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All the ideas for 'Confessions', 'Primary Truths' and 'Philosophical Logic'

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51 ideas

4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic

15413	With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess]
	Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply.
	From: John P. Burgess (Philosophical Logic [2009], 2.8)
	A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader.

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula

15415	The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
	Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas.
	From: John P. Burgess (Philosophical Logic [2009], 2.9)
	A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas.

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic

15430	Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
	Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and →
	From: John P. Burgess (Philosophical Logic [2009], 6.4)

15431	It is still unsettled whether standard intuitionist logic is complete [Burgess]
	Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved.
	From: John P. Burgess (Philosophical Logic [2009], 6.9)

4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic

15429	Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess]
	Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'.
	From: John P. Burgess (Philosophical Logic [2009], 5.8)

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

15404	Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess]
	Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods.
	From: John P. Burgess (Philosophical Logic [2009], Pref)
	A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision.

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

15405	Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
	Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible.
	From: John P. Burgess (Philosophical Logic [2009], 1.1)

15427	The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
	Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive.
	From: John P. Burgess (Philosophical Logic [2009], 5.3)

15421	Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
	Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics.
	From: John P. Burgess (Philosophical Logic [2009], 4.1)
	A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens.

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic

15403	Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
	Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science.
	From: John P. Burgess (Philosophical Logic [2009], Pref)
	A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

15407	Formalising arguments favours lots of connectives; proving things favours having very few [Burgess]
	Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible.
	From: John P. Burgess (Philosophical Logic [2009], 1.4)
	A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or

15424	Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess]
	Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice.
	From: John P. Burgess (Philosophical Logic [2009], 5.2)
	A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense.

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

15409	All occurrences of variables in atomic formulas are free [Burgess]
	Full Idea: All occurrences of variables in atomic formulas are free.
	From: John P. Burgess (Philosophical Logic [2009], 1.7)

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions

15414	The denotation of a definite description is flexible, rather than rigid [Burgess]
	Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible.
	From: John P. Burgess (Philosophical Logic [2009], 2.9)
	A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid.

5. Theory of Logic / H. Proof Systems / 1. Proof Systems

15406	'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess]
	Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'.
	From: John P. Burgess (Philosophical Logic [2009], 1.4)
	A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths.

5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi

15425	The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
	Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty.
	From: John P. Burgess (Philosophical Logic [2009], 5.3)
	A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity.

15426	We can build one expanding sequence, instead of a chain of deductions [Burgess]
	Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries.
	From: John P. Burgess (Philosophical Logic [2009], 5.3)

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

15408	'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
	Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic.
	From: John P. Burgess (Philosophical Logic [2009], 1.5)

5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction

15418	Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]
	Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics.
	From: John P. Burgess (Philosophical Logic [2009], 3.3)

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

15412	Models leave out meaning, and just focus on truth values [Burgess]
	Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values.
	From: John P. Burgess (Philosophical Logic [2009], 2.2)
	A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world.

15411	We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
	Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these.
	From: John P. Burgess (Philosophical Logic [2009], 1.8)
	A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered.

15416	We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
	Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth.
	From: John P. Burgess (Philosophical Logic [2009], 3.2)

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

15428	The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
	Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false).
	From: John P. Burgess (Philosophical Logic [2009], 5.7)
	A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once?

7. Existence / A. Nature of Existence / 2. Types of Existence

16588	I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine]
	Full Idea: I sooner judged that what lacks all form does not exist, than thought of as something in between form and nothing, neither formed nor nothing, unformed and next to nothing.
	From: Augustine (Confessions [c.398], XII.6), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1
	A reaction: Scholastics were struck by the contrast between this remark, and the remark of Averroes (Idea 16587) that prime matter was halfway existence. Their two great authorities disagreed! This sort of thing stimulated the revival of metaphysics.

7. Existence / D. Theories of Reality / 1. Ontologies

22979	Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine]
	Full Idea: I am told that I can ask three sorts of questions - whether a thing is, what it is, and what sort it is.
	From: Augustine (Confessions [c.398], X.10)
	A reaction: This seems to be a very Aristotelian approach. I am pleased to see that what it is and what sort it is are not conflated. The first one must be its individual essence, and the second its generic essence.

10. Modality / A. Necessity / 4. De re / De dicto modality

15420	De re modality seems to apply to objects a concept intended for sentences [Burgess]
	Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences?
	From: John P. Burgess (Philosophical Logic [2009], 3.9)
	A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic.

10. Modality / A. Necessity / 6. Logical Necessity

15419	General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
	Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality.
	From: John P. Burgess (Philosophical Logic [2009], 3.8)
	A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?).

15417	Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
	Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension.
	From: John P. Burgess (Philosophical Logic [2009], 3.3)
	A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'.

