In Fregean logic, reference does not equal extension
For logicians today, reference = (their) extension
The extension of a name is an object.
predicate →concept → class (extension)
(‘is red’) → (redness)→ (all red things)
extensionalism = all predicates in a sentence must have their own extension for the whole sentence to also have one.
In extensionalist logic ‘The king of France is bald’ is neither true nor false, but ‘meaningless’ because the ‘king of France’ has no extension. And if one part of that sentence has no extension, then the whole sentence cannot have one. The non-extensional part of ‘The king of France is bald’ makes the whole meaningless, just as the individual truth-values of p and q determine the truth of p & q.
Rigid Designators
If ‘The winner of the Derby’ is not a rigid designator, at some world it will not designate (our) George or his counterpart. If ‘George’ is a rigid designator, it will always refer to George at all possible worlds. Thus ‘The winner of the Derby’ is not a rigid designator because in our world it refers to George, but at other worlds it does not do so. It is, in fact, a description and therefore it is not referentially rigid. George also requires the de re necessary (or essential) property being the winner of the Derby. He has that property in our world, but it is not a necessary property.
i)◊ Franklin was not the first postmaster-general of the US.
ii)Franklin ◊ was not the first postmaster-general of the US.
The possibility operator in i) above is about the whole statement. ii) is about Franklin himself.
◊ Franklin… = de dicto – about the whole sentence
Franklin ◊ … = de re – about an individual (i.e., Franklin)
wide scope = de re
narrow scope = de re
The inventor of bifocals ◊ was not the first postmaster-general of the US.
Is about our Franklin in our world. That is because ‘◊’ doesn’t come before the definite description.
proper names → essential properties
descriptions→ contingent properties
How can we ‘designate’ an object’s essence only?
natural kind words – essential properties
‘being the winner of the Derby’ does not → the essential property winning the Derby
‘George’ – essential properties
Fregean Sense
‘Tony Blair’ – has no Fregean ‘sense’
‘Tony Blair’, in ‘Tony Blair is a liar’, has a sense.
Therefore the sense of the name ‘Tony Blair’ = ‘is a liar’ (or ‘the liar’). The sense of a name is the predicate of the sentence that is applied to the name’s reference. Thus:
[Tony Blair the liar] [is a liar] [?] – a tautology?
Russellian Sense
‘To understand a name is just to know which object it refers to.’ Therefore no ‘sense’? Russellian? Thus
the object = the sense
‘Hesperus’ is acceptable, but ‘the last star at night’ is not acceptable because it might not have been the case that it was the last star at night.
Russell’s on the Author of Waverley
Someone (better: something) wrote Waverley and was a poet. And nothing else wrote Waverley.
-Does not contain an ‘empty name’ or even a name, unlike ‘The author of Waverley’ which contains a definite description.
-Quantifiers = ‘each thing’, ‘two or more things’
-Variables instead of names
-Entity = the ‘value of a variable’
Truth-Conditions and T-Sentences
Isn’t it an analytic truth that statements require truth-conditions? That is, if these truth-conditions are conditions for the truth of all statements, then those without truth-conditions cannot, by definition, be true. Truth-conditions can take on many forms - even Platonic ones!
If the truth-conditions of a whole statement depend on the truth-conditions of all of its parts, then no wonder the truth-condition of ‘Snow is white’ is snow is white because every part of the truth-conditions must match those of each part of the statement.
Statements, just like objects, can have names. Thus ‘Snow is white’ is a name. And snow is white is the sentence itself. Thus ‘Snow is white’ is an example of Quine’s mention and snow is white is one of use.
‘Tony Blair’ = Tony Blair
‘Snow is white’ = snow is white
Why is ‘Snow is white’ the ‘name’ of a sentence, not a sentence itself? ‘By first naming the sentence and then using it.’ By first naming the sentence ‘Snow is white’ and then using snow is white. ‘Snow is white’ is naming because snow is white is the state of affairswhich is used.
Referential Opacity
‘Analytic’, ‘necessary’ and ‘a priori’ are not ‘referentially opaque’[Quine, etc.] because they have no reference themselves. They are so because they make the sentences in which they occur referentially opaque.
