Minilogic and Glossary
- Page ID
- 8306
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Like any discipline, philosophy has its own vocabulary. Here are some of the most basic terms and the connections among them:
- Position
- A position (or a thesis) is a claim or set of claims; for example, that the mind is identical to the brain, or that people act always from self-interest.
- Argument
- An argument is a set of claims (called ‘premises’) designed to show another claim (a conclusion) to be true. (This is a special use of the word: usually people use ‘argument’ to mean a verbal altercation). For example:Premise 1: If it’s raining outside, the lawnmower will get wet.
- Premise 2: It’s raining outside.Conclusion: The lawnmower will get wet.
As you can see, arguments aren’t peculiar to philosophy: we use them all the time to get around the world, although we almost never bother to make them explicit. Even in this class, we won’t always go to the trouble of putting arguments in this explicit form. But it can often be helpful to do so, and it’s important that arguments can be make explicit. To see why, consider an argument put forth by the British Medical Association:
Premise 1: Boxing is a dangerous activity.
Conclusion: Boxing should be banned.
Does the premise entail the conclusion? That is, does the premise show the conclusion to be true? In other words, is this a valid argument—one whose premises entail the conclusion? (Another way to put it: a valid argument is such that it’s impossible for the premises to be true and the conclusion false.)
Validity says nothing at all about whether the premises or conclusion are in fact true or not. Here’s a valid argument:
Premise 1: If I’m over 7’ tall, I’m over 6’ tall.
Premise 2: I’m over 7’ tall.
Conclusion: I’m over 6’ tall.
It’s impossible for Premises 1 and 2 to be true while the conclusion is false. So this is a valid argument. But it’s missing another virtue we look for in arguments: we want them to be valid and to have true premises. That is, we want sound arguments. The argument above is valid but not sound, since Premise 2 is false.
- If an argument is valid and sound, what can you tell about the conclusion?
Let’s go back to the boxing argument. Run our test on it: is it possible for Premise 1—‘boxing is a dangerous activity’—to be true, while the conclusion—‘boxing should be banned’—is false? If it is possible, what does that tell you about the validity or invalidity of the argument?
- There is something missing from the boxing argument. What is it? What could we add to make the argument valid? Is the argument, repaired in this way, sound?
- Objection
- An objection is an argument designed to show that a position is false. If theism (the claim that God exists) is our position, we would have to consider the objection that a benevolent deity would not allow innocent people to suffer.
- Reply
- A reply is an answer to an objection. In the above example, we might reply that God does not let innocent people suffer; their suffering is due to human free will. (Of course, this may not be a good reply.)
In addition to these concepts, we need to draw some distinctions among different kinds of positions or claims. These distinctions are controversial; Kant, in particular, will challenge some of the connections I draw between them. But we need to start somewhere!
The first distinction is between claims that are necessary and those that are possible.
- Necessary
- A claim is necessary (that is, necessarily true) if it holds in every possible state of affairs. There is no possible state of affairs in which a necessarily true claim is false; it is impossible for such a claim to be false.For example, many philosophers claim that if it is even possible that God exists, then it is necessary that God exists. This claim is part of what’s called the ‘modal argument’ for God’s existence. The full argument only needs a few more premises:
- It is possible that God exists.
- Since God is a perfect being, God possesses the property of necessary existence; in other words, the property of existing in all possible states of affairs.
- It is necessary that God exists.
The first premise claims that there is at least one possible state of affairs in which God exists. The second premise claims that God has the property of existing in all possible states of affairs. These two premises entail that if God exists in even one possible state of affairs, then God exists in all possible states of affairs. That is, if it is possible that God exists, then it is necessary that God exists.
- The modal argument just given for God’s existence is a valid argument. Is it a sound argument?
- Possible
- A claim is possible (that is, possibly true) if it holds in at least one possible state of affairs. For example, I don’t have green hair. But that doesn’t mean that it’s necessary that I don’t have green hair. I could have decided yesterday to dye my hair. If I could have decided to dye my hair, then there’s a possible state of affairs in which I do have green hair. So while I actually don’t have green hair, I possibly do have green hair.Suppose we could prove that it’s possible for you to exist without a body. Even though you haven’t existed in this state and probably never will, the claim that it’s possible is a very significant one. For it would then mean that you are not a physical being.
The second distinction is between claims that are analytic and those that are synthetic.