10. Modality / B. Possibility / 8. Conditionals / a. Conditionals

15422	Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
	Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability).
	From: John P. Burgess (Philosophical Logic [2009], 4.3)

15423	It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
	Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning.
	From: John P. Burgess (Philosophical Logic [2009], 4.9)
	A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world.

12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities

9155	An a priori proof is independent of experience [Leibniz]
	Full Idea: An a priori proof is a proof independent of experience.
	From: Gottfried Leibniz (Primary Truths [1686])
	A reaction: Burge says Leibniz gave the first modern account of a priori knowledge. There may be no explicit reference to experience involved, but it would beg many questions to deny that implicit experience may be at the root of the proof.

12. Knowledge Sources / E. Direct Knowledge / 4. Memory

22981	Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine]
	Full Idea: The mind and the memory are one and the same. We even call the memory the mind, for when we tell a person to remember something, we tell them to 'bear this in mind', and when we forget something 'it slipped out of my mind'.
	From: Augustine (Confessions [c.398], X.14)
	A reaction: This idea has become familiar in modern neuroscience, I think, presumably because we do not find distinct types of neurons for consciousness and for memory.

22980	Memory contains innumerable principles of maths, as well as past sense experiences [Augustine]
	Full Idea: The memory contains the innumerable principles and laws of numbers and dimensions. None of these can have been conveyed to me by the bodily senses.
	From: Augustine (Confessions [c.398], X.12)
	A reaction: Even if you have a fairly empirical view of the sources of mathematics (a view with which I sympathise), it must by admitted that our endless extrapolations from the sources also reside in memory. So we remember thoughts as well as experiences.

22983	We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine]
	Full Idea: If we had to experience sorrow or fear every time that we mentioned these emotions, no one would be willing to speak of them.
	From: Augustine (Confessions [c.398], X.14)
	A reaction: Remembering the death of a loved one can trigger fresh grief, but remembering their dangerous illness from which they recovered no longer contains the feeling of fear.

22977	I can distinguish different smells even when I am not experiencing them [Augustine]
	Full Idea: I can distinguish the scent of lilies from that of violets, even though there is no scent at all in my nostrils.
	From: Augustine (Confessions [c.398], X.08)
	A reaction: Augustine has a nice introspective account of how we experience memory, and identifies lots of puzzling features. I know I can identify the smell of vinegar, but I can't bring it to mind, the way I can the appearance of roses.

22982	Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine]
	Full Idea: How can it be that my mind can be happy because of the joy that is in it, and yet my memory is not sad by reason of the sadness that is in it?
	From: Augustine (Confessions [c.398], X.14)
	A reaction: This seems to contradict his thought in Idea 22981, that memory and mind are the same. Recall seems to be a part of consciousness which is not fully wired up to the rest of the mind.

15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism

22978	Memory is so vast that I cannot recognise it as part of my mind [Augustine]
	Full Idea: The memory is a vast immeasurable sanctuary. It is part of my nature, but I cannot understand all that I am. Hence the mind is too narrow to contain itself entirely. Is the other part outside of itself, and not within it? How then can it be a part?
	From: Augustine (Confessions [c.398], X.08)
	A reaction: He seems to understand the mind as entirely consisting of consciousness. Nevertheless, this seems to be the first inklings of the modern externalist view of the mind.

16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self

22984	Without memory I could not even speak of myself [Augustine]
	Full Idea: I do not understand the power of memory that is in myself, although without it I could not even speak of myself.
	From: Augustine (Confessions [c.398], X.16)
	A reaction: Even if the self is not identical with memory, this idea seems to establish that memory is an essential aspect of the self. This point is neglected by those who see the self as an entity (the 'soul pearl') which persists through all experience.

16. Persons / F. Free Will / 6. Determinism / a. Determinism

5982	If the future does not exist, how can prophets see it? [Augustine]
	Full Idea: How do prophets see the future, if there is not a future to be seen?
	From: Augustine (Confessions [c.398], XI.17)
	A reaction: The answer, I suspect, is that prophets can't see the future. The prospect that the future already exists would seem to saboutage human freedom and responsibility, and point to Calvinist predestination, and even fatalism.

18. Thought / B. Mechanics of Thought / 5. Mental Files

22976	Memories are preserved separately, according to category [Augustine]
	Full Idea: In memory everything is preserved separately, according to its category.
	From: Augustine (Confessions [c.398], X.08)
	A reaction: This strikes me as the first seeds of the idea that the mind functions by means of mental files. Our memories of cats are 'close to' or 'linked to' our memories of dogs.

