material disagreement

• G. E. Moore, Pyrrho: both accept the entailment thesis
• G. E. Moore: accepts K, accepts   , accepts K

Pyrrho: denies K, accepts   , denies K (= accepts K, accepts   , accepts K ?)

• G. E. Moore: reasons by Modus Ponens

Pyrrho: reasons by Modus Tollens Dialogue needs a minimal ag agreement about the premises to be relevant (cf. Socratic dialogues: from for formal to mater terial al agreement, through consistency of the whole)

Entailment thesis K,    ├ K ( and  are metavariables) : “I have a hand”, : “I am not a brain in a vat” A case of deaf dialogue: logical agreement, material disagreement

• G. E. Moore, Pyrrho: both accept the entailment thesis
• G. E. Moore: accepts K, accepts   , accepts K

Pyrrho: denies K, accepts   , denies K (= accepts K, accepts   , accepts K ?)

• G. E. Moore: reasons by Modus Ponens

Pyrrho: reasons by Modus Tollens Dialogue needs a minimal ag agreement about the premises to be relevant (cf. Socratic dialogues: from for formal to mater terial al agreement, through consistency of the whole)

Log

• gic

ical al truth needs mater terial ial truth to be relevant (cf. truth-preservation) How to obtain material agreement? Any relevant logical truth needs a reflection about truth simpliciter How to warrant the truth of a sentence (material truth)? Is truth ab absolu lute or relati tive ve? A number of competing th theorie ies of f tr truth th: Correspondence (truth is related to corresponding facts) Coherence (truth is consistency between sentences/beliefs) Pragmatic (truth is an epistemic agreement between agents) Only 3 theories? No overlapping about the nature of truth? 2 opposite: ob

• bje

jective ve-subje jecti tive, on

• nti

tic-epis iste temic ic views of truth

Log

• gic

ical al truth needs mater terial ial truth to be relevant (cf. truth-preservation) How to obtain material agreement? Any relevant logical truth needs a reflection about truth simpliciter How to warrant the truth of a sentence (material truth)? Is truth ab absolu lute or relati tive ve? A number of competing th theorie ies of f tr truth th: Correspondence (truth is related to corresponding facts) Coherence (truth is consistency between sentences/beliefs) Pragmatic (truth is an epistemic agreement between agents) Only 3 theories? No overlapping about the nature of truth? 2 opposite: ob

• bje

jective ve-subje jecti tive, on

• nti

tic-epis iste temic ic views of truth

Log

• gic

ical al truth needs mater terial ial truth to be relevant (cf. truth-preservation) How to obtain material agreement? Any relevant logical truth needs a reflection about truth simpliciter How to warrant the truth of a sentence (material truth)? Is truth ab absolu lute or relati tive ve? A number of competing th theorie ies of f tr truth th: Correspondence (truth is related to corresponding facts) Coherence (truth is consistency between sentences/beliefs) Pragmatic (truth is an epistemic agreement between agents) Only 3 theories? No overlapping about the nature of truth? 2 opposite: ob

• bje

jective ve-subje jecti tive, on

• nti

tic-epis iste temic ic views of truth

Log

• gic

ical al truth needs mater terial ial truth to be relevant (cf. truth-preservation) How to obtain material agreement? Any relevant logical truth needs a reflection about truth simpliciter How to warrant the truth of a sentence (material truth)? Is truth ab absolu lute or relati tive ve? A number of competing th theorie ies of f tr truth th: Correspondence (truth is related to corresponding facts) Coherence (truth is consistency between sentences/beliefs) Pragmatic (truth is an epistemic agreement between agents) Only 3 theories? No overlap about the nature of truth? 2 opposite: ob

• bje

jective ve-subje jecti tive, on

• nti

tic-epis iste temic ic views of truth

Niiniluoto (2013): “Is truth absolute or relative?” A list of overlapping theories from the aforementioned pairs

• Fallibilism (strong, weak)
• Pragmatism
• Critical realism
• Probabilism
• Verisimilitude
• Cultural relativism
• Perspectivism
• Provability

Niiniluoto (2013): “Is truth absolute or relative?” A list of overlapping theories from the aforementioned pairs:

• Fallibilism (strong, weak)
• Pragmatism
• Critical realism
• Probabilism
• Verisimilitude
• Cultural relativism
• Perspectivism
• Provability

Subjective truth: Subjective relativism (Protagoras: “Man is the measurement of everything”) Bp  p Plato against Protagoras’ relativism: reduction ad absurdum (log logical al vs mate terial al truth) The agent a believes p: “This wine is sweet”, therefore p is true for a Bap  p The agent b disbelieves p, therefore p is false for b Bbp  p

Subjective truth: Subjective relativism (Protagoras: “Man is the measurement of everything”) Bp  p Plato against Protagoras’ relativism: reduction ad absurdum (log logical al vs mate terial al truth) The agent a believes p: “This wine is sweet”, therefore p is true for a Bap  p The agent b disbelieves p, therefore p is false for b Bbp  p

Plato’s reasoning by con

• ntrap

apos

• siti

tion

• n:   ,  ├ 
• 1. If both a and b are right, then it is right to state both p and p

├ (Bap  Bbp)  (p  p)

• 2. Now every contradiction is logically false, i.e. its negation is true

├ (p  p)

• 3. Therefore a and b cannot be right together, i.e. one of them is wrong

├ (Bap  Bbp) Niiniluoto (2013): according to Twardoswki, Protagorean personal truth predicate would violate classical principles of logic

Plato’s reasoning by con

• ntrap

apos

• siti

tion

• n:   ,  ├ 
• 1. If both a and b are right, then it is right to state both p and p

├ (Bap  Bbp)  (p  p)

• 2. Now every contradiction is logically false, i.e. its negation is true

├ (p  p)

• 3. Therefore a and b cannot be right together, i.e. one of them is wrong

├ (Bap  Bbp) Niiniluoto (2013): according to Twardoswki, Protagorean personal truth predicate would violate classical principles of logic

Plato’s reasoning by con

• ntrap

apos

• siti

tion

• n:   ,  ├ 
• 1. If both a and b are right, then it is right to state both p and p

├ (Bap  Bbp)  (p  p)

• 2. Now every contradiction is logically false, i.e. its negation is true

├ (p  p)

• 3. Therefore a and b cannot be right together, i.e. one of them is wrong

├ (Bap  Bbp) Niiniluoto (2013): according to Twardoswki, Protagorean personal truth predicate would violate classical principles of logic

Plato’s reasoning by con

• ntrap

apos

• siti

tion

• n:   ,  ├ 
• 1. If both a and b are right, then it is right to state both p and p

├ (Bap  Bbp)  (p  p)

• 2. Now every contradiction is logically false, i.e. its negation is true

├ (p  p)

• 3. Therefore a and b cannot be right together, i.e. one of them is wrong

├ (Bap  Bbp) Niiniluoto (2013): according to Twardoswki, Protagorean personal truth predicate would violate classical principles of logic

Plato’s reasoning by con

• ntrap

apos

• siti

tion

• n:   ,  ├ 
• 1. If both a and b are right, then it is right to state both p and p

├ (Bap  Bbp)  (p  p)

• 2. Now every contradiction is logically false, i.e. its negation is true

├ (p  p)

• 3. Therefore a and b cannot be right together, i.e. one of them is wrong

├ (Bap  Bbp) Niiniluoto (2013): according to Twardoswki, Protagorean personal truth predicate would violate classical principles of logic

Plato assumes ob

• bje

jecti tive truth in the first premise: what is true for an agent is made true simpliciter (beyond anyone’s beliefs) Any agreement between a and b about p requires a ju justi tific ficati tion