Thus
John the bachelor is unmarried.
is true. But
Necessarily, John the bachelor is unmarried.
is false. Thus ‘John’ and ‘John the bachelor’ become referentially opaque because the former is de dicto and the latter is de re. And John the bachelor does not have the necessary property being unmarried. But the word ‘bachelor’ does necessarily mean ‘unmarried’.
Quine on Analytic Hypotheses and Meanings
‘analytic hypotheses’ (Quine) = the assumed synonymy of terms from the field researcher’s language and the native’s – or the correct translation of the basic words of the native: ‘the same as’, ‘belongs with’, ‘that one’ and number words.
(Quine’s) ‘meanings’ = plural noun - unacceptable
(Quine’s) ‘meaningful’ = adjective - acceptable
thing →essence
↕↕
word→ meaning
‘beautiful’ → ‘beauty’
(adjective) → (noun)
Meta-Statements and Self-referentiality
1) Can the statement ‘Truth is justified belief’ be justified?
2) Is the statement ‘Truth is justified belief’ true?
3) Take a coherentist’s mini-system: P«Q«R«S. Does P correspond with Q and S? If it does, the coherentist has smuggled in correspondence. Indeed we can see P as a quasi-statement or quasi-belief and Q as a quasi-fact. So P is true iff it corresponds with Q.
4) Can the statement ‘Truth is verification’ be verified (as in the logical positivists)?
5) Can the statement ‘Scientific theories must be falsifiable’ be falsified (as in Popper)?
6) Does the statement ‘Truth is correspondence with fact’ correspond with a fact?
7) Is the statement ‘Truth is unanalysable’ true and is it also unanalysable (as in G. E. Moore)?
Philosophy of Mind
Representations and Phenomenalism
A representation must have propositional content and be truth-evaluable, unlike mental images. Thus resemblance cannot be everything. Perceptions, too, have propositional content, unlike sensations. So perceptions make up Kantian experience.
perception = information about the world
‘Visual experiences are like beliefs.’ Not so with sensations.
When I see a facade, I see a three-dimensional building because of my ‘logical construction’ from sense-data.
Anti-phenomenalism = access to or perception of objects by other ways other than perception or experience.
-How could we perceive objects directly (as D. Davidson believes)?
-We cannot compare the perception of a representation to the perception of an object because, according to representationalism, we never do ‘perceive an object’, only a representation. And how can we perceive a representation is we cannot make mistakes about it?
-object → the mental idea of an object is perceived →another mental idea of the first idea is then perceived → …
-the representation is not perceived, ‘it is simply part of me’.
A perception of a representation implies the ‘Cartesian theatre’. The inner ‘I’ will need more representations of the representation he ‘perceives’ on the mind’s stage. The representation is the perception instead. No process; just a mental entity.
‘Clear and distinct ideas’ are seen as mental objects by Descartes. These objects are perceived and atomistic in nature.
The Cartesian Mind: the Rylian Mind
We cannot help but see the mind as some kind – whatever kind – of thing in which processes occur and mental entities are ‘seen’. Perhaps there are just processes – and that’s it, as when the philosopher disregards the self as a substance over and above processes, ideas, impressions, representations, etc (see Hume and Quine).
Cartesian – the mind/self is external to the world.
Heideggerian/Rylian – the mind/self is part of the world.
Cartesian – the mind as representor
Rylian- the mind as a do-er.
Cartesian – internalist
Rylian
Higher-Order Thoughts
First- and second-order thoughts, or thoughts about thoughts – i.e., introspection? This leads us to mental imagery and the problems it causes for certain theories of mind.
I believe that [my belief that] my belief [(that) politicians lie] is prejudicial.
(B3)(B2)(B1)
I will need to formulate a more satisfactory analysis of the above. Or at least a more acceptable logical schema to express it clearly.
I can separate my attitude to a mental image from the mental image itself in a way that makes propositions and attitudes seem inseparable according to the philosophy of mind literature. Take my mental image of a naked woman. I may have the image ‘in mind’ without an attitude towards it. However, I may have a second-order attitude towards it when I resurrect the mental image the day after. Can I have a proposition, or utterance, in mind without a corresponding attitude? Can I express or think ‘Tony Blair is a liar’ without an attitude towards it? Why would I express it without such a thing? (Unless, of course, I simply thought or expressed the words for the sake of it, as it were, in order to prove to myself that attitudes don’t necessarily accompany such sub-vocal or vocal statements or thoughts.)