22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness

22985	Everyone wants happiness [Augustine]
	Full Idea: Surely happiness is what everyone wants, so much so that there can be none who do not want it?
	From: Augustine (Confessions [c.398], X.20)
	A reaction: His concept of happiness is, of course, religious. Occasionally you meet habitual grumblers about life who give the impression that they are only happy when they are discontented. So happiness is achieving desires, not feeling good?

27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time

5984	Maybe time is an extension of the mind [Augustine]
	Full Idea: I begin to wonder whether time is an extension of the mind itself.
	From: Augustine (Confessions [c.398], XI.26)
	A reaction: The observation that the mind creates a 'specious present' (spreading experience out over a short fraction of second) reinforces this. Personally I like David Marshall's proposal that consciousness is entirely memory, which would deny this idea.

22888	To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon]
	Full Idea: Augustine answers that for us to be aware of time it must exist only in the mind, …and the difference between past and future is just the difference between memory and anticipation.
	From: report of Augustine (Confessions [c.398]) by Adrian Bardon - Brief History of the Philosophy of Time 1 'Augustine's'
	A reaction: This is an extreme idealist view. Are we to say that the past consists only of what can be remembered, and the future only of what is anticipated? Absurd anti-realism, in my view. Where do his concepts come from, asks Le Poidevin.

27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block

5980	How can ten days ahead be a short time, if it doesn't exist? [Augustine]
	Full Idea: A short time ago or a short time ahead we might put at ten days, but how can anything which does not exist be either long or short?
	From: Augustine (Confessions [c.398], XI.15)
	A reaction: A nice question, which gets at the paradoxical nature of time very nicely. How can it be long, but non-existent? We could break the paradox by concluding '..and therefore time does exist', even though we can't see how.

27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism

5979	If the past is no longer, and the future is not yet, how can they exist? [Augustine]
	Full Idea: Of the three divisions of time, how can two, the past and the future, be, when the past no longer is, and the future is not yet?
	From: Augustine (Confessions [c.398], XI.14)
	A reaction: This is the oldest bewilderment about time, which naturally leads us to the thought that time cannot actually 'exist'. The remark implies that at least 'now' is safe, but that also succumbs to paradox pretty quickly.

27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time

5981	The whole of the current year is not present, so how can it exist? [Augustine]
	Full Idea: We cannot say that the whole of the current year is present, and if the whole of it is not present, the year is not present.
	From: Augustine (Confessions [c.398], XI.15)
	A reaction: Another nice way of presenting the paradox of time. We are in a particular year, so it has to be real.

27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time

5978	I know what time is, until someone asks me to explain it [Augustine]
	Full Idea: I know well enough what time is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled.
	From: Augustine (Confessions [c.398], XI.14)
	A reaction: A justly famous remark, even though it adds nothing to our knowledge of time. This sort of thought pushes us towards accepting many things as axiomatic, such as time, space, identity, persons, mind.

27. Natural Reality / D. Time / 2. Passage of Time / h. Change in time

5983	I disagree with the idea that time is nothing but cosmic movement [Augustine]
	Full Idea: I once heard a learned man say that time is nothing but the movement of the sun and the moon and the stars, but I do not agree.
	From: Augustine (Confessions [c.398], XI.22)
	A reaction: It is tempting to say that you either take time or movement as axiomatic, and describe one in terms of the other, but you are stuck unable to give the initial statement of the axiom without mentioning the second property you were saving for later.

27. Natural Reality / E. Cosmology / 3. The Beginning

5977	Heaven and earth must be created, because they are subject to change [Augustine]
	Full Idea: The fact that heaven and earth are there proclaims that they were created, for they are subject to change and variation; ..the meaning of change and variation is that something is there which was not there before.
	From: Augustine (Confessions [c.398], XI.04)
	A reaction: It seems possible that the underlying matter is eternal (as in various conservation laws, such as that of energy), and that all change is in the form rather than the substance.

28. God / A. Divine Nature / 5. God and Time

22887	If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon]
	Full Idea: If nothing existed by God before creation, then what could have happened to, or within, God that led God to decide to create the universe at that particular moment? Why would an eternal or perfect being want or need to change?
	From: report of Augustine (Confessions [c.398]) by Adrian Bardon - Brief History of the Philosophy of Time 1 'Augustine's'
	A reaction: I suppose you could reply that change is superior to stasis, but then why did God delay the creation?

5976	If God is outside time in eternity, can He hear prayers? [Augustine]
	Full Idea: O Lord, since you are outside time in eternity, are you unaware of the things that I tell you?
	From: Augustine (Confessions [c.398], XI.01)
	A reaction: This strikes me as the single most difficult and most elusive question about the nature of a supreme divine being. If the being is trapped in time, as we are, it is greatly diminished, and if it is outside, it is hard to see how it could be a participant.