• n of their

beliefs Tp  (Bp  Jp) A reversal of Plato’s classical definition of knowledge: epis istemic ic truth ├ Kp  (Bp  Tp  Jp) ├ Kp  Bp ├ Kp  Tp We assume Tarski’s T-scheme: Tp  p (in L) ├ Kp  Jp Gettier’s Problem: justification may be insufficient to ground truth ├\ Jp  Kp

Plato assumes ob

• bje

jecti tive truth in the first premise: what is true for an agent is made true simpliciter (beyond anyone’s beliefs) Any agreement between a and b about p requires a ju justi tific ficati tion

• n of their

beliefs Tp  (Bp  Jp) A reversal of Plato’s classical definition of knowledge: epis istemic ic truth ├ Kp  (Bp  Tp  Jp) ├ Kp  Bp ├ Kp  Tp We assume Tarski’s T-scheme: Tp  p (in L) ├ Kp  Jp Gettier’s Problem: justification may be insufficient to ground truth ├\ Jp  Kp

Plato assumes ob

• bje

jecti tive truth in the first premise: what is true for an agent is made true simpliciter (beyond anyone’s beliefs) Any agreement between a and b about p requires a ju justi tific ficati tion

• n of their

beliefs Tp  (Bp  Jp) A reversal of Plato’s classical definition of knowledge: epis istemic ic truth ├ Kp  (Bp  Tp  Jp) ├ Kp  Bp ├ Kp  Tp We assume Tarski’s T-scheme: Tp  p (in L) ├ Kp  Jp Gettier’s Problem: justification may be insufficient to ground truth ├\ Jp  Kp

Plato assumes ob

• bje

jecti tive truth in the first premise: what is true for an agent is made true simpliciter (beyond anyone’s beliefs) Any agreement between a and b about p requires a ju justi tific ficati tion

• n of their

beliefs Tp  (Bp  Jp) A reversal of Plato’s classical definition of knowledge: epis istemic ic truth ├ Kp  (Bp  Tp  Jp) ├ Kp  Bp ├ Kp  Tp We assume Tarski’s T-scheme: Tp  p (in L) ├ Kp  Jp Gettier’s Problem: justification may be insufficient to ground truth ├* Jp  Kp

Do a and b discuss within the same model, M? If they disagree about p then, by con

• nsis

istency (logical truth): p is true-in-Ma p is true-in-Mb (or, equivalently: p is false-in-Mb) “Deaf dialogue”: more than one language in the dialogue Log

• gic

ical al truth is the sole basic criterion for mat aterial truth, thus far Plato’s argument assumes uniqueness/universality of truth How to obtain common agreement about p, accordingly? Intersubjective truth (fallibilism) Which theory of truth gives the best explanation of the relation between knowledge, truth, belief, and justification? (cf. rele levan ance) My answer: epis istemic truth (truth as assertion: Tap, “p is true-for-a”)

Do a and b discuss within the same model, M? If they disagree about p then, by con

• nsis

istency (logical truth): p is true-in-Ma p is true-in-Mb (or, equivalently: p is false-in-Mb) “Deaf dialogue”: more than one language in the dialogue Log

• gic

ical al truth is the sole basic criterion for mat aterial truth, thus far Plato’s argument assumes uniqueness/universality of truth How to obtain common agreement about p, accordingly? Intersubjective truth (fallibilism) Which theory of truth gives the best explanation of the relation between knowledge, truth, belief, and justification? (cf. rele levan ance) My answer: epis istemic truth (truth as assertion: Tap, “p is true-for-a”)

Do a and b discuss within the same model, M? If they disagree about p then, by con

• nsis

istency (logical truth): p is true-in-Ma p is true-in-Mb (or, equivalently: p is false-in-Mb) “Deaf dialogue”: more than one language in the dialogue Log

• gic

ical al truth is the sole basic criterion for mat aterial truth, thus far Plato’s argument assumes uniqueness/universality of truth How to obtain common agreement about p, accordingly? Intersubjective truth (fallibilism) Which theory of truth gives the best explanation of the relation between knowledge, truth, belief, and justification? (cf. rele levan ance) My answer: epis istemic truth (truth as assertion: Tap, “p is true-for-a”)

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (1) Relative truth Tap fails to satisfy Von Wright’s truth-logic ├ Ta(p  q)  Tap  Taq ├ Tap  Ta(p  q) ├ Tap  Tap ├ Tap  TaTap ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (1) Relative truth Tap fails to satisfy Von Wright’s truth-logic ├ Ta(p  q)  Tap  Taq ├ Tap  Ta(p  q) ├ Tap  Tap ├ Tap  TaTap ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (1) Relative truth Tap fails to satisfy Von Wright’s truth-logic ├ Ta(p  q)  Tap  Taq ├ Tap  Ta(p  q) ├ Tap  Tap ├ Tap  TaTap ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (2) It introduces om

• mnis

iscie ience into the concept of truth: Tap, p  q, Taq

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (3) There are no external constraints for truth and falsity, accordingly

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (4) Tarski’s T-equivale alence cannot be sustained, because Tap  p does not make sense not valid: Bap  p and p  Bap are not accepted in doxastic logic

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (4) Tarski’s T-equivale alence cannot be sustained, because Tap  p does not make sense not valid: Bap  p and p  Bap are not accepted in doxastic logic

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (4) Tarski’s T-equivale alence cannot be sustained, because Tap  p does not make sense not valid: Bap  p and p  Bap are not accepted in doxastic logic

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (5) Either relative truth has absolute truth-conditions: self-refu futin ting Or it doesn’t, and it results in endless iterations: Bap, BaBap, BaBaBaBaBap, …

Niiniluoto (2013): epis iste temic ic definitions of truth are not relevant, for: (5) Either relative truth has absolute truth-conditions: self-refuting Or it doesn’t, and it results in endless iterations: Bap, BaBap, BaBaBaBaBap, …

Reply to (1) “Relative truth Tap fails to satisfy Von Wright’s truth-logic”

• Why should all of von Wright’s axioms be maintained?
• Why is relative truth reduced to the doxastic operator B?
• Isn’t relative truth a more complex operator like (Tap  Bap & Jap)?
• What if relative truth behaves like a weak modality, ?

Reply to (1) “Relative truth Tap fails to satisfy Von Wright’s truth-logic”

• Why should all of von Wright’s axioms be maintained?
• Why is relative truth reduced to the doxastic operator B?
• Isn’t relative truth a more complex operator like (Tap  Bap & Jap)?
• What if relative truth behaves like a weak modality, ?

Reply to (1) “Relative truth Tap fails to satisfy Von Wright’s truth-logic”

• Why should all of von Wright’s axioms be maintained?
• Why is relative truth reduced to the doxastic operator B?
• Isn’t relative truth a more complex operator like (Tap  Bap & Jap)?
• What if relative truth behaves like a weak modality, ?

Reply to (1) “Relative truth Tap fails to satisfy Von Wright’s truth-logic”

• Why should all of von Wright’s axioms be maintained?
• Why is relative truth reduced to the doxastic operator B?
• Isn’t relative truth a more complex operator like (Tap  Bap & Jap)?
• What if relative truth behaves like a weak modality, ?

Reply to (1) “Relative truth Tap fails to satisfy Von Wright’s truth-logic”

• Why should all of von Wright’s axioms be maintained?
• Why is relative truth reduced to the doxastic operator B?
• Isn’t relative truth a more complex operator like (Tap  Bap & Jap)?
• What if relative truth behaves like a weak modality, ?