Anomalous Monism and (Mental) Determinism
Davidson’s ‘anomalous monism’ is as much an argument against (mental) determinism as it is for anything else. The mental does not fall under ‘strict laws’. And this
is a necessary condition for viewing action as autonomous.
In the Kantian scheme the mental is free from causal law – it is a noumenon. The physical phenomenon is ‘subject to the laws of nature’. This is why there cannot be psycho-physical laws in Davidson’s scheme. The mental, therefore, is outside nature.
But if there are no laws of the mental, or the psycho-physical, then things must be arbitrary in the mental domain. Things must occur ex nihilo (as with quantum theories of mind). Kant attempted to solve this with his supposition of non-natural ‘transcendental laws’ (whose existence could not be proved or even known). Davidson does not even tackle this problem.
In Spinoza’s fashion, Davidson’s clam that we can look at the mental qua mental and the mental qua physical. M-descriptions cannot be reduced down to p-descriptions. And, therefore, p-descriptions cannot be lifted up, as it were, to m-descriptions. But if Davidson is a monist of some kind, then m and p are the same. Therefore m = p. However, Davidson doesn’t accept the ‘identity theory’ of mind. Can one be an ontological or psycho-physical monist and not be some kind of identity theorist?
Heideggerian/Rylian, or ‘dynamical’, theories of mind are radically externalist, even more so than Putnam’s mitigated externalism, etc.
Churchland on Brandom’s Linguistic Bias
What would Paul Churchland have to say about the linguistic bias of Robert Brandom when he writes:
pre-linguistic animals… neither deploy concepts, acquire beliefs, nor count as having knowledge [).
If one’s entire philosophy of mind is based on propositional attitudes, then one would expect and understand such a chauvinistic account of mind and knowledge. However, why should beliefs, concepts and knowledge all depend on propositional attitudes? Indeed Churchland writes something that shows us how prejudicial Brandom’s account is:
language use is something that is learned by a brain already capable of vigorous cognitive activity… language use appears as an extremely peripheral activity… Why accept, then, a theory of cognitive activity that models its elements on the elements of human language? (128).
And, of course, something equivalent to language use, and language itself, must have existed prior to language proper, both in terms of the aetiology of the contemporary human and of the human race itself.
If concepts are linguistically infested, then of course a parrot can’t have a ‘concept of red’ (Brandom, 425). But need they be so? There are no generally-accepted necessary and sufficient conditions for being a concept. Perhaps Brandom shouldn’t be so anthropocentric.
Surely the parrot does believe that it is red. It does not formulate the sentence: ‘That is red.’ It may not have formulated any sentence. But why are beliefs squared with propositions or sentences? Let’s not forget that human non-linguistic thought must have been prior to language proper, otherwise why was there a need for language in the first place? Where did it come from?
Brandom is explicit about his bias against non-linguistic thought:
Non- or pre-linguistic animals do not have a standing or status in the space of reasons’ (431).
How can Brandom know that animals don’t ‘deploy concepts, acquire beliefs, nor count as having knowledge’? Does animal behaviour tell him this? Does neurophysiological research tell him this? Or does his a priori theorising tell him this? Or perhaps it’s simply a question of concepts and meaning.
Only men are rational. (Aristotle)
Therefore women and animals are not rational.
In any case, isn’t rationality something over and above the reality of having concepts and beliefs? Can’t an animal have beliefs without, for example, indulging in inference? Must concepts be inferentially related? It is strange that if Brandom accepts the existence of ‘non-inferential beliefs’ for human beings, then why can’t animals have such things too?
Are there Mental States?
Do we really have a mental state? When does one mental state end and another begin? Is a mental state a quasi-entity or object which has its own identity conditions or criteria of existence and perdurance? Perhaps it is simply too neat and tidy to think in terms of circumscribed mental states. Perhaps there is a continuous flow of different mental states in which there are no clear lines of demarcation between one and another. Consciousness may, therefore, be like a flowing river, as in William James. This would mean that all mental states are more intimately connected to each other than we may otherwise think when we cut mental states are their supposed joints. A single mental state may simply be rather arbitrarily circumscribed according to certain fixed criteria such as time or length.