- Analytic
- Analytic claims are true in virtue of the meanings of the words involved. They are necessarily true. For example, consider ‘bachelors are unmarried men.’The denial of an analytic claim is a contradiction and is true in no possible world. There’s no possible state of affairs in which a bachelor is married, because that contradicts the meaning of the word ‘bachelor.’ Analytic claims can be very interesting, even informative, but what they tell us seems to be about how we use words or symbols, not about how the world is independently of us. This is clearer if we look at how one argues for an analytic claim. All analytic claims are a priori, or capable of being known independently of experience. Mathematicians don’t have to travel to the center of the earth to find out if 2+2 still equals 4 there; they know it a priori. Similarly, we don’t have to look to experience to justify an analytic claim; all we need to look at is the concepts involved.
- Synthetic
- By contrast, some claims are synthetic, or true (if true at all) in virtue of how the world happens to be. The vast majority of claims we make fall into this category. They are not necessary truths, they are contingent, or merely possible: they could have been otherwise. Such claims are true only in some possible states of affairs. This means we have to find a different way to justify them than the way we justify an analytic claim. We capture this by saying that synthetic claims can be known only a posteriori or through experience. We need to find evidence for them that goes beyond the meanings of the words involved. Someone might know what ‘rain’ and ‘Blacksburg’ mean, and how to use dates, and still not have a clue whether it rained in Blacksburg on August 22.
There’s another important distinction between kinds of claims. This distinction bears on how we go about justifying claims.
- Descriptive
- Descriptive claims concern what is actually the case. All of the synthetic or analytic claims above are descriptive.
- Normative
- Normative claims concern what should be the case. If Bobo argues that no one ought to have more money than anyone else, you can’t object that society isn’t organized according to that principle, and that there’s already lots of inequality. Bobo’s making a claim about what ought to be the case, not what is actually the case.
Homer Simpson provides a nice example of someone who doesn’t appreciate this difference. As he’s about to break into a liquor store, Marge says, ‘but Homer, that would be wrong.’ Homer replies, ‘if we agree, Marge, what are we arguing about?’
- Look again at the boxing argument above. What kind of premise did you have to insert in order to make it valid, a descriptive or a normative one?
- Burden of proof
- Debates that arise in philosophy often require us to decide who has the burden of proof. If a position violates our intuitions or asks us to accept a larger set of claims than we otherwise would be willing to accept, the person holding that claim has the burden of proof. For example: if I claim that, despite all appearances, all humans are selfish, I have the burden of proof: it is up to me to prove to you that people are selfish. If I can’t do this, then I have lost. If I argue that, despite appearances, Fess Parker follows me everywhere I go, I have the burden of proof. If I cannot meet it, we have to conclude that my view is false. It’s not up to you to prove me wrong: it’s up to me to prove my position true.
Fallacies are errors in reasoning. There are lots of them, but the one about which we should be most worried in this class is:
- Strawman fallacy
- We commit the strawman fallacy if we argue against a bad or distorted version of our opponent’s position. Suppose that Jimmy is arguing with Bobo over evolution. Bobo believes evolution is true. Jimmy counters: ‘I’ll never believe evolution till I see a fish turn into a man.’
If you’re not getting the opposing position right, you can’t argue against it. A core philosophical skill is being able to state an opposing position as carefully and persuasively as your own.
This is a skill we’ll cultivate in this class, as we’ll inevitably read philosophers with whom we disagree.
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Which of the following claims are analytic, and which are synthetic?
- Any black cat is black.
- There is life on other planets.
- ‘One try makes a customer’ (slogan of a popular Richmond restaurant).
- ‘Unexpected disasters can happen … With little or no warning.’1
- From Plan 9 from Outer Space: ‘He’s been murdered, and somebody’s responsible!’
Glossary of Philosophical Positions
In what follows, I set out some of the basic positions we’ll be working with. All of these characterizations are controversial. Again, we have to start somewhere. Don’t worry if you don’t fully grasp them now; we’ll clarify and extend them as we go.
Metaphysics
The most basic distinction is between a thing or a substance and a property. Fess Parker, a table, and the moon are all substances. These substances have properties: Fess Parker is the world’s greatest actor, the table is stained, and so on. A state of affairs is a substance’s having a property; that Socrates is bald is a state of affairs.
Some properties are intrinsic: the ones that things have just because of the way they are, like the property bald. Other properties are relations, like loves or is taller than.