Reply to (2) “It introduces the case of omniscience into the concept of truth” What is p  q, if not Ta(p  q)? Unless objective truth is restored, omniscience is just Modus Ponens

Reply to (2) “It introduces the case of omniscience into the concept of truth”

• What is p  q, if not Ta(p  q)?
• Unless objective truth is restored, omniscience is just Mod
• dus Pon
• nens

Reply to (2) “It introduces the case of omniscience into the concept of truth”

• What is p  q, if not Ta(p  q)?
• Unless objective truth is restored, omniscience is just Mod
• dus Pon
• nens

Reply to (3): “There are no external constraints for truth and falsity, accordingly”

• Tap can be enriched beyond merely personal belief (see (1))
• “Personal” needn’t mean “individual” (cf. intersubjective agreement)

Reply to (3): “There are no external constraints for truth and falsity, accordingly”

• Tap can be enriched beyond merely personal belief (see (1))
• “Personal” needn’t mean “single” (cf. intersubjective agreement)

Reply to (3): “There are no external constraints for truth and falsity, accordingly”

• Tap can be enriched beyond merely personal belief (see (1))
• “Personal” needn’t mean “single” (cf. in

inter tersubje jecti tive ve agreement)

Reply to (4): “Tarski’s T-equivalence cannot be sustained”

• Obje

jective ve truth is restored again through the formula “p”

• What if “p” means p-in-L, or “p for a”?

Reply to (4): “Tarski’s T-equivalence cannot be sustained”

• Obje

jective ve truth is restored again through the formula “p”

• What if “p” means p-in-L, or “p for a”?

Reply to (4): “Tarski’s T-equivalence cannot be sustained”

• Obje

jective ve truth is restored again through the formula “p”

• What if “p” means p-in-L, or “p for a”?

Reply to (5): “Either relative truth has absolute truth-conditions: self-refuting Or it doesn’t, and it results in endless iterations”

• Relativity needn’t be univ

iversal al, or self-referential

• What does iterated (relative) truth mean?

Endless iteration relies upon the failure of Axiom 4 (Hintikka (1962))

• An argument against the mod
• dal

al interpretation of truth, at the best What if truth is rendered as as asserti tion

• n, or tr

truth th-clai aim?

Reply to (5): “Either relative truth has absolute truth-conditions: self-refuting Or it doesn’t, and it results in endless iterations”

• Relativity needn’t be univ

iversal al, or self-referential

• What does iterated (relative) truth mean?

Endless iteration relies upon the failure of Axiom 4 (Hintikka (1962))

• An argument against the mod
• dal

al interpretation of truth, at the best What if truth is rendered as as asserti tion

• n, or tr

truth th-clai aim?

Reply to (5): “Either relative truth has absolute truth-conditions: self-refuting Or it doesn’t, and it results in endless iterations”

• Relativity needn’t be univ

iversal al, or self-referential

• What does iterated (relative) truth mean?

Endless iteration relies upon the failure of Axiom 4 (Hintikka (1962))

• An argument against the mod
• dal

al interpretation of truth, at the best What if truth is rendered as as asserti tion

• n, or tr

truth th-clai aim?

Reply to (5): “Either relative truth has absolute truth-conditions: self-refuting Or it doesn’t, and it results in endless iterations”

• Relativity needn’t be univ

iversal al, or self-referential

• What does iterated (relative) truth mean?

Endless iteration relies upon the failure of Axiom 4 (Hintikka (1962))

• An argument against the mod
• dal

al interpretation of truth, at the best What if truth is rendered as as asserti tion

• n, or tr

truth th-clai aim?

(1)-(5) reduce epistemic truth to mere relativism: Tap = Bap assume ob

• bje

jective ve truth in the definition of Ta (cf. Plato) Two biases in the objections to epis iste temic ic truth:

• Uniq

iqueness of truth is taken to be granted

• Truth is presented as a valu

alue (can there be more than one?) An alternative solution: defla lati tion

• nis

ism? “p is true”: the sentence S is (true-)in-M You can escape your shadow, by turning the light off You can avoid the debate about the nature of truth, by begging it out How to think of the nature of truth, if not as some ag agreement? With what: reality, system, community, …, ?

(1)-(5) reduce epistemic truth to mere relativism: Tap = Bap assume ob

• bje

jective ve truth in the definition of Ta (cf. Plato) Two biases in the objections to epis iste temic ic truth:

• Uniq

iqueness of truth is taken to be granted

• Truth is presented as a valu

alue (can there be more than one?) An alternative solution: defla lati tion

• nis

ism? “p is true”: the sentence S is (true-)in-M You can escape your shadow, by turning the light off You can avoid the debate about the nature of truth, by begging it out How to think of the nature of truth, if not as some ag agreement? With what: reality, system, community, …, ?

(1)-(5) reduce epistemic truth to mere relativism: Tap = Bap assume ob

• bje

jective ve truth in the definition of Ta (cf. Plato) Two biases in the objections to epis iste temic ic truth:

• Uniq

iqueness of truth is taken to be granted

• Truth is presented as a valu

alue (can there be more than one?) An alternative solution: defla lati tion

• nis

ism? “p is true”: the sentence S is (true-)in-M You can escape your shadow, by turning the light off You can avoid the debate about the nature of truth, by begging it out How to think of the nature of truth, if not as some ag agreement? With what: reality, system, community, …, ?

(1)-(5) reduce epistemic truth to mere relativism: Tap = Bap assume ob

• bje

jective ve truth in the definition of Ta (cf. Plato) Two biases in the objections to epis iste temic ic truth:

• Uniq

iqueness of truth is taken to be granted

• Truth is presented as a valu

alue (can there be more than one?) An alternative solution: defla lati tion

• nis

ism? “p is true”: the sentence S is (true-)in-M You can escape your shadow, by turning the light off You can avoid the debate about the nature of truth, by begging it out How to think of the nature of truth, if not as some ag agreement? With what: reality, system, community, …, ?

(1)-(5) reduce epistemic truth to mere relativism: Tap = Bap assume ob

• bje

jective ve truth in the definition of Ta (cf. Plato) Two biases in the objections to epis iste temic ic truth:

• Uniq

iqueness of truth is taken to be granted

• Truth is presented as a valu

alue (can there be more than one?) An alternative solution: defla lati tion

• nis

ism? “p is true”: the sentence S is (true-)in-M You can escape your shadow, by turning the light off You can avoid the debate about the nature of truth, by begging it out How to think of the nature of truth, if not as some ag agreement? With what: reality, system, community, …, ?

Russell (1923): truth as correspondence with fac facts ts A proposition is therefore a class of facts, psychological or linguistic, defined as standing into a certain relation (it can be either assertion or denial, according to the cases) to a certain fact. Beliefs/sentences: truth-bearers “Psychological facts”: assertions

Russell (1923): truth as correspondence with fac facts ts A proposition is therefore a class of facts, psychological or linguistic, defined as standing into a certain relation (it can be either assertion or denial, according to the cases) to a certain fact. Fact: truth-maker Beliefs/sentences: truth-bearers “Psychological facts”: assertions, denials “Linguistic facts”: sentences (affirmative, negative) Beliefs/Sentences are individuated by a fact making these true A proposition is the class of such beliefs/sentences How to warrant the occurrence of such facts, in in prac actic tice?