I am certainly never aware of a clearly demarcated single mental state existing as some kind of atom. Often there is a kind of chaos of interacting mental states. Therefore perhaps there are no single mental states at all. Many philosophers, as per usual, have often tried to make mentality too neat and tidy and therefore more amenable to philosophical analysis.
When I am thinking about Tony Blair’s propensity to lie, I may also be listening to music, having certain bodily feelings and looking at a picture in front of me. Not only all that, but other thoughts often intrude on the ‘central’ thought. Are all these mental and bodily happenings a single mental state or a chorus of them? I can, however, say that at any one time there is indeed a central thought or a central mental state. But it is never left to its own devices, as it were. Other mental states, if they are other states, crowd in upon it, although this may not always be the case.
Most of the above, or all of it, can also be applied to the having of a single belief, if we do ‘have’ them in any literal sense. What about representations, concepts, etc? The primary problem of all this is our propensity to think of all these thing as objects or entities of some kind, even if admittedly abstract in nature.
Philosophy of Science
Quine, Quantum Mechanics and the Law of Excluded Middle
What could be more pragmatist than a revision of the logical law of excluded middle in order to ‘simplify’ quantum mechanics? This revision is not based on the truth or falsehood of A ornot-A, but on its rejection being helpful in another domain – that of physics. Quine is not necessarily arguing that it is false. He is arguing that quantum mechanics appears to contradict it. Shouldn’t this conclusion, instead, have led Quine to question some of the statements or data found in quantum mechanical theory? No. The reason is that Quine accepts all – or most – of the conclusive findings which come out of physics. Indeed science is the starting-point of the whole of Quine’s ‘naturalistic’ philosophy. So if some physicists have rejected the truth of A or not-A, and for good reasons, then so too must Quine.
We can ask, however, that if Quine got all his nourishment from science, or at the least from physics, then why was he a philosopher at all? Was he simply doing a tidying-up job, as he more or less puts it somewhere? Perhaps, however, he should tidy up the denials of the truth of A or not-A. Indeed what does such a denial of the law of excluded middle amount to? Can empirical findings, or the findings of quantum physics, ever have such a radical effect on the supposed truth of such an ancient logical law?
Scientific Secondary Properties
The philosophical distinction between ‘primary’ and ‘secondary’ properties is, in fact, scientific in origin (see Gassendi, Boyle, etc.).
Berkley: the secondary/primary distinction is bogus
The contingent/essential distinction is bogus (?).
Theory before Observation
Without a pre-existing theory the observer could have:
x = a black feathered thing
not:
x = raven.
Classifications, then observations. (e.g., Peircian abduction)
Peirce on Convergence
If scientifically ‘we advance by clear steps to a truer picture’ [C. S. Peirce], soon we will reach the truth. Alternatively, why haven’t we done so already? Peirce’s ‘convergence’? What would it be like to reach the scientific truth? Weren’t many previous classifications and theories completely wrong, not ‘largely accurate first shots’?
*)
modes of presentation = theories (?)
both of which are ‘underdetermined’ by reference, evidence, etc.
*)
Does ‘ontological economy’ = truth?
Does ‘explanatory power’ = truth ?
Or are they the signs of truth?
*)
‘Everything can eventually be explained’ = a presupposition of science?
A ‘law of nature’ = that nature can be observed and explained?
Metaphysics
Frege on Number
For Frege, a number is the set of sets of n-membered sets. It is a single set. But if numbers were sets, not sets of sets, which one would we choose as our number?
Are equations, mathematical propositions, etc. also in a Platonic realm, or just the abstract numbers which constitute such things?
Universals and Mental Images
‘This chair’ stands for this chair. So what does ‘brave’ stand for?
-a universal?
-a bed → the universal Bed→another universal Bed →…
-a bed → a mental image of a bed →another mental image of a bed→… (see Philosophical Investigations)
Or a bed only: no universals and no mental image.