A kind is a group or set of substances, properties, or states of affairs. Some kinds are natural: there is some reason for thinking everything in the kind belongs together. Some philosophers think that everything in a natural kind shares the same causal powers—they can do the same things in the same conditions. (Consider the periodic table, for instance: why is it important whether an atom is an oxygen or hydrogen atom?)
Other kinds are unnatural: they don’t share enough features, or enough of the right kind of feature, in order to qualify as a natural kind.
- List three things that form an unnatural kind.
- One of David Letterman’s best bits was a list of ‘Top 10 Rejected Oprah Themes.’ Among them was ‘Problems of Guys Named Don’. Why is this a bad idea for a talk-show theme?
On the Aristotelian picture, an essence (a.k.a. ‘species,’ ‘form,’ ‘substantial form’) has the following three features:
- it is the most fundamental explanatory property a thing possesses;
- the thing that has it cannot lose its essence and continue to exist;
- things with similar (or identical) essences form a natural kind.
Philosophy of Mind
- Dualism
- Dualism is the thesis that mind and body are distinct substances. According to dualists, the mind is not the body, nor does it ‘arise’ naturally as a function of the body’s behavior (in the way that, say, digestion does).
- Identity theory
- The identity theory is the thesis that the mind and the body (in particular, the brain) are just the same thing. ‘Mind’ and ‘brain’ are like ‘Clark Kent’ and ‘Superman’: two ways of referring to the same thing.
Free will
- Determinism
- Determinism is the thesis that every state of affairs follows necessarily from every prior state of affairs. For instance, if it is true that I am typing now, the determinist claims that I could not possibly be doing anything else, given the immediately prior state of the universe. So far, determinism says nothing at all about free will.
The hard determinist holds that since determinism is true, we cannot have free will.
The libertarian holds that since determinism is false, we can have free will.
- The hard determinist and libertarian agree about the consequences of determinism. What do they both think must be the case if determinism is true?
The compatibilist or soft determinist claims that determinism and free will are compatible. This position denies the inference above.
Epistemology
Empiricism is a cluster of different claims about knowledge, all emphasizing the role of experience.
- Materials empiricism
- Materials empiricism is the thesis that all the materials for knowledge come from experience. The content of all of our thoughts is ultimately traceable back to some experience or other.
- Justification empiricism
- Justification empiricism is the thesis that any justification for a claim has to appeal to experience.
Note that the two can come apart. So I might be a materials empiricist and yet deny justification empiricism, because I think that some claims (e.g., analytic claims) can be justified merely by the concepts involved.
Largely opposed to empiricism is a set of claims we will call rationalism:
- Materials rationalism
- Materials rationalism is the thesis that at least some of the materials for knowledge do not come from experience.
- Justification rationalism
- Justification rationalism is the thesis that at least some justifications do not appeal exclusively to experience.
Independent of the empiricist/rationalist debate is a question about the order of knowledge:
- Existentialism
- Existentialism is the thesis that before one can know the essence of a thing, one must first know that it exists.
- Essentialism
- Essentialism is the thesis that one can (or even must) know the essence of a thing before one can know that it exists.
Another debate in epistemology relates to the role of perception:
- Direct realism
- Direct realism is the thesis that, in perception, we are directly perceiving real, ordinary objects.
- Indirect realism
- The opposing thesis, indirect realism, claims that in perception we directly perceive only our own ideas or sensations. It is only because these ideas represent (or are ‘about’) objects in the world that we can be said to perceive those objects.
Glossary of Principles
The principles listed below were controversial in the modern period; some of the philosophers we will read try to argue for them, some just assume them, and others assume that they are false. Try to identify when these principles are mentioned (sometimes implicitly) in the readings below, especially in the writings of Hume and Descartes.
- Conceivability Principle (CP)
- If x is conceivable, x is possible. Note the contrapositive: if x is impossible, x is inconceivable.
These are logically equivalent. The converse, however, is not: if x is possible, x is conceivable. This principle seems to be far too strong. Can you see why?
- Causal Principle (CAP)
- There must be at least as much reality (being, or perfection) in the cause as there is in the effect. This principle is from Descartes.
- Epistemic Principle (EP)
- Everything (that is, every proposition) I clearly and distinctly perceive (that is, believe and thoroughly understand) is true. This principle is from Descartes.
- Copy Principle (CPY)
- Every idea is a copy of some impression or set of impressions. This principle is from Hume.
- Separability Principle (SP)
- Any two distinct perceptions can, in thought, be separated. This principle is from Hume.
- Virginia Department of Emergency Management.↩