Russell (1923): truth as correspondence with fac facts ts A proposition is therefore a class of facts, psychological or linguistic, defined as standing into a certain relation (it can be either assertion or denial, according to the cases) to a certain fact. Fact: truth-maker Beliefs/sentences: truth-bearers “Psychological facts”: assertions, denials “Linguistic facts”: sentences (affirmative, negative) Beliefs/Sentences are individuated by a fact making these true A proposition is the class of such beliefs/sentences How to warrant the occurrence of such facts, in in prac actic tice?

Russell (1923): truth as correspondence with fac facts ts A proposition is therefore a class of facts, psychological or linguistic, defined as standing into a certain relation (it can be either assertion or denial, according to the cases) to a certain fact. Fact: truth-maker Beliefs/sentences: truth-bearers “Psychological facts”: assertions, denials “Linguistic facts”: sentences (affirmative, negative) Beliefs/Sentences are individuated by a fact making these true A proposition is the class of such beliefs/sentences How to warrant the occurrence of such facts, in in prac actic tice?

Russell (1923): truth as correspondence with fac facts ts A proposition is therefore a class of facts, psychological or linguistic, defined as standing into a certain relation (it can be either assertion or denial, according to the cases) to a certain fact. Fact: truth-maker Beliefs/sentences: truth-bearers “Psychological facts”: assertions, denials “Linguistic facts”: sentences (affirmative, negative) Beliefs/Sentences are individuated by a fact making these true A proposition is the class of such beliefs/sentences How to warrant the occurrence of such facts, in in prac actic tice?

Peirce (1877: 7): truth as ideal convergence of op

• pin

inion ions The question therefore is, how is true belief (or belief in the real) distinguished from false belief (or belief in fiction). Now, as we have seen (…) the ideas of truth and falsehood, in their full development, appertain exclusively to the experiential method of settling opinion. Truth: agreement between speakers in an ideal community any sentence that ou

• ught

t to be believed by every agent the result of an inquiry process related to agreed beliefs What is the rationale (proto-logic) of such an inquiry process? How to come from simple sentences expressing beliefs to true propositions warranting knowledge?

Peirce (1877: 7): truth as ideal convergence of op

• pin

inion ions The question therefore is, how is true belief (or belief in the real) distinguished from false belief (or belief in fiction). Now, as we have seen (…) the ideas of truth and falsehood, in their full development, appertain exclusively to the experiential method of settling opinion. Truth: agreement between speakers in an ideal community any sentence that ou

• ught

t to be believed by every agent the result of an inquiry process related to agreed beliefs What is the rationale (proto-logic) of such an inquiry process? How to come from simple sentences expressing beliefs to true propositions warranting knowledge? Peirce (1877: 7): truth as ideal convergence of op

• pin

inion ions

Peirce (1877: 7): truth as ideal convergence of op

• pin

inion ions The question therefore is, how is true belief (or belief in the real) distinguished from false belief (or belief in fiction). Now, as we have seen (…) the ideas of truth and falsehood, in their full development, appertain exclusively to the experiential method of settling opinion. Truth: agreement between speakers in an ideal community any sentence that ou

• ught

t to be believed by every agent the result of an inquiry process related to agreed beliefs What is the rationale (proto-logic) of such an inquiry process? How to come from simple sentences expressing beliefs to true propositions warranting knowledge?

2. Truth-Values

Frege: truth is the valu value of a proposition (its logical con

• ntent)

The word “true” indicates the aim of logic as does “beautiful” that of aesthetics or “good” that of ethics. (Frege 1956: 289) Cannot truth be relative as a multi-faceted value (cf. cultu ltural al relati tivis vism)? Proposition: the “thought” (Gedanke) expressed by a sentence “A sentence proper is a proper name, and its Bedeutung, if it has one, is a truth-value: the True or the False. Truth is an ob

• bje

jecti tive value: only one value for every proposition (true/false), but different propositions (senses) for the same value

Frege: truth is the valu value of a proposition (its logical con

• ntent)

The word “true” indicates the aim of logic as does “beautiful” that of aesthetics or “good” that of ethics. (Frege 1956: 289) Cannot truth be relative as a multi-faceted value (cf. cultu ltural al relati tivis vism)? Proposition: the “thought” (Gedanke) expressed by a sentence “A sentence proper is a proper name, and its Bedeutung, if it has one, is a truth-value: the True or the False. Truth is an ob

• bje

jecti tive value: only one value for every proposition (true/false), but different propositions (senses) for the same value

Frege: truth is the valu value of a proposition (its logical con

• ntent)

The word “true” indicates the aim of logic as does “beautiful” that of aesthetics or “good” that of ethics. (Frege 1956: 289) Cannot truth be relative as a multi-faceted value (cf. cultu ltural al relati tivis vism)? Proposition: the “thought” (Gedanke) expressed by a sentence A sentence proper is a proper name, and its reference, if it has one, is a truth-value: the True or the False. Truth is an ob

• bje

jecti tive value: only one value for every proposition (true/false), but different propositions (senses) for the same value

Frege: truth is the valu value of a proposition (its logical con

• ntent)

The word “true” indicates the aim of logic as does “beautiful” that of aesthetics or “good” that of ethics. (Frege 1956: 289) Cannot truth be relative as a multi-faceted value (cf. cultu ltural al relati tivis vism)? Proposition: the “thought” (Gedanke) expressed by a sentence A sentence proper is a proper name, and its reference, if it has one, is a truth-value: the True or the False. Truth is an ob

• bje

jecti tive value: only one value for every proposition (true/false), but different propositions (senses) for the same value

“Frege’s Axiom” (Suszko): a unique referent for declarative sentences We are therefore driven into accepting the truth-value of a sentence as constituting its reference. By the truth value of a sentence I understand the circumstance that it is true or false. There are no further truth-

• values. For brevity I call the one the True, the other the False. Every

declarative sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its reference, if it has

• ne, is either the true or the false.

(Frege 1960: 63) One, or two truth-values? The meaning of biv ivale lence “Falsity”: whatever rejected by the speaker in the inquiry process Only one expected ted value, two possible outcomes (success vs failure)

“Frege’s Axiom” (Suszko): a unique referent for declarative sentences We are therefore driven into accepting the truth-value of a sentence as constituting its reference. By the truth value of a sentence I understand the circumstance that it is true or false. There are no further truth-

• values. For brevity I call the one the True, the other the False. Every

declarative sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its reference, if it has

• ne, is either the true or the false.

(Frege 1960: 63) One, or two truth-values? The meaning of biv ivale lence “Falsity”: whatever rejected by the speaker in the inquiry process Only one expected ted value, two possible outcomes (success vs failure)

2 preconditions for sentences to express a “thought” (Frege 1960: 127)

• A common object of investigation:

The being of a thought may also be taken to lie in the possibility of different thinkers’ grasping the thought as one and the same thought.

• An object prior to any investigation:

But even the act of grasping a thought is not a production of the thought, is not an act of setting its parts in order; for the thought was already true, and so was already there with its parts in order, before it was

• grasped. A traveler who crosses a mountain-range does not thereby

make the mountain-range; no more does the judging subject make a thought by acknowledging its truth. Thought is prior to judgment; what is prior to thought itself?

2 preconditions for sentences to express a “thought” (Frege 1960: 127)

• A common object of investigation:

The being of a thought may also be taken to lie in the possibility of different thinkers’ grasping the thought as one and the same thought.

• An object prior to any investigation:

But even the act of grasping a thought is not a production of the thought, is not an act of setting its parts in order; for the thought was already true, and so was already there with its parts in order, before it was

• grasped. A traveler who crosses a mountain-range does not thereby

make the mountain-range; no more does the judging subject make a thought by acknowledging its truth. Thought is prior to judgment; what is prior to thought itself?