Hume, Kant and Kripke on Necessity
What’s the central message of Kripke’s ‘Identity and Necessity’? That those things known a posteriori may also be necessary. What is necessity? Something supplied by the mind, as in both Hume and Kant’s scheme? Is it something in the world?
A = A is necessary because its contradiction, A ¹ A, is self-contradictory. But this logical necessity is nothing like causal necessity. So why do we use the same word for the two?
It is necessarily the case that if A happens, B will follow.
Whence the necessity? According to Hume, there is no necessity. According to Kant, necessity is, as it were, imposed on A and B by the mind. In other words, the necessity of B following A, or A causing B, is determined by the mind in experience. It is a ‘condition’ of our experience. In logic:
((A⊃B)(A) ⊃ (B))
Carnap’s Conventions and Their Internal Questions
If truth is an ‘internal question’ for a Carnapian ‘convention’, why would the convention be chosen in the first place? Why did Carnap adopt the ‘framework’ of the ‘thing-world’? Why not one based on abstract entities or even goblins? Truth, as ever, is lurking in the background – that is, truth as antecedent to the adoption of a convention. For example, is it true that the convention ‘works’, provides ‘results’, solves problems, handles experience, etc? Pragmatists must face these antecedent questions, even if they are already in a convention prior to their adoption of a new one. (In this case, we need not reject Putnam’s ‘internal realism’.) Again, why adopt a thing-language rather than a ‘sense-data language’ [see Quine also]? For reasons of truth? Perhaps Carnap might have argued that both prior conventions are adoptable, but not in terms of trans-conventional truth [as Quine argues].
There are, of course, metaphysically realist criticisms of Carnap’s conventionalism. Which comes first – the world, as it were, or the convention? Metaphysical realists would say that it is the world that comes first. Carnap would have said the convention. But could - or should - he have said this? What would have made him adopt convention1 is the first place? He couldn’t have adopted C1 from within C1. Therefore when he adopted C1 he must have been outside it. It follows that his reasons for adopting C1 could – and should - not have been ‘internal’ to it. Where did they come from? Didn’t truths and facts external to C1 determine his choice? His reasons for rejecting his current convention, say C2, couldn’t have come from C1. So he had good reasons for adopting C1 which were not part of C1. Were they part of C2? Or were there many concurrent conventions which Carnap was internal to? Did he live within one convention or many? We may need conventions, ‘language-games’, ‘conceptual schemes’, etc., but are we internal to just one of them? If Carnapian conventions determine what we think and what we say, then one convention must itself determine our adoption of another. But there is something strange about this conclusion because conventions are often deemed to be self-contained and, as it were, self-referential (they are closed universes). This can’t be true if we can move from C2 to C1, for example. In much of the contemporary literature, why are conventions, or Davidsonian conceptual schemes, deemed to be so powerful and restricting? We may need conventions in the Carnapian sense; but we can still jump from one to another. They are not like Kantian transcendental categories of experience that determine, a priori, how we must perceive the world. They are thoroughly contingent and adaptable, even according to Carnap himself.
Quine and Davidson on Sensory Stimulations
Quine
makes interpretation depend on patterns of sensory stimulation (Davidson).
Davidson (161), on the other hand, makes interpretation depend on ‘external events and objects’. The latter philosopher, clearly, doesn’t deny that there are sensory stimulations, only that the sensations which make up our perception and knowledge of events and objects are already interpreted. Or, more correctly, there is no conscious interpretation, such as x is P. There is no separation between sensations and objects, or sensations and events, at the epistemic level, though there is at the causal level. We see a cat as a cat instantaneously. We do not infer that the cat is a cat. Of course, the sensations which have their causes in the physical cat must come before the belief that the cat is a cat. But this is a causal, not an epistemic, antecedent.
Quine should have accepted Davidson’s position. After all he gave us the gavangai/rabbit scenario. The same cause, ‘a rabbit scampering by’, causes different beliefs. Therefore sensations can’t be everything, as it were. To one native it might have been a ‘rabbit-part’ or ‘rabbit-stage’. A scampering rabbit may also give us, not the native, another belief: ‘Red things always run fast.’ Rather than: ‘That is a scampering rabbit.’