2 preconditions for sentences to express a “thought” (Frege 1960: 127)

• A common object of investigation:

The being of a thought may also be taken to lie in the possibility of different thinkers’ grasping the thought as one and the same thought.

• An object prior to any investigation:

But even the act of grasping a thought is not a production of the thought, is not an act of setting its parts in order; for the thought was already true, and so was already there with its parts in order, before it was

• grasped. A traveler who crosses a mountain-range does not thereby

make the mountain-range; no more does the judging subject make a thought by acknowledging its truth. Thought is prior to judgment; what is prior to thought itself?

2 preconditions for sentences to express a “thought” (Frege 1960: 127)

• A common object of investigation:

The being of a thought may also be taken to lie in the possibility of different thinkers’ grasping the thought as one and the same thought.

• An object prior to any investigation:

But even the act of grasping a thought is not a production of the thought, is not an act of setting its parts in order; for the thought was already true, and so was already there with its parts in order, before it was

• grasped. A traveler who crosses a mountain-range does not thereby

make the mountain-range; no more does the judging subject make a thought by acknowledging its truth. Thought is prior to judgment; what is prior to thought itself?

2 problems:

• 1. The reference: a “truth-value”, not a fact? (cf. Slingshot’s Argument)

The theory with which Frege’s name is especially associated is one which is apt to strike one at first rather fantastic, being usually expressed as a theory that sentences are names of truth-values. (Prior 1953: 55)

• 2. What is a Fregean tr

truth-make ker, accordingly? The value is not an ideal ob

• bject, but an ideal ac

activi vity ty of agreement It is the striving for truth that drives us always to advance from the sense to the reference. (Frege 1960: 63)

2 problems:

• 1. The reference: a “truth-value”, not a fact? (cf. Slingshot’s Argument)

The theory with which Frege’s name is especially associated is one which is apt to strike one at first rather fantastic, being usually expressed as a theory that sentences are names of truth-values. (Prior 1953: 55)

• 2. What is a Fregean tr

truth-make ker, accordingly? The value is not an ideal ob

• bject, but an ideal ac

activi vity ty of agreement It is the striving for truth that drives us always to advance from the sense to the reference. (Frege 1960: 63)

2 problems:

• 1. The reference: a “truth-value”, not a fact? (cf. Slingshot’s Argument)

The theory with which Frege’s name is especially associated is one which is apt to strike one at first rather fantastic, being usually expressed as a theory that sentences are names of truth-values. (Prior 1953: 55)

• 2. What is a Fregean tr

truth-make ker, accordingly? The value is not an ideal ob

• bject, but an ideal ac

activi vity ty of agreement It is the striving for truth that drives us always to advance from the sense to the reference. (Frege 1960: 63)

Frege on skeptics: scientific models assume existence (no ju justi tifi ficat ation ion) Assumption (judgeable content) vs Assertion (judgment) of propositions Idealists or sceptics will perhaps long since have objected: ‘You talk, without further ado, of the Moon as an object; but how do you know that the name ‘the Moon’ has any reference? How do you know anything whatsoever has a reference?’ I reply that when we say ‘the Moon’, we do not intend to speak of our idea of the Moon, nor are we satisfied with the sense alone, but we presuppose a reference.” (Frege 1960: 61) Bivalence holds for sentences whose referents are assumed

• some sentences are neither-true-nor-false
• these do not express prop
• pos
• siti

tion

• ns (out of the scientific inquiry)

Frege on skeptics: scientific models assume existence (no ju justi tifi ficat ation ion) Assumption (judgeable content) vs Assertion (judgment) of propositions Idealists or sceptics will perhaps long since have objected: ‘You talk, without further ado, of the Moon as an object; but how do you know that the name ‘the Moon’ has any reference? How do you know anything whatsoever has a reference?’ I reply that when we say ‘the Moon’, we do not intend to speak of our idea of the Moon, nor are we satisfied with the sense alone, but we presuppose a reference.” (Frege 1960: 61) Bivalence holds for sentences whose referents are assumed

• some sentences are neither-true-nor-false
• these do not express prop
• pos
• siti

tion

• ns (out of the scientific inquiry)

The scientific inquiry: a question-answer game A propositional question (Satzfrage) contains a demand that we should either acknowledge the truth of a thought, or reject it as false. (…) The answer to a question is an assertion based upon a judgment; this is so equally whether the answer is affirmative or negative. (Frege 1960: 117) A three-fold distinction: sentence, prop

• pos
• siti

tion

• n, sta

tatement (judgment) Logic: a science related to the laws of truth-preservation A sentence is the expression of a proposition The statement “p” is a tr truth th-clai aim: acknowledging the truth of p Assertion ion: a truth-claim, the statement that p (“p is the case”)

The scientific inquiry: a question-answer game A propositional question (Satzfrage) contains a demand that we should either acknowledge the truth of a thought, or reject it as false. (…) The answer to a question is an assertion based upon a judgment; this is so equally whether the answer is affirmative or negative. (Frege 1960: 117) A three-fold distinction: sentence, prop

• pos
• siti

tion

• n, sta

tatement (judgment) Logic: a science related to the laws of truth-preservation A sentence is the expression of a proposition The statement “p” is a tr truth th-clai aim: acknowledging the truth of p Assertion ion: a truth-claim, the statement that p (“p is the case”)

The scientific inquiry: a question-answer game A propositional question (Satzfrage) contains a demand that we should either acknowledge the truth of a thought, or reject it as false. (…) The answer to a question is an assertion based upon a judgment; this is so equally whether the answer is affirmative or negative. (Frege 1960: 117) A three-fold distinction: sentence, prop

• pos
• siti

tion

• n, sta

tatement (judgment) Logic: a science related to the laws of truth-preservation A sentence is the expression of a proposition The statement “p” is a tr truth th-clai aim: acknowledging the truth of p Assertion ion: a truth-claim, the statement that p (“p is the case”)

A description of the inquiry process: Begriffschrift (id ideog

• grap

aphy) Frege’s turnstile ├: symbol of a truth-claim ├p: “the proposition (that) p is the case” (stated by a speaker) “p is a logical truth (axiom, or theorem)” Difference between rela lativ ive (assertion) and ab absolu

• lute

te (logical truth) Three grades of epistemic truth ├p may mean “I take p to be true” “p is true for everyone-in-the-model” “p is true in every model (everyone-in-every-model)” There is no difference of natu ature between these three grades of epistemic truth, but a difference of degree (of acceptance)

A description of the inquiry process: Begriffschrift (id ideog

• grap

aphy) Frege’s turnstile ├: symbol of a truth-claim ├p: “the proposition (that) p is the case” (stated by a speaker) “p is a logical truth (axiom, or theorem)” Difference between rela lativ ive (assertion) and ab absolu

• lute

te (logical truth) Three grades of epistemic truth ├p may mean “I take p to be true” “p is true for everyone-in-the-model” “p is true in every model (everyone-in-every-model)” There is no difference of natu ature between these three grades of epistemic truth, but a difference of degree (of acceptance)

A description of the inquiry process: Begriffschrift (id ideog

• grap

aphy) Frege’s turnstile ├: symbol of a truth-claim ├p: “the proposition (that) p is the case” (stated by a speaker) “p is a logical truth (axiom, or theorem)” Difference between rela lativ ive (assertion) and ab absolu

• lute

te (logical truth) Three grades of epistemic truth ├p may mean “I take p to be true” “p is true for everyone-in-the-model” “p is true in every model (everyone-in-every-model)” There is no difference of natu ature between these three grades of epistemic truth, but a difference of degree (of acceptance)

A description of the inquiry process: Begriffschrift (id ideog

• grap

aphy) Frege’s turnstile ├: symbol of a truth-claim ├p: “the proposition (that) p is the case” (stated by a speaker) “p is a logical truth (axiom, or theorem)” Difference between rela lativ ive (assertion) and ab absolu

• lute

te (logical truth) Three grades of epistemic truth ├p may mean “I take p to be true” “p is true for everyone-in-the-model” “p is true in every model (everyone-in-every-model)” There is no difference of natu ature between these three grades of epistemic truth, but a difference of degree (of acceptance)

An example of reasoning : by Modus Pon

• nens

If the accused was not in Berlin at the time of the deed, he did not commit the murder; now the accused was not in Berlin at the time of the murder; therefore he did not commit the murder. (Frege 1960: 125) p: “the accused was not in Berlin at the time of the deed” q: “he (the accused) did not commit the murder” ├ (p  q) ├ (  ) ├  p ├  ├ (  ), ,  ├ q ├  Compare with the mod

• dal

al K-str tructu ture, replacing “” by “├”

An example of reasoning : by Modus Pon

• nens

If the accused was not in Berlin at the time of the deed, he did not commit the murder; now the accused was not in Berlin at the time of the murder; therefore he did not commit the murder. (Frege 1960: 125) p: “the accused was not in Berlin at the time of the deed” q: “he (the accused) did not commit the murder” ├ (p  q) ├ (  ) ├  p ├  ├ (  ), ,  ├ q ├  Compare with the mod

• dal

al K-str tructu ture, replacing “” by “├”

An example of reasoning : by Modus Pon

• nens

If the accused was not in Berlin at the time of the deed, he did not commit the murder; now the accused was not in Berlin at the time of the murder; therefore he did not commit the murder. (Frege 1960: 125) p: “the accused was not in Berlin at the time of the deed” q: “he (the accused) did not commit the murder” ├ (p  q) ├ (  ) ├ p ├  ├ (  ), ,  ├ q ├  Compare with the mod

• dal

al K-str tructu ture, replacing “” by “├”

An example of reasoning : by Modus Pon

• nens

If the accused was not in Berlin at the time of the deed, he did not commit the murder; now the accused was not in Berlin at the time of the murder; therefore he did not commit the murder. (Frege 1960: 125) p: “the accused was not in Berlin at the time of the deed” q: “he (the accused) did not commit the murder” ├ (p  q) ├ (  ) ├ p ├  ├ (  ), ,  ├ q ├  Compare with the mod

• dal

al K-str tructu ture, replacing “” by “├”

An example of reasoning : by Modus Pon

• nens

If the accused was not in Berlin at the time of the deed, he did not commit the murder; now the accused was not in Berlin at the time of the murder; therefore he did not commit the murder. (Frege 1960: 125) p: “the accused was not in Berlin at the time of the deed” q: “he (the accused) did not commit the murder” ├ (p  q) ├ (  ) ├ p ├  ├ (  ), ,  ├ q ├  Compare with the mod

• dal

al K-str tructu ture, replacing “” by “├”

An example of reasoning : by Modus Pon

• nens

If the accused was not in Berlin at the time of the deed, he did not commit the murder; now the accused was not in Berlin at the time of the murder; therefore he did not commit the murder. (Frege 1960: 125) p: “the accused was not in Berlin at the time of the deed” q: “he (the accused) did not commit the murder” ├ (p  q) ├ (  ) ├ p ├  ├ (  ), ,  ├ q ├  Compare with the mod

• dal

al K-str tructu ture, replacing “” by “├”

Back to Niiniluoto (2003), objection #1 to epis iste temic truth: How to account for the failure of: ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap Reading Ta as a truth-claim, or assertion ├:

• asserting a disjunction needn’t entail any of the disjuncts (cf. -E)
• failure of conclusive evidence may prevent from asserting either (Ta)
• what should asserting an assertion mean?

Assertion is not an operator but, rather, an operand: the log logic ical al valu alue at hand in any scientific inquiry

Back to Niiniluoto (2003), objection #1 to epis iste temic truth: How to account for the failure of: ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap Reading Ta as a truth-claim, or assertion ├:

• asserting a disjunction needn’t entail any of the disjuncts (cf. -E)
• failure of conclusive evidence may prevent from asserting either (Ta)
• what should asserting an assertion mean?

Assertion is not an operator but, rather, an operand: the log logic ical al valu alue at hand in any scientific inquiry

Back to Niiniluoto (2003), objection #1 to epis iste temic truth: How to account for the failure of: ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap Reading Ta as a truth-claim, or assertion ├:

• asserting a disjunction needn’t entail any of the disjuncts (cf. -E)
• failure of conclusive evidence may prevent from asserting either (Ta)
• what should asserting an assertion mean?

Assertion is not an operator but, rather, an operand: the log logic ical al valu alue at hand in any scientific inquiry

Back to Niiniluoto (2003), objection #1 to epis iste temic truth: How to account for the failure of: ├* Ta(p  q)  Tap  Taq ├* Tap  Tap ├* TaTap  Tap Reading Ta as a truth-claim, or assertion ├:

• asserting a disjunction needn’t entail any of the disjuncts (cf. -E)
• failure of conclusive evidence may prevent from asserting either (Ta)
• what should asserting an assertion mean?

Assertion is not an operator but, rather, an operand: the log logic ical al valu alue at hand in any scientific inquiry

3. The like

A Questi tion

• n-Answer Semantic

tics for a logic of epis iste temic ic truth Any sentence p of a language has:

• a sense: a set of n ordered questions about p

Q(p) = q1(p), …, qn(p)

• a reference: a corresponding set of ordered answers

A(p) = a1(p), …, an(p) n: the number of rele levan ant questions expressing the value of p Frege: n = 1, i.e. “Is p true?” There is only one sort of judgment: assertive judgment

• either a1(p) = 1, therefore p is (claimed to be) tr

true

• or a1(p) = 0, therefore p is (claimed to be) fals

false Frege assumes that every sentence can be assessed about its value For every p: a(p) = 1 or a(p) = 0, i.e. a(p) = 1

A Questi tion

• n-Answer Semantic

tics for a logic of epis iste temic ic truth Any sentence p of a language has:

• a sense: a set of n ordered questions about p

Q(p) = q1(p), …, qn(p)

• a reference: a corresponding set of ordered answers

A(p) = a1(p), …, an(p) n: the number of rele levan ant questions expressing the value of p Frege: n = 1, i.e. “Is p true?” There is only one sort of judgment: assertive judgment

• either a1(p) = 1, therefore p is (claimed to be) tr

true

• or a1(p) = 0, therefore p is (claimed to be) fals

false Frege assumes that every sentence can be assessed about its value For every p: a(p) = 1 or a(p) = 0, i.e. a(p) = 1

A Questi tion

• n-Answer Semantic

tics for a logic of epis iste temic ic truth Any sentence p of a language has:

• a sense: a set of n ordered questions about p

Q(p) = q1(p), …, qn(p)

• a reference: a corresponding set of ordered answers

A(p) = a1(p), …, an(p) n: the number of rele levan ant questions expressing the value of p Frege: n = 1, i.e. “Is p accepted?” There is only one sort of judgment: assertive judgment

• either a1(p) = 1, therefore p is (claimed to be) tr

true

• or a1(p) = 0, therefore p is (claimed to be) fals

false Frege assumes that every sentence can be assessed about its value For every p: a(p) = 1 or a(p) = 0, i.e. a(p) = 1