Of course you can have an experience, if it is an experience, of a cat and not register it as a cat. One may be drunk or concentrating on something else. This won’t stop the sensory stimulations from emanating from the cat and then entering our sensory receptors. But this non-cognitive mental state cannot count as ‘evidence’ or even, in the Kantian sense, as an experience of a cat as a cat. There is an experience of something, but not one of a cat (even though it was a cat in front of us). Similarly, while I was writing what I have just written the sound-waves from the church bells outside entered my ear, but I didn’t hear them as churchbells.
Epistemology
Induction on Induction
One must accept the reliability of general inductive generalisations in order to reject or question induction’s logical status or logical foundations. How would I know, for instance, that my anti-inductivist beliefs today are the same as they were yesterday? Say, for example, I make some inductions about induction – that inductive reasoning cannot provide conclusive truth or law. Clearly induction has never proved conclusively that x must be an F or x must beF. This is an inductive inference about other inductive inferences (or conclusions) – meta-induction, as it were. Similarly, how do I know that the people who understood my anti-inductivist arguments yesterday will understand the same arguments today? How do I know, not how do others know, that my arguments are the same today as they were yesterday? As Wittgenstein puts it: how do I know I am going right or wrong (about induction, etc.)?
Inductive reasoning is not only ‘reliable’ and perhaps ‘according to nature’, but it is unavoidable and inescapable for both logical and psychological reasons.
Cartesian Indubitable Beliefs versus Inferential Beliefs
There are no beliefs that are ‘directly justified’. All beliefs stand in some relation to other beliefs. It is the case that no belief can be a singular atom sitting in the middle of a temporarily empty void. Take Descartes’ ‘I think, therefore I am’. Descartes must have had other beliefs in order to formulate this one:
i)A belief about what it is to think.
ii)A belief about what it is to exist.
iii)A belief that his French words corresponded to these concepts.
iv)A belief about the I who thought.
v)A belief in correct inference from the ‘I think’ to the ‘therefore I exist’.
Take: ‘This is a red ball.’
i)A belief about the ball falling under the type ball.
ii)A belief in this case of red falling under the concept [red].
iii)A belief that his English words correctly corresponded to the concept [red] and the concept [ball].
These beliefs need not be articulated, of course. But many beliefs aren’t expressly articulated. I believe that Tony Blair is a liar. However, this is the first time I have articulated it for quite some time.
Perhaps I cannot be wrong when I say: ‘I am in pain.’ However, this expression is still dependent on other beliefs. The pain itself may not be so dependent, but we are talking here about beliefs. Someone or something could feel pain without having any beliefs. But he or it would not have an ‘indubitable belief’ about the pain he or it is in. It certainly wouldn’t be at the Cartesian apex of his deductive edifice.
Logic and the Philosophy of Logic
Religious Systems Can Be Valid but Not True
Many religious arguments (and beliefs) are valid but not true. That is, if the premises or foundational beliefs of a religion are taken to be true, or even if they are true, then what follows from them, the conclusions or other beliefs, would be both valid and true. But the premises or foundational beliefs may in fact be false. So the arguments and the conclusions are valid but they may not also be true. This is why many religious people reason correctly. They are indeed rational. Once the suppositions of a particular religious system are taken to be true, then all sorts of weird conclusions and beliefs, valid ones, will - or must - follow. It follows that an insane man can be rational or reason correctly. He may believe that pigs can fly and then reason correctly from this false premise or belief-premise. For example, if pigs can indeed fly, then pigs may have wings – hidden ones! In addition, if pigs can fly, then even if they can’t swim, they could easily get over deep rivers without swimming. All these strange conclusions are valid but not true because the premises are themselves false.
Now imagine what could – and what does – follow from the following belief-premises:
i) God exists.
ii) God is omnipotent.
iii) God is omniscient.
From these premises alone, when not taken as being themselves some kind of conclusion to prior beliefs or arguments, could – and have – built huge and internally coherent/consistent religious systems. That is, it would be rational to believe in these religious systems and the reasonings contained within them, or some of them, may indeed be logically valid. But what of the premises?
Keeping all this in mind, there could be, and there are, multitudes of internally coherent and valid belief-systems!