A Questi tion

• n-Answer Semantic

tics for a logic of epis iste temic ic truth Any sentence p of a language has:

• a sense: a set of n ordered questions about p

Q(p) = q1(p), …, qn(p)

• a reference: a corresponding set of ordered answers

A(p) = a1(p), …, an(p) n: the number of rele levan ant questions expressing the value of p Frege: n = 1, i.e. “Is p accepted?” There is only one sort of judgment: assertive judgment

• either a1(p) = 1, therefore p is (claimed to be) tr

true

• or a1(p) = 0, therefore p is (claimed to be) fals

false Frege assumes that every sentence can be assessed about its value For every p: a(p) = 1 or a(p) = 0, i.e. a(p) = 1

A Questi tion

• n-Answer Semantic

tics for a logic of epis iste temic ic truth Any sentence p of a language has:

• a sense: a set of n ordered questions about p

Q(p) = q1(p), …, qn(p)

• a reference: a corresponding set of ordered answers

A(p) = a1(p), …, an(p) n: the number of rele levan ant questions expressing the value of p Frege: n = 1, i.e. “Is p accepted?” There is only one sort of judgment: assertive judgment

• either a(p) = 1, therefore p is (claimed to be) tr

true

• or a(p) = 0, therefore p is (claimed to be) fals

alse Frege assumes that every sentence can be assessed about its value For every p: a(p) = 1 or a(p) = 0, i.e. a(p) = 1

A Questi tion

• n-Answer Semantic

tics for a logic of epis iste temic ic truth Any sentence p of a language has:

• a sense: a set of n ordered questions about p

Q(p) = q1(p), …, qn(p)

• a reference: a corresponding set of ordered answers

A(p) = a1(p), …, an(p) n: the number of rele levan ant questions expressing the value of p Frege: n = 1, i.e. “Is p accepted?” There is only one sort of judgment: assertive judgment

• either a(p) = 1, therefore p is (claimed to be) tr

true

• or a(p) = 0, therefore p is (claimed to be) fals

alse Frege assumes that every sentence can be assessed about its value For every p: a(p) = 1 or a(p) = 0, i.e. a(p) = 1

On negati tive ju judgments ts: sentential vs statemental negation

• Not every sentence can be asserted or denied:

Positive assertion: “p is is the case” (as assertion ion) Negative assertion: “p is is not the case”, or “p is the case” (strong denial al)

• Two in

independent logical values (n = 2): ac acceptan ance, and denial al aj(p) = 1 iff p is accepted aj(p) = 0 iff p is denied (not accepted) A broader logic of acceptance and refusal: Q(p) = q1(p),q2(p) q1(p): “Is p accepted?” q2(p): “Is p denied”?

On negati tive ju judgments ts: sentential vs statemental negation

• Not every sentence can be asserted or denied:

Positive assertion: “p is is the case” (as assertion ion) Negative assertion: “p is is not the case”, or “p is the case” (strong denial al)

• Two in

independent logical values (n = 2): ac acceptan ance, and denial al aj(p) = 1 iff p is accepted aj(p) = 0 iff p is denied (not accepted) A broader logic of acceptance and refusal: Q(p) = q1(p),q2(p) q1(p): “Is p accepted?” q2(p): “Is p denied”?

On negati tive ju judgments ts: sentential vs statemental negation

• Not every sentence can be asserted or denied:

Positive assertion: “p is is the case” (as assertion ion) Negative assertion: “p is is not the case”, or “p is the case” (strong denial al)

• Two in

independent logical values (n = 2): ac acceptan ance, and denial al aj(p) = 1 iff p is accepted aj(p) = 0 iff p is denied (not accepted) A broader logic of acceptance and refusal: Q(p) = q1(p),q2(p) q1(p): “Is p accepted?” q2(p): “Is p denied”?

On negati tive ju judgments ts: sentential vs statemental negation

• Not every sentence can be asserted or denied:

Positive assertion: “p is is the case” (as assertion ion) Negative assertion: “p is is not the case”, or “p is the case” (strong denial al)

• Two in

independent logical values (n = 2): ac acceptan ance, and denial al aj(p) = 1 iff p is accepted aj(p) = 0 iff p is denied (not accepted) A broader logic of acceptance and refusal: Q(p) = q1(p),q2(p) q1(p): “Is p accepted?” q2(p): “Is p denied”?

The logical value of a sentence p is the resulting pair of answers to it: 1,1, 1,0, 0,1, 0,0 Frege’s “truth-values” T and F correspond to 1,0 and 0,1 1,1 and 0,0 correspond to the “glutty” (B) and “gappy” (N) values Man any-valuedness: there is more than 2 sorts of statements of p Prag agmati tic bivalence: there are only 2 sorts of answers to each question consistency: no sentence can be both accepted ted and denied There can be various constraints on a truth-claim 1,1: weak affirmation (plausible evidence) for par arac acon

• nsis

istent logics 0,0: strong affirmation (conclusive evidence) for par arac acom

• mple

lete te logics

The logical value of a sentence p is the resulting pair of answers to it: 1,1, 1,0, 0,1, 0,0 Frege’s “truth-values” T and F correspond to 1,0 and 0,1 1,1 and 0,0 correspond to the “glutty” (B) and “gappy” (N) values Man any-valuedness: there is more than 2 sorts of statements of p Prag agmati tic bivalence: there are only 2 sorts of answers to each question consistency: no sentence can be both accepted ted and denied There can be various constraints on a truth-claim 1,1: weak affirmation (plausible evidence) for par arac acon

• nsis

istent logics 0,0: strong affirmation (conclusive evidence) for par arac acom

• mple

lete te logics

The logical value of a sentence p is the resulting pair of answers to it: 1,1, 1,0, 0,1, 0,0 Frege’s “truth-values” T and F correspond to 1,0 and 0,1 1,1 and 0,0 correspond to the “glutty” (B) and “gappy” (N) values Man any-valuedness: there is more than 2 sorts of statements of p Prag agmati tic bivalence: there are only 2 sorts of answers to each question consistency: no sentence can be both accepted ted and denied There can be various constraints on a truth-claim 1,1: weak affirmation (plausible evidence) for par arac acon

• nsis

istent logics 0,0: strong affirmation (conclusive evidence) for par arac acom

• mple

lete te logics

The logical value of a sentence p is the resulting pair of answers to it: 1,1, 1,0, 0,1, 0,0 Frege’s “truth-values” T and F correspond to 1,0 and 0,1 1,1 and 0,0 correspond to the “glutty” (B) and “gappy” (N) values Man any-valuedness: there is more than 2 sorts of statements of p Prag agmati tic bivalence: there are only 2 sorts of answers to each question consistency: no sentence can be both accepted ted and denied There can be various constraints on a truth-claim 1,1: weak affirmation (plausible evidence) for par arac acon

• nsis

istent logics 0,0: strong affirmation (conclusive evidence) for par arac acom

• mple

lete te logics

The logical value of a sentence p is the resulting pair of answers to it: 1,1, 1,0, 0,1, 0,0 Frege’s “truth-values” T and F correspond to 1,0 and 0,1 1,1 and 0,0 correspond to the “glutty” (B) and “gappy” (N) values Man any-valuedness: there is more than 2 sorts of statements of p Prag agmati tic bivalence: there are only 2 sorts of answers to each question consistency: no sentence can be both accepted ted and denied There can be various constraints on a truth-claim 1,1: weak affirmation (plausible evidence) for par arac acon

• nsis

istent logics 0,0: strong affirmation (conclusive evidence) for par arac acom

• mple

lete te logics

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ question about a proposition: q1(…) or q2(…) ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p: q1(p) ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p: q2(p) │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ the assertion of a proposition: a1(…) or a2(…) ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ┼ p assertion or denial of p (p is the case, or p is not the case) ├ the assertion of p (p is the case): a1(p) = 1 ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ┼ p assertion or denial of p (p is the case, or p is not the case) ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ┼ p assertion or denial of p (p is the case, or p is not the case) ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case): a2(p) = 1 ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ┼ p assertion or denial of p (p is the case, or p is not the case) ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) + one additional judgment: denial al ┤ the denial of p (not: p is the case)

Frege’s Begriffschrift: an ideography about propositions and judgments ─ content stroke: symbol for propositions ─ p the proposition (that) p ┬ p the proposition that not-p │ judgment-stroke ┼ p assertion or denial of p (p is the case, or p is not the case) ├ the assertion of p (p is the case) ├┬ the assertion of not-p (p is not the case) + one additional judgment: denial al ┤ the denial of p (not: p is the case): a1(p) = 0

From epistemic logic to epistemology of logic:

• axioms of epistemic logic are made relevan

vant by equating K and ├

• as

asserti tion

• n, truth-claim, belief are on a par
• no conflation of knowledge and belief: degrees of epistemic truth

From to sentential to statemental logic:

• truth-claim

aims as the prag agmati tic value of sentences (what is done with) science is an inquiry games where answers are given to questions

• Frege’s an

anti ti-psyc ychol

• log
• gis

ism made reference independent of the inquiry statements afford values within a logic of ac acceptan ance-preservation From classical logic to alternative language-games

• logic is an activity with ruled purposes: a language-game
• truth-preservation is only but one of these language-games
• op
• ppos
• siti

tion

• n beyond consequence: about agreement and disagreement

From epistemic logic to epistemology of logic:

• axioms of epistemic logic are made relevan

vant by equating K and ├

• as

asserti tion

• n, truth-claim, belief are on a par
• no conflation of knowledge and belief: degrees of epistemic truth

From to sentential to statemental logic:

• truth-claim

aims as the prag agmati tic value of sentences (what is done with) science is an inquiry games where answers are given to questions

• Frege’s an

anti ti-psyc ychol

• log
• gis

ism made reference independent of the inquiry statements afford values within a logic of ac acceptan ance-preservation From classical logic to alternative language-games

• logic is an activity with ruled purposes: a language-game
• truth-preservation is only but one of these language-games
• op
• ppos
• siti

tion

• n beyond consequence: about agreement and disagreement

From epistemic logic to epistemology of logic:

• axioms of epistemic logic are made relevan

vant by equating K and ├

• as

asserti tion

• n, truth-claim, belief are on a par
• no conflation of knowledge and belief: degrees of epistemic truth

From to sentential to statemental logic:

• truth-claim

aims as the prag agmati tic value of sentences (what is done with) science is an inquiry games where answers are given to questions

• Frege’s an

anti ti-psyc ychol

• log
• gis

ism made reference independent of the inquiry statements afford values within a logic of ac acceptan ance-preservation From classical logic to alternative language-games:

• logic is an activity with ruled purposes: a language-game
• truth-preservation is only but one of these language-games
• op
• ppos
• siti

tion

• n beyond consequence: about agreement and disagreement

L,Cn

L,Op

The language L: formal ontology (arbitrary entities)

• A finite set of mean

anin ingful objects, given by questions-answers Every object: a set of properties given by sentences

• A reversal in formal ontology: objects are made by sentences

The number of relevant sentences/questions is context-dependent

• Example: A(a) = 1011001, in a bits

itstr trin ing of 7 ordered answers Each single answer is nor

• rmati

tive: what ou

• ught be accepted/denied

The abstract relation Op: opposition (as difference)

• A set of relations between objects in L

The relation between logical values yields an algebraic semantics: QAS

The language L: formal ontology (arbitrary entities)

• A finite set of mean

anin ingful objects, given by questions-answers Every object: a set of properties given by sentences

• A reversal in formal ontology: objects are made by sentences

The number of relevant sentences/questions is context-dependent

• Example: A(a) = 1011001, in a bits

itstr trin ing of 7 ordered answers Each single answer is nor

• rmati

tive: what ou

• ught be accepted/denied

The abstract relation Op: opposition (as difference)

• A set of relations between objects in L

The relation between logical values yields an algebraic semantics: QAS

The language L: formal ontology (arbitrary entities)

• A finite set of mean

anin ingful objects, given by questions-answers Every object: a set of properties given by sentences

• A reversal in formal ontology: objects are made by sentences

The number of relevant sentences/questions is context-dependent

• Example: A(a) = 1011001, in a bits

itstr trin ing of 7 ordered answers Each single answer is nor

• rmati

tive: what ou

• ught be accepted/denied

The abstract relation Op: opposition (as difference)

• A set of relations between objects in L

The relation between logical values yields an algebraic semantics: QAS

The language L: formal ontology (arbitrary entities)

• A finite set of mean

anin ingful objects, given by questions-answers Every object: a set of properties given by sentences

• A reversal in formal ontology: objects are made by sentences

The number of relevant sentences/questions is context-dependent

• Example: A(a) = 1011001, in a bits

itstr trin ing of 7 ordered answers Each single answer is nor

• rmati

tive: what ou

• ught be accepted/denied

The abstract relation Op: opposition (as difference)

• A set of relations between objects in L

The relation between logical values yields an algebraic semantics: QAS

The language L: formal ontology (arbitrary entities)

• A finite set of mean

anin ingful objects, given by questions-answers Every object: a set of properties given by sentences

• A reversal in formal ontology: objects are made by sentences

The number of relevant sentences/questions is context-dependent

• Example: A(a) = 1011001, in a bits

itstr trin ing of 7 ordered answers Each single answer is nor

• rmati

tive: what ou

• ught be accepted/denied

The abstract relation Op: opposition (as difference)

• A set of relations between objects in L

The relation between logical values yields an algebraic semantics: QAS

The language L: formal ontology (arbitrary entities)

• A finite set of mean

anin ingful objects, given by questions-answers Every object: a set of properties given by sentences

• A reversal in formal ontology: objects are made by sentences

The number of relevant sentences/questions is context-dependent

• Example: A(a) = 1011001, in a bits

itstr trin ing of 7 ordered answers Each single answer is nor

• rmati

tive: what ou

• ught be accepted/denied

The abstract relation Op: opposition (as difference)

• A set of relations between objects in L

The relation between logical values yields an algebraic semantics: QAS

Re References

• G. Frege. “The Thought. A Logical Inquiry”, Mind, Vol. 65(1956): 289-311
• G. Frege. Transcription for the Philosophical Writings of Gottlob Frege, P. Geach & Max Black

(eds.), Basil Blackwell, Oxford (1960)

• J. Hintikka. Knowledge and Belief, Ithaca Press (1962)
• F. Martela. “Truth as intersubjective epistemological commitment – a pragmatic account of

truth”, draft (2010)

• C. S. Peirce. “The Fixation of Belief”, Popular Science Monthly, Vol. 12(1877): 1-15
• I. Niiniluoto. “Is truth relative or absolute?”, talk presented at the conference Logic and

Philosophy, University of Kiev (23-25 May 2013)

• B. Russell. “Truth-functions and meaning-functions”, in The Collected Pa-pers of Bertrand Russell.
• Vol. 9 : “Language, Mind and Matter : 1919-26”. London, Boston: Unwin Hyman, 1988: 158

Merci! Thank you! Cпасибо! Kiitos!